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Development of a microprocessor based control system for a pneumatic rotary actuator
Mechatronics Vol. 5, No. 5, pp. 541-560, 1995
© 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved. 0957-4158/95 $9.50+0.00
Pergamon 0957-4158 (95) 00025-9
DEVELOPMENT OF A MICROPROCESSOR BASED CONTROL SYSTEM FOR A PNEUMATIC ROTARY ACTUATOR H. M. M A H G O U B and I. A. C R A I G H E A D Department of Mechanical Engineering, University of Strathclyde, Glasgow G1 1XJ, U.K.
(Received 19 October 1994; revised 15 February 1995; accepted 15 February 1995) Abstract--A microprocessor based control system has been developed and used to provide satisfactory control of a pneumatic servo system. This paper describes how microprocessor based controls can be used to produce low cost pneumatic servo drives which could find a wide range of application in manufacturing industries. The pneumatic actuator is a piston air motor constructed of aluminium, utilising a proportional spool valve to allow air flow control. The dynamics of the air motor in conjunction with the solenoid valve have been experimentally determined. Control is based on a modified PID (proportional, integral and derivative) controller which adjusts the command issued to the control valve. This takes account of the inherent non-linear behaviour of the air motor. The motor has been used to actuate a single-degree-of-freedom(SDOF) robot arm. The results show that digitally controlled air motors have the potential of providing an alternative solution to their electric and hydraulic motor counterparts. Air motors, through inherent low cost, good power to weight ratio and intrinsically safe operation, can be utilised to control a wide range of industrial machines. 1. I N T R O D U C T I O N Intelligent servo pneumatics have now reached a stage in development where they show a competitive advantage in certain application areas over electric and hydraulic drive counterparts. However, a lack of confidence still prevails in industry when considering pneumatic drives as an option for servo drive technology [1]. Many servo drive pneumatic systems have become commercially available, but their application is still limited mainly to simple machines. Pneumatic actuation is used widely in industrial applications to provide low cost motion. These actuators are capable of achieving end stop positional accuracy comparable with electric and hydraulic servos [2]. The pneumatic servos are controlled by various forms of valves which control the direction of air flow. For applications which require positioning of payloads, usually either hydraulic or electric servo drive systems are used. Although such drives can provide considerable flexibility and satisfactory characteristics, in many manufacturing applications their use introduces significant cost penalties so that if a low cost pneumatic drive was adequate it would be preferred. Previous analysis [3] has shown that pneumatic drives exhibit very significant non-linearities; the natural stiffness of the drive varies considerably over its working range [4], as does the inherent damping of the drive when the magnitude of valve opening is changed. In practice, however, correct estimation of such parameters which govern the dynamics of pneumatic drives is difficult to achieve. The existence 541
542
H.M. MAHGOUB and I. A. CRAIGHEAD
of significant and unpredictable drift and hysteresis has limited the use of pneumatic servos to application areas where some unpredictability in dynamic responses can be tolerated. There are two major problems which make the application of air motors difficult. Firstly, it is not an easy task to maintain an absolutely constant supply pressure, particularly when the motor is running at high speeds. To solve this, a local reservoir can be used to ensure that fluctuations in supply pressure are reduced to an acceptable level. Secondly, the valve response characteristics usually are not linear. Much research interest over the last 20 years has centred on the modelling and implementation studies of pneumatic servo drives which have been aimed at overcoming the inherent limitations of air servos [3-5]. However, the compressibility of air as a working fluid introduces significant control problems relating to time delays, low stiffness, little natural damping and non-linearities. Also, most pneumatic systems suffer to some degree from air leakage and frictional effects. In recent years a number of researchers [6-9] have investigated the use of computer controls in an attempt to compensate for the effect of such problems. When modelling pneumatic drives, the equations describing the motion are complex [6]. Due to their non-linear and complex nature, pneumatic system characteristics are very much dependent upon the operating conditions of the drive. Due to the above factors, a pure proportional, integral and derivative (PID) controller will not be adequate for controlling pneumatic servos, so an alternative approach must be found to ensure satisfactory behaviour. Two distinct classes of actuator are available. These are the reciprocating actuators (e.g. cylinders) and continuous actuators (e.g. air motors and vane actuators). However, to date the majority of research aimed at studying such drives has been focused on reciprocating actuators [2-4, 10]. Only a very limited amount of research effort has been directed to the study of vane type [11, 12] and air servo motors [13, 141. This paper describes a control scheme which has been devised to improve the dynamic response obtained with the air motor previously described by [13, 14].
2. THE AIR M O T O R S
Air motors are prime movers powered by compressed air and have certain desirable characteristics when compared to more conventional types of motors [13, 14]. The Motron air motor has largely overcome the fundamental problem of using air, which is compressibility, by keeping the volumes of gas small and gearing out the effects of compression. This gives it similar characteristics to a D.C. motor. However, pneumatic systems possess significant inherent non-linearities due to complex fluid/ mechanical interactions, so it is not possible to use the same control techniques. The air motor employs four radial free floating pistons acting on the three-lobed cam. This means that each piston will rise and fall three times per shaft revolution. This gives the motor 12 power strokes per revolution. Figure 1 shows the cam and piston arrangement within the motor. At the heart of the motor is the tri-lobed cam. This cam has two functions: the first is to convert the linear motion of the piston into rotary motion, the second is to provide the correct valve timing. The valves are in the
Control system for a pneumatic rotary actuator
543
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sides of the pistons. Each piston contains the valve that controls the next piston in a clockwise direction. Considering the pistons marked A, B, and C in Fig. 1, when piston B is at top dead centre, ready to produce a power stroke, piston A will have just closed the exhaust port for piston B and piston C will have just opened the inlet port. When piston C reaches top dead centre, piston B will open the inlet port for C, and so on. In this way commutation of the pistons is carried out. When the motor is rotating in a clockwise direction, all the slipper pad valves on the back face are acting as exhaust valves, and all those on the front face as inlet valves. In the anticlockwise direction the opposite is true. The motor valve is supplied with 24 V, 1 A electrical supply and can be operated with oil-free air. The motor has the following advantages in industrial applications: (1) high starting torque providing fast smooth acceleration; (2) high torque-to-weight ratio; (3) ability to sustain stall without overheating; (4) use of oil-free air means there is no environmental contamination; (5) absence of electrical risk; (6) simplicity in structure, easy to design and to maintain; (7) positional accuracy; (8) maintenance free; (9) low shaft speed at high torque; (10) no high pressure leakage problem; (11) local high current supply not required; (12) no heat dissipation problems; and (13) low operational cost [13].
3. THE PROPORTIONAL VALVE In order to control the position, speed or steady state torque developed by the air motor, a control valve capable of proportional action is required. Such a valve is
544
H.M. MAHGOUB and I. A. CRAIGHEAD
interfaced directly to a proportional solenoid, resulting in spool movement in a manner related to the variation in solenoid current/voltage [13, 14]. The dither is a high frequency, low amplitude vibration which is imposed on the spool valve to reduce stiction. It is generated using 555 timer at TTL levels of +5 V. This is reduced by a potential divider to approximately 0.1 V. The frequency of the dither is set to 100 Hz. The air flow rate through the motor determines its velocity. As the motor is symmetrical, reversing the air flow reverses the direction of the motor rotation. A five-port spool valve controls the air flow; its schematic is shown in Fig. 2. The spool valve works by moving the centre spool within a sleeve. When the spool is in the centre position, as in Fig. 2a, no air flows through the motor. Moving the spool to the left allows air to flow from the inlet to the right hand motor port (Fig. 2b). The end of the spool closes the right hand exhaust port. The air flows through the motor and back to the left hand side of the spool, and out through the left hand exhaust port. If the spool is moved to the right, air flows through the valve in the opposite direction, as shown in Fig. 2c. The position of the spool is determined by the force generated by the solenoid pushing the spool against the spring at the end of the spool. The centre, off position is achieved when the solenoid is at approximately half power. Fully open to the left is achieved when the solenoid is at full power, and fully open to the right when the solenoid is off.
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Control system for a pneumatic rotary actuator
545
A 24 W proportional solenoid is used to control the spool valve. The current supplied to the solenoid determines the force it generates. Changing the force on the solenoid varies the spool position and thus the flow through the valve. This relationship is non-linear [13] and is illustrated in Fig. 4. Hysteresis is caused by stiction in the valve and can be reduced by adding dither to the control signal. This causes the spool to vibrate with a low amplitude. The dither keeps the spool continuously moving and thus prevents stiction. The amplitude of the dither is so small that it has a minimal effect on the control signal.
4. EXPERIMENTAL EVALUATION OF THE SYSTEM DYNAMICS The actuator used in the experimental work was the Motron piston air motor. The motor was used to power a load (fly wheel) and in order to control the dynamics of this load its state must be known at any instant so that the correct control decision can be taken. The specification data relating to the air motor, control valve and other elements of the system are given in Table 1. The experimental hardware consists of actuator, valve and sub-systems. The sub-systems include computer control hardware, feedback sensor, electronic/electrical interface components, mechanical component interface and mechanical component hardware. The worm and worm wheel were chosen for compactness as the ultimate aim of the research is to develop a pneumatically powered robot arm where space and weight will be restricted. An open loop test rig was constructed (Fig. 3). A command signal is generated by a signal generator. The analogue signal is amplified to produce a valve command current in the range of 0-1 A. In addition to the proportional valve signal a small Table 1. Operating data of system components Actuator
Valve Load Digital to analogue converter Position sensor
Supply pressure Exhaust pressure Servo amplifiers Reduction gear box
(DAC)
Piston air motor N o . of pistons = 4 Speed range = 40 rpm at m a x . t o r q u e - 8 5 0 rpm unloaded Weight = 10.5 kg Lubrication of the air supply to the motor is optional Pneumatic servo valve five-port, solenoid actuator Single solenoid manipulation with return spring Mass moment of inertia = 0.281 k g . m E 12 bits Servo mount potentiometer Wiper current ( m a x . ) -- 10 mA Electrical rotation = 340 + 4 ° Temperature range = - 5 5 ° C to + 1 2 5 °C Mechanical rotation = 360 ° continuous Rotational life >107 shaft revolutions Starting torque ( m a x . ) = 28 x 10 -4 Nm Running torque ( m a x . ) = 21 x 10 -4 N m 80 psi Atmospheric Input voltage: 0 - 1 V Output current: 0 - 1 A Worm and worm wheel ( 1 : 1 5 )
546
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oscillatory component is included; this dither component is used to reduce hysteresis due to friction in the system. Velocity information is sensed by a tachogenerator and fed back to the computer. The relationship between the input (command) signal to the valve and the output rotational velocity of the motor is shown in Fig. 4. It can be seen that the motor rotational velocity varies non-linearly with the command signal. The non-linearities arise from the valve and are the result of a dead zone, hysteresis and saturation. The motor also adds significant friction to the system. A series of step input functions with different amplitudes were applied to the system. Figures 5 and 6 show some of the results from the step inputs. From these figures, it can be seen that an oscillatory motion is observed and this arose from flexibility in the tachogenerator-transducer coupling which was used in the measurement. At low velocity (which corresponds to small valve spool displacements), more oscillatory motion can be observed. 600300-
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Sinusoidal inputs were applied to the system and Fig. 7 shows the sinusoidal input and its corresponding output. From this figure it can be observed that the system is non-linear (it has a dead zone, asymmetric gains and saturation).
5. CONTROL STRATEGY Numerous adaptive control strategies (e.g. [15, 16]) have been proposed for use with non-linear systems. Most of them involve considerable on line computation
548
H. M. M A H G O U B and 1. A. C R A I G H E A D Step input voltage at volt = 0.85 -- -- Step input voltage at volt = 0.90
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which can restrict the a p p l i c a b i l i t y of the c o n t r o l a l g o r i t h m a n d r e q u i r e s t h e use o f a high p o w e r ( a n d e x p e n s i v e ) c o m p u t e r . T h e m o d i f i e d P I D c o n t r o l s t r a t e g y is an a l t e r n a t i v e a p p r o a c h to c o n t r o l l i n g the a c t u a t o r s which d o e s n o t r e q u i r e e x t e n s i v e c o m p u t a t i o n o r p r e v i o u s k n o w l e d g e o f the t r a j e c t o r y . This s t r a t e g y w o r k s i n d e p e n d ently o f the p a y l o a d , s p e e d , etc. a l t h o u g h the e r r o r is likely to b e l a r g e r for h e a v i e r payloads and quicker operation. In any p r a c t i c a l s y s t e m the t o r q u e will b e a p p l i e d by an a c t u a t o r which m a y b e p o w e r e d b y electricity, h y d r a u l i c s o r p n e u m a t i c s a n d the a c t u a t o r will h a v e a m a x i m u m a n d m i n i m u m v a l u e o f t o r q u e which it can a p p l y . T h e c o n t r o l t a s k is to a p p l y a t o r q u e T so t h a t the a n g u l a r p o s i t i o n 0 is at s o m e
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desired value at any time t. Rather than calculate the absolute value of T that is required, the proposed control strategy determines the change in torque AT which should be added or subtracted to the existing torque. The determination of AT is achieved by a modified PID feedback loop and updated repeatedly. In practical terms, the actual value of 0(0a) would need to be measured, the desired value of 0(0d) would have to be specified for the next time step and the controller could then calculate AV and modify the actuator torque accordingly. The correction control effort is calculated as follows: AV(k) = k p ( O o ( k ) - Oa(k)) + kd(0d(k) -- 0a(k)) (1) + kil(Od(k) J
-- O a ( k ) ) d t ,
550
H.M. MAHGOUB and I. A. CRAIGHEAD
where kp is the proportional gain, and the total control effort is
kd
is the derivative gain and ki is the integral gain
V(k + 1) = V(k) + AV(k).
(2)
Pneumatic systems possess significant inherent non-linearities due to complex fluid/mechanical interactions. To take account of these non-linearities the simple proportional gain in the system was replaced with an interpolation function which accounted for the saturation, dead zone and rotation direction dependent gains. The modified PID control loop for the pneumatic system is illustrated schematically in Fig. 8. The interpolation function is based on specifying the relationship between applied voltage and error to take account of the dead zone, saturation and direction dependent gains. A linear interpolation is used to obtain intermediate voltages.
6. THE DEAD ZONE AND NULL REGION
The null value for the pneumatic system with a given payload is the digital number transmitted from the microprocessor exit port to the D/A converter causing no movement of the motor. The D/A converter command output S which activates the solenoid of the servo valve comprises two parts as follows: S = Nv + S',
(3)
where Nv is defined as the D/A converter command for which the system is expected to be stationary; and S' is the demand offset which offsets the spool of the valve to increase the flow rate. When the payload is stationary the effect of S' is governed by the nature of the control laws implemented within the controller. Considering the case of the PID control algorithm S ' = AT,
(4)
where AT is defined as the correction effort, then Eqn (3) can be rewritten in the form s = Uv + A T .
(5)
From Eqn (5) it can be seen that when the system is at null the D/A converter command S equals Vs, therefore V~ = Nv + AT.
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Control system for a pneumatic rotary actuator
551
Note, however, that Vs is not uniquely defined. By reference to Fig. 4 it can be seen that Vs will in fact be some where within the dead zone, i.e. V2 ~< Vs ~ V1. The analysis suggests that position error can overcome by choosing a null value Nv which is equal to either V2 or VI (i.e. one the two boundary values). The choice between VI and V2 is made with reference the value of the position error. So, Eqn (3) can be written in the form VI + AT
whenAT>0
V2+ AT
whenAT<0.
s =
(7) of be of to
(8)
The values of V1 and V2 were obtained experimentally (for the test system V1 = 0.727 V and V2 = 0.68 V). The null values and dead zone of the system depend largely on the friction forces.
7. ON-LINE CONTROL SOFTWARE Evaluations of the characteristics of the air motor were obtained by using a 486 computer to control the motor, in conjunction with a data acquisition processor. This data acquisition processor is a microcomputer based data acquisition system which enables the computer to measure signals from transducers and to output signals to control the system and use a ROM resident operating system called DAPL [17]. On-line control algorithms were designed and implemented to facilitate the modified PID control scheme. Software modules were produced to run on the computer controller to evaluate the effectiveness of the control strategy. The modules were written in FORTRAN and DAPL languages. The structure of these real time control algorithms is illustrated in the flow chart in Fig. 9. Accurate positioning is one of the most important tasks which has to be carried out in mechanical handling systems. Control methods based on the position feedback control algorithm were used for the dosed loop control of the pneumatic system. The closed loop test rig is shown in Fig. 10. The command signal is converted by the D/A converter into an analogue signal, which is then amplified by the servo amplifier so that the output signal takes the form of current. The current thus produced is supplied to the solenoid which in turn generates a magnetic field at one end of the valve spool to offset the spring. Thus the mass flow rate across the five-port valve can be controlled by manipulating the spool offset, i.e. by controlling the current supplied to the solenoid. The minimum data necessary to control the load are its current position value and its desired position. The position value was obtained from a potentiometric position sensor fixed to the fly wheel axis. The resolution of the potentiometer will ultimately determine the repeatability and accuracy with which positioning of the drive can be
552
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HuL~lpiy In~Ce~P~¢lon of posl~clon el*PoP by K I Aerrt - K t f e ,,¢
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achieved. However, any errors in the m e a s u r e m e n t will depend on other characteristics of the feedback transmission elements, i.e. backlash, dead zone, hysteresis, etc. More accurate position m e a s u r e m e n t could be achieved using an optical encoder. Two types of forcing function were applied to the closed loop pneumatic system
Control system for a pneumatic rotary actuator
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Fig. 10. Closedloop test system. shown in Fig. 10. These forcing functions were step inputs and sinusoidal inputs. The inputs were applied to the system with different amplitudes, different frequencies and payload. Figure 11a shows the experimental results using the step input with different amplitudes. Figure l l b shows one example of the applied voltage to the valve. Step input tests with and without payload (fly wheel) were applied to the system and the results were very similar. The second forcing function was a sinusoidal input which was applied to the system with different amplitudes, frequencies and payload. Figure 12 shows results using a sinusoidal input at a frequency of 0.025 Hz with different amplitudes. Figure 13 shows results using sinusoidal input at a frequency of 0.2 Hz with different amplitudes. It is clear that the characteristic properties of the control valve and air motor should be considered in any control strategy as they affect the behaviour of the complete control system. All of these tests were conducted with a supply pressure of 6 bar.
8.
APPLICATION: SINGLE-DEGREE-OF-FREEDOM ROBOT ARM
Initial experimental results using the modified PID controller and on-line control algorithm showed that the air motor exhibited smooth operation with good control
554
H.M. MAHGOUB and I. A. CRAIGHEAD [] D e s i r e d a n g l e (0 ° - 30 °) + M e a s u r e d a n g l e (0 ° - 30 °) * D e s i r e d a n g l e (0 ° - 6 0 °) L~ M e a s u r e d a n g l e (0 ° - 6 0 °) × D e s i r e d a n g l e (0 ° - 9 0 °) [] M e a s u r e d a n g l e (0 ° - 9 0 °) • D e s i r e d a n g l e (0 ° - 120 °) • M e a s u r e d a n g l e (0 ° - 120 °) o D e s i r e d a n g l e (0 ° - 150 °) z M e a s u r e d a n g l e (0 ° - 150 °) • D e s i r e d a n g l e (0 ° - 180 °) v M e a s u r e d a n g l e (0 ° - 180 °) 270 ~ ~
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and stopping characteristics. Therefore further experimental work was carried out using a single-degree-of-freedom (SDOF) robot arm (Fig. 14). Two types of forcing function were applied. These forcing functions were step inputs and sinusoidal input. The inputs were applied to the system with different amplitudes, different frequencies and different payloads. Figure 15 shows the experimental results using step input with different amplitudes. Step input tests with different payloads (1 and 2 kg) were applied to the system, and the results were similar to the step input test without load.
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The sinusoidal input was applied to the system with different amplitudes, different frequencies and different payloads. Figure 16 shows results using a sinusoidal input with different amplitudes, different frequencies and with 2 kg payload. The torque produced by the gravitational force varies with angular displacement, resulting in a non-linear system to be controlled by a motor possessing non-linear characteristics.
9. DISCUSSION The development of a pneumatic actuation system which allows the accurate control of a system under a variety of shaft speeds and loading has been described.
556
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Fig. 13. Closed loop system, sinusoidal input with different amplitudes and different frequencies.
The use of a microprocessor based control system facilitating compensation of pneumatic servo drives has allowed significant improvement in characteristics to be achieved and offers the opportunity for control of a non-linear system to be implemented in a cost effective and user friendly way. Such performance characteristics coupled with the low cost of drive elements should ensure commercial exploitation in many areas of automated manufacture, especially in the robotic field [18]. This research work has shown a way in which a digital computer can be used to obtain the dynamic response of a pneumatic actuator and valve combination. Because of the complex nature of the non-linearities, a computer program was developed
Control system for a pneumatic rotary actuator
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Fig. 14. Single-degree-of-freedomtest system.
using FORTRAN and DAPL commands. Pneumatic servos have until now been used with a limited range of pneumatic drive system components (cylinders and vane actuators). This work has been concerned with a piston air motor which overcomes many of the problems usually associated with conventional pneumatic actuators. A control algorithm for pneumatic servos has been presented. The control method involves using a modified PID control system to account for the non-linear behaviour of the pneumatic system. It is important to determine the actuator characteristics in any control system as they generally are not ideal as assumed in many theoretical studies. To determine these, two types of forcing function were applied to the system, which are realistic in the real world: step input and sinusoidal input functions. Observations from the air motor tests highlighted the non-linear behaviour of the air motor. To take account of these non-linearities the simple proportional gain in the system was replaced with an interpolation function which accounted for the saturation, dead zone and rotation direction dependent gains. Two types of forcing functions were applied to the system, first a step input with different amplitudes (0-30, 0-60, 0-90, 0-120, 0-150 and 0-180 °) was applied. Secondly, sinusoidal inputs with different amplitudes (+30, +60 and +90 °) and different frequencies (0.025-0.8 Hz) were applied. From the results it was found that the system, controlled by the modified PID approach, performed well. The response to the step input was completed in approximately 0.7 s even for a motion of 180°; the largest final position error was found to be 2° and considered to be due to the gear reduction and the resolution of the potentiometer. An initial delay of 0.27 s is evident from the graphs and is due to
558
H.M. MAHGOUB and I. A. CRAIGHEAD [] A c t u a l a n g l e (0 ° - 60 °) + Desired a n g l e (0 ° - 60 °) * A c t u a l a n g l e (0 ° - 90 °) D e s i r e d a n g l e (0 ° - 90 °) × Actual a n g l e (0 ° - 120 °) [] D e s i r e d a n g l e (0 ° - 120 °) • A c t u a l a n g l e (0 ° - 180 °) • D e s i r e d a n g l e (0 ° - 180 °)
270
9 135
67
0[~---
0
0~
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0~5
~0
~5
,~0
i
i
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time delays inherent in the A/D board used. It is envisaged that eventually this will be substantially reduced, resulting in a step response within 0.5 s. The ability of the system to track a sinusoidal trajectory was found also to be highly satisfactory (Figs 12 and 13). For the case of an amplitude of 90 ° and a frequency of 0.025 Hz the root mean square error was 2.2 °, and at 0.7 Hz and amplitude 60 ° the root mean square error increased to 3.31 ° . The performance of an SDOF robot using the pneumatic actuator was established. Two types of forcing function were applied to the system. First, a step input with different amplitudes (0-30, 0-60, 0-90, 0-120, 0-150 and 0-180 °) and different payloads (1, 2, 3 and 4 kg) was applied. Secondly, sinusoidal inputs with different amplitudes (_+30, _+60 and _+90°) and different frequencies ( 0 . 0 2 5 - 0 . 8 H z ) were applied. From the results it was found that the S D O F robot arm controlled by modified PID approach performed well. Heavier payload (in this system greater than 3 kg) and faster operation (for frequency greater than 1 Hz) result in greater error and eventually unstable behaviour. The experimental results presented in this paper show that the pneumatic air motor can exhibit excellent characteristics and can offer a cost-effective solution in certain application areas. The results show that with constant control parameters (loop gains) a range of different trajectories can be followed. For control purposes the characteristics of the air motor in terms of steady state and transient behaviour were identified. Satisfactory control of a pneumatic servo motor was achieved. The air motor exhibited smooth operation with good control and stopping characteristics.
I0. CONCLUSIONS A PC based control system for the Motron air motor was developed. The system was used to obtain the motor characteristics. The motor behaviour was found to be
Control system for a pneumatic rotary actuator
[] + * A x 270
559
M e a s u r e d a n g l e (-30 ° - 30 °) D e s i r e d a n g l e (-30 ° - 30 °) M e a s u r e d a n g l e (-60 ° - 6 0 °) D e s i r e d a n g l e (-60 ° - 6 0 °) M e a s u r e d a n g l e (-90 ° - 9 0 °) D e s i r e d a n g l e (-90 ° - 9 0 °)
i 80
90 o
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iO
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45
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(a)
,,
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M e a s u r e d a n g l e (-30 ° - 30 °) D e s i r e d a n g l e (-30 ° - 30 °) M e a s u r e d a n g l e (-60 ° - 60 °) D e s i r e d a n g l e (-60 ° - 6 0 °) M e a s u r e d a n g l e (-90 ° - 90 °) D e s i r e d a n g l e (-90 ° - 9 0 ° )
o 180 ~
9o
o0
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10
20
25
30
35
T i m e (see) S i n u s o i d a l input at f r e q u e n c y - 0.10 H z
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[] + * A x 270
g
15
M e a s u r e d a n g l e (-30 ° - 30 °) D e s i r e d a n g l e (-30 ° - 30 °) M e a s u r e d a n g l e (-60 ° - 6 0 °) D e s i r e d a n g l e (-60 ° - 6 0 °) M e a s u r e d a n g l e (-90 ° - 9 0 °) D e s i r e d a n g l e (-90 ° - 9 0 °)
180
90 0
0
(c)
0
I
2
3
4
5
6
7
8
9
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T i m e (see) S i n u s o i d a l i n p u t at f r e q u e n c y - 0.40 Hz Fig. 16. S i n g l e - d e g r e e - o f - f r e e d o m system: s i n u s o i d a l input.
11
560
H.M.
MAHGOUB
a n d I. A. C R A I G H E A D
non-linear with a dead zone in the null region, differing proportional gains and saturation. A modified PID control strategy was developed which compensated these non-linearities and was found to give satisfactory control of the system. Response to step inputs up to 180 ° was achieved within 0.7 s with an accuracy of approximately + 2 °. Satisfactory sinusoidal frequency response was obtained with amplitudes up to 90 ° and frequencies up to 0.7 Hz. The largest root mean square error was found to be 3.31 °. The use of a microprocessor based control system facilitating compensation of a pneumatic servo drive was developed and used to provide satisfactory control of an S D O F robot arm. Acknowledgements--The authors gratefully acknowledge the assistance and advice provided by Mr L. Wright, Mr A. Holmes, Mr S. Barrett and Mr M. Brisland of Motron Dynamics Ltd, Barnsley, U.K.
REFERENCES 1. Pu J., Harrison R., Moore P. R. and Weston R. H., Design and use of intelligent servo pneumatics as an alternative to electric servo drives. Proc. lMeehE March (1993). 2. Morgan G., Programmable positioning of pneumatic actuators. Appl. Pneumatics May, 16-20 (1985). 3. Bowns D. E. and Ballard R. L., Digital computation for the analysis of pneumatic actuator systems. Proc. Inst. Mech. Engrs 186,881-889 (1972). 4. Burrows C. R., Effect of position on the stability of pneumatic servo mechanisms. Res. Notes Mech. Engng Sci. II(6), 615-616 (1969). 5. Chitty A. and Lambert T. H., Modelling a two-way pneumatic actuator. J. Meas. Control 9, 19-25 (1976). 6. Weston R. H., Moore P. R., Thatcher T. W. and Morgan G., Computer controlled pneumatic servo drives. 1Mech. 198B, 275-281 (1984). 7. Pu J., Moore P. R. and Weston R. H., High gain control and tuning strategy for vane type reciprocating pneumatic servo drives. Int. J. Prod. Res. 29(8), 1587-1601 (1991). 8. Pu J. and Weston R. H., Motion control of pneumatic drives. J. Microprocessors Microsyst. 12(7), 373-382 (1988). 9. Moore P. R., Weston R. H. and Thatcher T. W., Compensation in pneumatically actuated servomechanisms. Trans. Inst. Meas. Control 7(5), 238-244 (1985). 10. Mannetje J. J., Pneumatic servo design method improves system bandwidth twenty-fold. Control Engng 28, June, 79-83 (1981). 11. Pu J., Moore P. R. and Weston R. H., Digital servo motion control of air motors. Int. J. Prod. Res. 29(3), 599-618 (1991). 12. Backe W., The application of servo pneumatic drives for flexible mechanical handling techniques. Robotics 2, 45-56 (1986). 13. Shahi S. S., Characterisation and control of actuators for a smart pneumatic system. Institute of Physics Short Meeting Series "Actuators Update", pp. 59-76, London, 22 September (1988). 14. Dunlop R. W., Development of pneumatic devices to provide integrated motion control using oil-free air. 8th International Symposium on Fluid Power, Paper BI, pp. 87-106, Birmingham, 19-21 April (1989). 15. Schwarzenbach J. and Gill K. F., System Modelling and Control. Edward Arnold, London (1992). 16. Fu K. S., Gonzalez R. C. and Lee C. S. G., Robotics: Control, Sensing, Vision, and Intelligence. McGraw-Hill, New York (1987). 17. Data Acquisition Processor DAPL manual, Version 4.1, Analog Accelerator Series, Microstar Laboratories, Inc., Bellevue, WA 98004 (1993). 18. Mahgoub H. M. and Craighead I. A., Robot actuation using air motors. Int. J. Adv. Manufact. Technol. (accepted).
© 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved. 0957-4158/95 $9.50+0.00
Pergamon 0957-4158 (95) 00025-9
DEVELOPMENT OF A MICROPROCESSOR BASED CONTROL SYSTEM FOR A PNEUMATIC ROTARY ACTUATOR H. M. M A H G O U B and I. A. C R A I G H E A D Department of Mechanical Engineering, University of Strathclyde, Glasgow G1 1XJ, U.K.
(Received 19 October 1994; revised 15 February 1995; accepted 15 February 1995) Abstract--A microprocessor based control system has been developed and used to provide satisfactory control of a pneumatic servo system. This paper describes how microprocessor based controls can be used to produce low cost pneumatic servo drives which could find a wide range of application in manufacturing industries. The pneumatic actuator is a piston air motor constructed of aluminium, utilising a proportional spool valve to allow air flow control. The dynamics of the air motor in conjunction with the solenoid valve have been experimentally determined. Control is based on a modified PID (proportional, integral and derivative) controller which adjusts the command issued to the control valve. This takes account of the inherent non-linear behaviour of the air motor. The motor has been used to actuate a single-degree-of-freedom(SDOF) robot arm. The results show that digitally controlled air motors have the potential of providing an alternative solution to their electric and hydraulic motor counterparts. Air motors, through inherent low cost, good power to weight ratio and intrinsically safe operation, can be utilised to control a wide range of industrial machines. 1. I N T R O D U C T I O N Intelligent servo pneumatics have now reached a stage in development where they show a competitive advantage in certain application areas over electric and hydraulic drive counterparts. However, a lack of confidence still prevails in industry when considering pneumatic drives as an option for servo drive technology [1]. Many servo drive pneumatic systems have become commercially available, but their application is still limited mainly to simple machines. Pneumatic actuation is used widely in industrial applications to provide low cost motion. These actuators are capable of achieving end stop positional accuracy comparable with electric and hydraulic servos [2]. The pneumatic servos are controlled by various forms of valves which control the direction of air flow. For applications which require positioning of payloads, usually either hydraulic or electric servo drive systems are used. Although such drives can provide considerable flexibility and satisfactory characteristics, in many manufacturing applications their use introduces significant cost penalties so that if a low cost pneumatic drive was adequate it would be preferred. Previous analysis [3] has shown that pneumatic drives exhibit very significant non-linearities; the natural stiffness of the drive varies considerably over its working range [4], as does the inherent damping of the drive when the magnitude of valve opening is changed. In practice, however, correct estimation of such parameters which govern the dynamics of pneumatic drives is difficult to achieve. The existence 541
542
H.M. MAHGOUB and I. A. CRAIGHEAD
of significant and unpredictable drift and hysteresis has limited the use of pneumatic servos to application areas where some unpredictability in dynamic responses can be tolerated. There are two major problems which make the application of air motors difficult. Firstly, it is not an easy task to maintain an absolutely constant supply pressure, particularly when the motor is running at high speeds. To solve this, a local reservoir can be used to ensure that fluctuations in supply pressure are reduced to an acceptable level. Secondly, the valve response characteristics usually are not linear. Much research interest over the last 20 years has centred on the modelling and implementation studies of pneumatic servo drives which have been aimed at overcoming the inherent limitations of air servos [3-5]. However, the compressibility of air as a working fluid introduces significant control problems relating to time delays, low stiffness, little natural damping and non-linearities. Also, most pneumatic systems suffer to some degree from air leakage and frictional effects. In recent years a number of researchers [6-9] have investigated the use of computer controls in an attempt to compensate for the effect of such problems. When modelling pneumatic drives, the equations describing the motion are complex [6]. Due to their non-linear and complex nature, pneumatic system characteristics are very much dependent upon the operating conditions of the drive. Due to the above factors, a pure proportional, integral and derivative (PID) controller will not be adequate for controlling pneumatic servos, so an alternative approach must be found to ensure satisfactory behaviour. Two distinct classes of actuator are available. These are the reciprocating actuators (e.g. cylinders) and continuous actuators (e.g. air motors and vane actuators). However, to date the majority of research aimed at studying such drives has been focused on reciprocating actuators [2-4, 10]. Only a very limited amount of research effort has been directed to the study of vane type [11, 12] and air servo motors [13, 141. This paper describes a control scheme which has been devised to improve the dynamic response obtained with the air motor previously described by [13, 14].
2. THE AIR M O T O R S
Air motors are prime movers powered by compressed air and have certain desirable characteristics when compared to more conventional types of motors [13, 14]. The Motron air motor has largely overcome the fundamental problem of using air, which is compressibility, by keeping the volumes of gas small and gearing out the effects of compression. This gives it similar characteristics to a D.C. motor. However, pneumatic systems possess significant inherent non-linearities due to complex fluid/ mechanical interactions, so it is not possible to use the same control techniques. The air motor employs four radial free floating pistons acting on the three-lobed cam. This means that each piston will rise and fall three times per shaft revolution. This gives the motor 12 power strokes per revolution. Figure 1 shows the cam and piston arrangement within the motor. At the heart of the motor is the tri-lobed cam. This cam has two functions: the first is to convert the linear motion of the piston into rotary motion, the second is to provide the correct valve timing. The valves are in the
Control system for a pneumatic rotary actuator
543
Spool valve
...............
o~
:
, LI
\ '!i
Solenoid
Cam 7-.~-~, ~
Piston
lipper pad
Fig. 1. Solenoid motor showing piston cam arrangement.
sides of the pistons. Each piston contains the valve that controls the next piston in a clockwise direction. Considering the pistons marked A, B, and C in Fig. 1, when piston B is at top dead centre, ready to produce a power stroke, piston A will have just closed the exhaust port for piston B and piston C will have just opened the inlet port. When piston C reaches top dead centre, piston B will open the inlet port for C, and so on. In this way commutation of the pistons is carried out. When the motor is rotating in a clockwise direction, all the slipper pad valves on the back face are acting as exhaust valves, and all those on the front face as inlet valves. In the anticlockwise direction the opposite is true. The motor valve is supplied with 24 V, 1 A electrical supply and can be operated with oil-free air. The motor has the following advantages in industrial applications: (1) high starting torque providing fast smooth acceleration; (2) high torque-to-weight ratio; (3) ability to sustain stall without overheating; (4) use of oil-free air means there is no environmental contamination; (5) absence of electrical risk; (6) simplicity in structure, easy to design and to maintain; (7) positional accuracy; (8) maintenance free; (9) low shaft speed at high torque; (10) no high pressure leakage problem; (11) local high current supply not required; (12) no heat dissipation problems; and (13) low operational cost [13].
3. THE PROPORTIONAL VALVE In order to control the position, speed or steady state torque developed by the air motor, a control valve capable of proportional action is required. Such a valve is
544
H.M. MAHGOUB and I. A. CRAIGHEAD
interfaced directly to a proportional solenoid, resulting in spool movement in a manner related to the variation in solenoid current/voltage [13, 14]. The dither is a high frequency, low amplitude vibration which is imposed on the spool valve to reduce stiction. It is generated using 555 timer at TTL levels of +5 V. This is reduced by a potential divider to approximately 0.1 V. The frequency of the dither is set to 100 Hz. The air flow rate through the motor determines its velocity. As the motor is symmetrical, reversing the air flow reverses the direction of the motor rotation. A five-port spool valve controls the air flow; its schematic is shown in Fig. 2. The spool valve works by moving the centre spool within a sleeve. When the spool is in the centre position, as in Fig. 2a, no air flows through the motor. Moving the spool to the left allows air to flow from the inlet to the right hand motor port (Fig. 2b). The end of the spool closes the right hand exhaust port. The air flows through the motor and back to the left hand side of the spool, and out through the left hand exhaust port. If the spool is moved to the right, air flows through the valve in the opposite direction, as shown in Fig. 2c. The position of the spool is determined by the force generated by the solenoid pushing the spool against the spring at the end of the spool. The centre, off position is achieved when the solenoid is at approximately half power. Fully open to the left is achieved when the solenoid is at full power, and fully open to the right when the solenoid is off.
Exhaust
Air in
Exhaust
i ..... jr L - ~ ~
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D
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i
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Fig. 2. Five-port spool valve.
Control system for a pneumatic rotary actuator
545
A 24 W proportional solenoid is used to control the spool valve. The current supplied to the solenoid determines the force it generates. Changing the force on the solenoid varies the spool position and thus the flow through the valve. This relationship is non-linear [13] and is illustrated in Fig. 4. Hysteresis is caused by stiction in the valve and can be reduced by adding dither to the control signal. This causes the spool to vibrate with a low amplitude. The dither keeps the spool continuously moving and thus prevents stiction. The amplitude of the dither is so small that it has a minimal effect on the control signal.
4. EXPERIMENTAL EVALUATION OF THE SYSTEM DYNAMICS The actuator used in the experimental work was the Motron piston air motor. The motor was used to power a load (fly wheel) and in order to control the dynamics of this load its state must be known at any instant so that the correct control decision can be taken. The specification data relating to the air motor, control valve and other elements of the system are given in Table 1. The experimental hardware consists of actuator, valve and sub-systems. The sub-systems include computer control hardware, feedback sensor, electronic/electrical interface components, mechanical component interface and mechanical component hardware. The worm and worm wheel were chosen for compactness as the ultimate aim of the research is to develop a pneumatically powered robot arm where space and weight will be restricted. An open loop test rig was constructed (Fig. 3). A command signal is generated by a signal generator. The analogue signal is amplified to produce a valve command current in the range of 0-1 A. In addition to the proportional valve signal a small Table 1. Operating data of system components Actuator
Valve Load Digital to analogue converter Position sensor
Supply pressure Exhaust pressure Servo amplifiers Reduction gear box
(DAC)
Piston air motor N o . of pistons = 4 Speed range = 40 rpm at m a x . t o r q u e - 8 5 0 rpm unloaded Weight = 10.5 kg Lubrication of the air supply to the motor is optional Pneumatic servo valve five-port, solenoid actuator Single solenoid manipulation with return spring Mass moment of inertia = 0.281 k g . m E 12 bits Servo mount potentiometer Wiper current ( m a x . ) -- 10 mA Electrical rotation = 340 + 4 ° Temperature range = - 5 5 ° C to + 1 2 5 °C Mechanical rotation = 360 ° continuous Rotational life >107 shaft revolutions Starting torque ( m a x . ) = 28 x 10 -4 Nm Running torque ( m a x . ) = 21 x 10 -4 N m 80 psi Atmospheric Input voltage: 0 - 1 V Output current: 0 - 1 A Worm and worm wheel ( 1 : 1 5 )
546
H . M . M A H G O U B and I. A. C R A I G H E A D Air motor / v lSero Signal .[so,vo.,.,iorl l .0d ~-~ WV Generator
I~ - ~
/
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,
Comnuter ~ - - ~
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1
Fig. 3. Open loop test system.
oscillatory component is included; this dither component is used to reduce hysteresis due to friction in the system. Velocity information is sensed by a tachogenerator and fed back to the computer. The relationship between the input (command) signal to the valve and the output rotational velocity of the motor is shown in Fig. 4. It can be seen that the motor rotational velocity varies non-linearly with the command signal. The non-linearities arise from the valve and are the result of a dead zone, hysteresis and saturation. The motor also adds significant friction to the system. A series of step input functions with different amplitudes were applied to the system. Figures 5 and 6 show some of the results from the step inputs. From these figures, it can be seen that an oscillatory motion is observed and this arose from flexibility in the tachogenerator-transducer coupling which was used in the measurement. At low velocity (which corresponds to small valve spool displacements), more oscillatory motion can be observed. 600300-
i
>
i
ii
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-300-
vI -600 -j-
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Fig. 4. Relationship between input command and output velocity.
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547
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~
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Step input response Fig. 5. O p e n loop system, step input in clockwise direction.
Sinusoidal inputs were applied to the system and Fig. 7 shows the sinusoidal input and its corresponding output. From this figure it can be observed that the system is non-linear (it has a dead zone, asymmetric gains and saturation).
5. CONTROL STRATEGY Numerous adaptive control strategies (e.g. [15, 16]) have been proposed for use with non-linear systems. Most of them involve considerable on line computation
548
H. M. M A H G O U B and 1. A. C R A I G H E A D Step input voltage at volt = 0.85 -- -- Step input voltage at volt = 0.90
-
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50
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i
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i
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i
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400 I
450 i
500 i
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Step input response Fig. 6. Open loop system, step input in counter clockwise direction.
which can restrict the a p p l i c a b i l i t y of the c o n t r o l a l g o r i t h m a n d r e q u i r e s t h e use o f a high p o w e r ( a n d e x p e n s i v e ) c o m p u t e r . T h e m o d i f i e d P I D c o n t r o l s t r a t e g y is an a l t e r n a t i v e a p p r o a c h to c o n t r o l l i n g the a c t u a t o r s which d o e s n o t r e q u i r e e x t e n s i v e c o m p u t a t i o n o r p r e v i o u s k n o w l e d g e o f the t r a j e c t o r y . This s t r a t e g y w o r k s i n d e p e n d ently o f the p a y l o a d , s p e e d , etc. a l t h o u g h the e r r o r is likely to b e l a r g e r for h e a v i e r payloads and quicker operation. In any p r a c t i c a l s y s t e m the t o r q u e will b e a p p l i e d by an a c t u a t o r which m a y b e p o w e r e d b y electricity, h y d r a u l i c s o r p n e u m a t i c s a n d the a c t u a t o r will h a v e a m a x i m u m a n d m i n i m u m v a l u e o f t o r q u e which it can a p p l y . T h e c o n t r o l t a s k is to a p p l y a t o r q u e T so t h a t the a n g u l a r p o s i t i o n 0 is at s o m e
Control system for a pneumatic rotary actuator [
549
Sinus°idal lnput I
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<
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desired value at any time t. Rather than calculate the absolute value of T that is required, the proposed control strategy determines the change in torque AT which should be added or subtracted to the existing torque. The determination of AT is achieved by a modified PID feedback loop and updated repeatedly. In practical terms, the actual value of 0(0a) would need to be measured, the desired value of 0(0d) would have to be specified for the next time step and the controller could then calculate AV and modify the actuator torque accordingly. The correction control effort is calculated as follows: AV(k) = k p ( O o ( k ) - Oa(k)) + kd(0d(k) -- 0a(k)) (1) + kil(Od(k) J
-- O a ( k ) ) d t ,
550
H.M. MAHGOUB and I. A. CRAIGHEAD
where kp is the proportional gain, and the total control effort is
kd
is the derivative gain and ki is the integral gain
V(k + 1) = V(k) + AV(k).
(2)
Pneumatic systems possess significant inherent non-linearities due to complex fluid/mechanical interactions. To take account of these non-linearities the simple proportional gain in the system was replaced with an interpolation function which accounted for the saturation, dead zone and rotation direction dependent gains. The modified PID control loop for the pneumatic system is illustrated schematically in Fig. 8. The interpolation function is based on specifying the relationship between applied voltage and error to take account of the dead zone, saturation and direction dependent gains. A linear interpolation is used to obtain intermediate voltages.
6. THE DEAD ZONE AND NULL REGION
The null value for the pneumatic system with a given payload is the digital number transmitted from the microprocessor exit port to the D/A converter causing no movement of the motor. The D/A converter command output S which activates the solenoid of the servo valve comprises two parts as follows: S = Nv + S',
(3)
where Nv is defined as the D/A converter command for which the system is expected to be stationary; and S' is the demand offset which offsets the spool of the valve to increase the flow rate. When the payload is stationary the effect of S' is governed by the nature of the control laws implemented within the controller. Considering the case of the PID control algorithm S ' = AT,
(4)
where AT is defined as the correction effort, then Eqn (3) can be rewritten in the form s = Uv + A T .
(5)
From Eqn (5) it can be seen that when the system is at null the D/A converter command S equals Vs, therefore V~ = Nv + AT.
[- ~ Integration~
d '
~
- ~
r Sampler ServoValveH A i r Motorand Load~
Fig. 8. ModifiedPID controlloop.
(6)
Control system for a pneumatic rotary actuator
551
Note, however, that Vs is not uniquely defined. By reference to Fig. 4 it can be seen that Vs will in fact be some where within the dead zone, i.e. V2 ~< Vs ~
whenAT>0
V2+ AT
whenAT<0.
s =
(7) of be of to
(8)
The values of V1 and V2 were obtained experimentally (for the test system V1 = 0.727 V and V2 = 0.68 V). The null values and dead zone of the system depend largely on the friction forces.
7. ON-LINE CONTROL SOFTWARE Evaluations of the characteristics of the air motor were obtained by using a 486 computer to control the motor, in conjunction with a data acquisition processor. This data acquisition processor is a microcomputer based data acquisition system which enables the computer to measure signals from transducers and to output signals to control the system and use a ROM resident operating system called DAPL [17]. On-line control algorithms were designed and implemented to facilitate the modified PID control scheme. Software modules were produced to run on the computer controller to evaluate the effectiveness of the control strategy. The modules were written in FORTRAN and DAPL languages. The structure of these real time control algorithms is illustrated in the flow chart in Fig. 9. Accurate positioning is one of the most important tasks which has to be carried out in mechanical handling systems. Control methods based on the position feedback control algorithm were used for the dosed loop control of the pneumatic system. The closed loop test rig is shown in Fig. 10. The command signal is converted by the D/A converter into an analogue signal, which is then amplified by the servo amplifier so that the output signal takes the form of current. The current thus produced is supplied to the solenoid which in turn generates a magnetic field at one end of the valve spool to offset the spring. Thus the mass flow rate across the five-port valve can be controlled by manipulating the spool offset, i.e. by controlling the current supplied to the solenoid. The minimum data necessary to control the load are its current position value and its desired position. The position value was obtained from a potentiometric position sensor fixed to the fly wheel axis. The resolution of the potentiometer will ultimately determine the repeatability and accuracy with which positioning of the drive can be
552
H . M . MAHGOUB and I. A. CRAIGHEAD
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achieved. However, any errors in the m e a s u r e m e n t will depend on other characteristics of the feedback transmission elements, i.e. backlash, dead zone, hysteresis, etc. More accurate position m e a s u r e m e n t could be achieved using an optical encoder. Two types of forcing function were applied to the closed loop pneumatic system
Control system for a pneumatic rotary actuator
553
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i
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Fig. 10. Closedloop test system. shown in Fig. 10. These forcing functions were step inputs and sinusoidal inputs. The inputs were applied to the system with different amplitudes, different frequencies and payload. Figure 11a shows the experimental results using the step input with different amplitudes. Figure l l b shows one example of the applied voltage to the valve. Step input tests with and without payload (fly wheel) were applied to the system and the results were very similar. The second forcing function was a sinusoidal input which was applied to the system with different amplitudes, frequencies and payload. Figure 12 shows results using a sinusoidal input at a frequency of 0.025 Hz with different amplitudes. Figure 13 shows results using sinusoidal input at a frequency of 0.2 Hz with different amplitudes. It is clear that the characteristic properties of the control valve and air motor should be considered in any control strategy as they affect the behaviour of the complete control system. All of these tests were conducted with a supply pressure of 6 bar.
8.
APPLICATION: SINGLE-DEGREE-OF-FREEDOM ROBOT ARM
Initial experimental results using the modified PID controller and on-line control algorithm showed that the air motor exhibited smooth operation with good control
554
H.M. MAHGOUB and I. A. CRAIGHEAD [] D e s i r e d a n g l e (0 ° - 30 °) + M e a s u r e d a n g l e (0 ° - 30 °) * D e s i r e d a n g l e (0 ° - 6 0 °) L~ M e a s u r e d a n g l e (0 ° - 6 0 °) × D e s i r e d a n g l e (0 ° - 9 0 °) [] M e a s u r e d a n g l e (0 ° - 9 0 °) • D e s i r e d a n g l e (0 ° - 120 °) • M e a s u r e d a n g l e (0 ° - 120 °) o D e s i r e d a n g l e (0 ° - 150 °) z M e a s u r e d a n g l e (0 ° - 150 °) • D e s i r e d a n g l e (0 ° - 180 °) v M e a s u r e d a n g l e (0 ° - 180 °) 270 ~ ~
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and stopping characteristics. Therefore further experimental work was carried out using a single-degree-of-freedom (SDOF) robot arm (Fig. 14). Two types of forcing function were applied. These forcing functions were step inputs and sinusoidal input. The inputs were applied to the system with different amplitudes, different frequencies and different payloads. Figure 15 shows the experimental results using step input with different amplitudes. Step input tests with different payloads (1 and 2 kg) were applied to the system, and the results were similar to the step input test without load.
Control system for a pneumatic rotary actuator n + • ix × g
555
Desired a n g l e (-30" - 30 °) Measured a n g l e (-30 ° - 30 °) D e s i r e d a n g l e (-60 ° - 60 °) Measured a n g l e (-60 ° - 60 °) D e s i r e d angle (-90 ° - 9 0 °) Measured a n g l e (-90 ° - 90 °)
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Fig. 12. Closed loop system, sinusoidal input with different amplitudes.
The sinusoidal input was applied to the system with different amplitudes, different frequencies and different payloads. Figure 16 shows results using a sinusoidal input with different amplitudes, different frequencies and with 2 kg payload. The torque produced by the gravitational force varies with angular displacement, resulting in a non-linear system to be controlled by a motor possessing non-linear characteristics.
9. DISCUSSION The development of a pneumatic actuation system which allows the accurate control of a system under a variety of shaft speeds and loading has been described.
556
H . M . MAHGOUB and I. A. CRAIGHEAD o Desired angle (-30 ° - 30 °) + Measured angle (-30 ° - 30 °) .
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Fig. 13. Closed loop system, sinusoidal input with different amplitudes and different frequencies.
The use of a microprocessor based control system facilitating compensation of pneumatic servo drives has allowed significant improvement in characteristics to be achieved and offers the opportunity for control of a non-linear system to be implemented in a cost effective and user friendly way. Such performance characteristics coupled with the low cost of drive elements should ensure commercial exploitation in many areas of automated manufacture, especially in the robotic field [18]. This research work has shown a way in which a digital computer can be used to obtain the dynamic response of a pneumatic actuator and valve combination. Because of the complex nature of the non-linearities, a computer program was developed
Control system for a pneumatic rotary actuator
557
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using FORTRAN and DAPL commands. Pneumatic servos have until now been used with a limited range of pneumatic drive system components (cylinders and vane actuators). This work has been concerned with a piston air motor which overcomes many of the problems usually associated with conventional pneumatic actuators. A control algorithm for pneumatic servos has been presented. The control method involves using a modified PID control system to account for the non-linear behaviour of the pneumatic system. It is important to determine the actuator characteristics in any control system as they generally are not ideal as assumed in many theoretical studies. To determine these, two types of forcing function were applied to the system, which are realistic in the real world: step input and sinusoidal input functions. Observations from the air motor tests highlighted the non-linear behaviour of the air motor. To take account of these non-linearities the simple proportional gain in the system was replaced with an interpolation function which accounted for the saturation, dead zone and rotation direction dependent gains. Two types of forcing functions were applied to the system, first a step input with different amplitudes (0-30, 0-60, 0-90, 0-120, 0-150 and 0-180 °) was applied. Secondly, sinusoidal inputs with different amplitudes (+30, +60 and +90 °) and different frequencies (0.025-0.8 Hz) were applied. From the results it was found that the system, controlled by the modified PID approach, performed well. The response to the step input was completed in approximately 0.7 s even for a motion of 180°; the largest final position error was found to be 2° and considered to be due to the gear reduction and the resolution of the potentiometer. An initial delay of 0.27 s is evident from the graphs and is due to
558
H.M. MAHGOUB and I. A. CRAIGHEAD [] A c t u a l a n g l e (0 ° - 60 °) + Desired a n g l e (0 ° - 60 °) * A c t u a l a n g l e (0 ° - 90 °) D e s i r e d a n g l e (0 ° - 90 °) × Actual a n g l e (0 ° - 120 °) [] D e s i r e d a n g l e (0 ° - 120 °) • A c t u a l a n g l e (0 ° - 180 °) • D e s i r e d a n g l e (0 ° - 180 °)
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time delays inherent in the A/D board used. It is envisaged that eventually this will be substantially reduced, resulting in a step response within 0.5 s. The ability of the system to track a sinusoidal trajectory was found also to be highly satisfactory (Figs 12 and 13). For the case of an amplitude of 90 ° and a frequency of 0.025 Hz the root mean square error was 2.2 °, and at 0.7 Hz and amplitude 60 ° the root mean square error increased to 3.31 ° . The performance of an SDOF robot using the pneumatic actuator was established. Two types of forcing function were applied to the system. First, a step input with different amplitudes (0-30, 0-60, 0-90, 0-120, 0-150 and 0-180 °) and different payloads (1, 2, 3 and 4 kg) was applied. Secondly, sinusoidal inputs with different amplitudes (_+30, _+60 and _+90°) and different frequencies ( 0 . 0 2 5 - 0 . 8 H z ) were applied. From the results it was found that the S D O F robot arm controlled by modified PID approach performed well. Heavier payload (in this system greater than 3 kg) and faster operation (for frequency greater than 1 Hz) result in greater error and eventually unstable behaviour. The experimental results presented in this paper show that the pneumatic air motor can exhibit excellent characteristics and can offer a cost-effective solution in certain application areas. The results show that with constant control parameters (loop gains) a range of different trajectories can be followed. For control purposes the characteristics of the air motor in terms of steady state and transient behaviour were identified. Satisfactory control of a pneumatic servo motor was achieved. The air motor exhibited smooth operation with good control and stopping characteristics.
I0. CONCLUSIONS A PC based control system for the Motron air motor was developed. The system was used to obtain the motor characteristics. The motor behaviour was found to be
Control system for a pneumatic rotary actuator
[] + * A x 270
559
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11
560
H.M.
MAHGOUB
a n d I. A. C R A I G H E A D
non-linear with a dead zone in the null region, differing proportional gains and saturation. A modified PID control strategy was developed which compensated these non-linearities and was found to give satisfactory control of the system. Response to step inputs up to 180 ° was achieved within 0.7 s with an accuracy of approximately + 2 °. Satisfactory sinusoidal frequency response was obtained with amplitudes up to 90 ° and frequencies up to 0.7 Hz. The largest root mean square error was found to be 3.31 °. The use of a microprocessor based control system facilitating compensation of a pneumatic servo drive was developed and used to provide satisfactory control of an S D O F robot arm. Acknowledgements--The authors gratefully acknowledge the assistance and advice provided by Mr L. Wright, Mr A. Holmes, Mr S. Barrett and Mr M. Brisland of Motron Dynamics Ltd, Barnsley, U.K.
REFERENCES 1. Pu J., Harrison R., Moore P. R. and Weston R. H., Design and use of intelligent servo pneumatics as an alternative to electric servo drives. Proc. lMeehE March (1993). 2. Morgan G., Programmable positioning of pneumatic actuators. Appl. Pneumatics May, 16-20 (1985). 3. Bowns D. E. and Ballard R. L., Digital computation for the analysis of pneumatic actuator systems. Proc. Inst. Mech. Engrs 186,881-889 (1972). 4. Burrows C. R., Effect of position on the stability of pneumatic servo mechanisms. Res. Notes Mech. Engng Sci. II(6), 615-616 (1969). 5. Chitty A. and Lambert T. H., Modelling a two-way pneumatic actuator. J. Meas. Control 9, 19-25 (1976). 6. Weston R. H., Moore P. R., Thatcher T. W. and Morgan G., Computer controlled pneumatic servo drives. 1Mech. 198B, 275-281 (1984). 7. Pu J., Moore P. R. and Weston R. H., High gain control and tuning strategy for vane type reciprocating pneumatic servo drives. Int. J. Prod. Res. 29(8), 1587-1601 (1991). 8. Pu J. and Weston R. H., Motion control of pneumatic drives. J. Microprocessors Microsyst. 12(7), 373-382 (1988). 9. Moore P. R., Weston R. H. and Thatcher T. W., Compensation in pneumatically actuated servomechanisms. Trans. Inst. Meas. Control 7(5), 238-244 (1985). 10. Mannetje J. J., Pneumatic servo design method improves system bandwidth twenty-fold. Control Engng 28, June, 79-83 (1981). 11. Pu J., Moore P. R. and Weston R. H., Digital servo motion control of air motors. Int. J. Prod. Res. 29(3), 599-618 (1991). 12. Backe W., The application of servo pneumatic drives for flexible mechanical handling techniques. Robotics 2, 45-56 (1986). 13. Shahi S. S., Characterisation and control of actuators for a smart pneumatic system. Institute of Physics Short Meeting Series "Actuators Update", pp. 59-76, London, 22 September (1988). 14. Dunlop R. W., Development of pneumatic devices to provide integrated motion control using oil-free air. 8th International Symposium on Fluid Power, Paper BI, pp. 87-106, Birmingham, 19-21 April (1989). 15. Schwarzenbach J. and Gill K. F., System Modelling and Control. Edward Arnold, London (1992). 16. Fu K. S., Gonzalez R. C. and Lee C. S. G., Robotics: Control, Sensing, Vision, and Intelligence. McGraw-Hill, New York (1987). 17. Data Acquisition Processor DAPL manual, Version 4.1, Analog Accelerator Series, Microstar Laboratories, Inc., Bellevue, WA 98004 (1993). 18. Mahgoub H. M. and Craighead I. A., Robot actuation using air motors. Int. J. Adv. Manufact. Technol. (accepted).