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PID control for a distributed system with a smart actuator
Control Engineering Practice 9 (2001) 1235–1244
PID control for a distributed system with a smart actuator Dongik Lee*, Jeff Allan, Haydn A. Thompson, Stuart Bennett Rolls-Royce University Technology Centre in Control and Systems Engineering, Department of Automatic Control and Systems Engineering, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK Received 6 April 2001; accepted 6 April 2001
Abstract The emergence of distributed architectures based on smart components and fieldbus networks is promoting changes in proportional-integral-derivative (PID) controller design issues. This paper explores how PID control can benefit from smart actuator and fieldbus technologies. Firstly, this paper discusses a smart actuator scheme to improve the efficiency of PID controller retuning, as well as an implementation using a low-cost stepper-motor. Then, the smart actuator is applied to on-line adaptation of PID parameters using a standard pole-placement design method. Finally, experimental validation of the proposed approach is conducted using a controller area network (CAN) bus-based distributed architecture demonstrator. r 2001 Elsevier Science Ltd. All rights reserved. Keywords: PID control; Actuators; Nonlinearity; Fieldbus; Distributed control
1. Introduction Distributed architectures based on smart component and fieldbus technologies are becoming more common in modern control systems. Not only does a distributed architecture offer reduced wiring and simplified maintenance, it also provides the opportunity to implement more sophisticated control laws. Consequently, the emergence of distributed control systems leads to changes in process controller design issues (Clarke, 1995). From the viewpoint of PID controller design, one of the issues that is most significantly affected is antiwindup. Anti-windup algorithms (for example, Alsop, 1995; Peng, Vrancic, & Hanus, 1996) can be designed more efficiently if the actuator position and/or rate saturation limits are known. By employing a ‘smart’ actuator that can provide the process controller with this information through a fieldbus network it is possible to adapt the anti-windup parameters. For example, in Alsop (1995), a PI configuration with actuator feedback using the information from the smart
*Corresponding author. Tel.: +44-114-222-5236; fax: +44-114-2731729. E-mail address: cop97dl@sheffield.ac.uk (D. Lee).
actuator has been used to resolve integrator windup caused by the actuator saturation. Another key area where benefit may be derived is in automatic tuning, on which this paper focuses. The automatic tuning of PID control parameters has attracted significant interest (Astrom & Hagglund, 1995; Astrom, 1996; McCormack & Godfrey, 1998; Liu & Daley, 1999). Unfortunately, most of the automatic tuning techniques suffer from two drawbacks: (a) interruption of the normal closed-loop operation; and (b) poor results caused by undesirable actuator characteristics. The former is introduced because many automatic tuning techniques rely on a pre-defined test, such as relay test, for which disconnection of the closedloop control is needed. Such interruption is often undesirable. For example, an on-line approach without the closed-loop interruption is usually required when the automatic tuning technique is applied to adaptation of the controller to cope with time-varying disturbances. The latter drawback is introduced by the assumption that an actuator is an ideal element having unity gain, instantaneous response and no steady-state offset. However, actuators in reality are nonlinear, slow, and limited in their operation. In practice, actuator faults are the largest source of control system degradation. For instance, an analysis in a pulp and paper mill revealed that 70% of the actuators had significant operating
0967-0661/01/$ - see front matter r 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 7 - 0 6 6 1 ( 0 1 ) 0 0 0 6 9 - 7
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problems (Harrold, 1999). Undesirable actuator characteristics result in many problems, such as large overshoot for set-point changes, limit cycles, and stickslip motions. If automatic tuning techniques are to be effective for industrial processes, then, as Astrom and Hagglund (1995) have emphasized, the actuators must be checked carefully before tuning the controller. As actuator properties change with time it is necessary to monitor on-line the actuator characteristic during normal operation. Unfortunately, this is not easy with a conventional ‘dumb’ actuator. However, by employing a distributed architecture based on a smart actuator and a fieldbus network, on-line monitoring can be obtained. A ‘smart’ actuator (or ‘intelligent’ actuator) has a builtin microprocessor and a standard fieldbus interface, so that it has the capability for local computation and thus intelligent functionality with bi-directional communications to the ‘higher-level’ process controller (Clarke, 1995). This paper aims to show how standard PID control techniques, especially with regard to on-line retuning, can benefit from smart actuator and fieldbus technologies. A smart actuator scheme suitable for PID controller retuning is identified and implemented. In order to make the PID controller retuning more efficient, the proposed smart actuator scheme focuses on developing the capability for self-diagnosis, selfcompensation, and bi-directional communications to the process controller. Then, the smart actuator is applied to on-line retuning of PID parameters based on a standard pole-placement design method. Finally, experimental validation of the proposed approach is conducted using a distributed architecture demonstrator which consists of a set of PCs, a stepper-motor-based smart actuator, and a CAN (Bosch, 1991) bus network.
2. The smart actuator concept Before developing a PID controller retuning strategy, it is necessary to identify the content of intelligent functionality which can be embedded in a smart actuator. Several researchers have suggested schemes for smart actuators (Isermann & Raab, 1993; Xie, Pu, & Moore, 1998; Yang & Clarke, 1999), which provide decision on the actuator health status and information on the changes of physical parameters. However, this information is not of direct use in PID controller retuning. Controller retuning or reconfiguration requires static and dynamic actuator characteristics, such as saturation limits and time constant, which have a direct influence on the control system performance. The proposed smart actuator scheme focuses on selfdiagnosis and self-compensation of the actuator characteristics, and on a digital communication interface for exchange of extra information with the process con-
troller. Key features of the suggested smart actuator scheme are given below: *
*
*
*
Self-compensation: Actuators may have undesirable static and dynamic characteristics introducing many problems for the PID control loop. For instance, limit cycles caused by actuator backlash cannot be removed by adjusting PID parameters (Astrom & Hagglund, 1995). Therefore, a nonlinearity compensation algorithm using an inverse model and a simple position controller are implemented in order to maintain the actuator characteristics to be as linear as possible within the attainable actuation range. Self-diagnosis: An adaptive nonlinearity estimation algorithm (Tao & Kokotovic, 1996) is employed since actuator nonlinearities vary with time. In addition to the nonlinearity estimation, on-line estimation of the actuator input-output dynamic characteristic is also implemented. Condition data: A set of condition data describing the actuator characteristics is defined, with which the PID controller retuning will be performed. Fieldbus interface: For data exchanges between the smart actuator and the process controller, a CAN bus interface is employed.
3. Smart actuator implementation based on a low-cost stepper-motor 3.1. System overview A smart actuator can be implemented with either integrated intelligence or add-on intelligence (Masten, 1997). In the integrated intelligence type implementation, actuator intelligence and actuation are combined into a single material. A piezoceramic actuator is a typical example of this type. However, the integrated intelligence is still not commonly used due to technological difficulties. On the other hand, in the add-on intelligence type of implementation, a smart unit based on a microprocessor or DSP, is added to a ‘dumb’ actuator. A benefit of the add-on intelligence approach is that a low-cost device can be used instead of a high precision manufactured device. Enhanced capabilities are obtained with embedded microprocessor power. As shown in Fig. 1, for experimental purposes, the smart actuator concept described in Section 2 is implemented using an add-on intelligence, CAN bus, and an actuator rig. A PC provides local computation to achieve the add-on intelligence described in Section 2. The actuator rig consists of a 4-phase hybrid steppermotor and a linear variable differential transformer (LVDT). The rotary torque of the stepper-motor is transferred through a gear train to the leadscrew which generates back-and-forth straight line motion. The
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stepper-motor runs with constant stepping rate. The LVDT measures the position of the leadscrew, which is fed back to the add-on intelligence through the CAN bus. To generate an output backlash a clearance between the LVDT and the leadscrew is inserted. A simplified model of the smart actuator implementation with output backlash is depicted in Fig. 2. Details on the implementation are given below. 3.2. Self-compensation 3.2.1. Actuator nonlinearity compensation An inverse model-based approach is a powerful tool to compensate for process input or output nonlinearity (Tao & Kokotovic, 1996). For an input nonlinearity, N; the output of its inverse model N# * is given by vðtÞ ¼ N# * ðud ðtÞÞ;
ð1Þ
where ud is the actuator demand position and the argument t denotes discrete time. If the inverse model estimated is exact, then the actuator output ðua Þ follows the demand, and Eq. (2) can be achieved: ua ðtÞ ¼ NðN# * ðud ðtÞÞÞ ¼ ud ðtÞ:
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The output nonlinearity shown in Fig. 3 is difficult to deal with because the output of the unknown linear part GðsÞ is not completely observable from ua ðtÞ; which results in a bounded error even if the parameter estimate is equal to the true value. For achieving ua ðtÞ ¼ ud ðtÞ; a more complicated control algorithm is needed. In this work, the scheme shown in Fig. 4 is adopted. If the tracking error eðtÞ ¼ zm ðtÞ z#ðtÞ goes to zero, then the actuator output ua ðtÞ converges to the demand ud ðtÞ with a bounded error in finite time steps.
3.2.2. Actuator position control A three-state position controller, along with pulsewidth modulation (PWM), is exploited for the actuator position control since the stepper-motor is driven at a constant stepping rate. A deadband (d) between two active states is added so as to prevent frequent changes of the motor direction due to measurement noise. The width of the deadband is chosen as the amount of measurement noise. Since the controller has only proportional action, actual position of the actuator will come to rest somewhere around the active zone (i.e.,
ð2Þ
Fig. 3. Output nonlinearity (N) compensation using its inverse model (N# * ).
Fig. 1. Schematic of a smart actuator implementation using actuator rig and add-on intelligence. Fig. 4. Block diagram of the output backlash compensation scheme.
Fig. 2. Simplified model of the smart actuator implementation with an output backlash.
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around 7d), so that offset at the actual position will appear. This offset is reduced by employing a feedforward compensation wðtÞ as 8 if zm ðtÞ > zm ðt 1Þ; > : wðt 1Þ otherwise:
3.3.1. On-line output backlash estimation As indicated in Section 3.1, the ‘dumb’ actuator rig is configured with output backlash. To identify such nonlinearities, an off-line estimation approach, which collects steady-state data through testing over the full range, is usually used (e.g., Sun, Liu, & Sano, 1999). However, the off-line estimation methods are not very realistic because nonlinearities typically change with time. In Alsop (1995) a recursive least squares (RLS) algorithm was used to estimate actuator nonlinearities. In particular, the nonlinearity model is represented with a set of straight line functions, so that the parameters of each line are estimated by applying linear least-squares algorithm based on only steady-state data. However, it may be difficult to obtain the steady-state data when the actuator demand values vary continuously (e.g., ramp input), so that convergence of the estimates can be delayed. In this paper, an adaptive estimation method (Tao & Kokotovic, 1996) based on transient data is applied to on-line estimation of the output backlash. A discrete-time model for output backlash is given by 8 > < mðzðtÞ cc Þ if zðtÞpzc ; vðtÞ ¼ NðzðtÞÞ ¼ mðzðtÞ cr Þ if zðtÞXzr ; ð4Þ > : vðt 1Þ if zc ozðtÞozr ;
ð5aÞ
vðt 1Þ þ cr : ð5bÞ m The meaning of m; cc and cr is depicted in Figs. 4 and 5 where m is the backlash slope and cr > 0 is the right crossing, whilst cc o0, is the left crossing. The backlash width is given by (cr cc ). For this backlash model,
zr ¼
z#ðtÞ ¼
w# r w# c r Þ þ c ðvðtÞ þ mc c c Þ; ðvðtÞ þ mc m# m#
where ( w# r ¼
3.3. Self-diagnosis
where vðt 1Þ þ cc ; zc ¼ m
estimated output of the unknown linear part GðsÞ using the backlash inverse model is represented by
( w# c ¼
1 if z#ðtÞ ¼ vðtÞ=m# þ c#r ; 0 otherwise 1
if z#ðtÞ ¼ vðtÞ=m# þ c#c ;
0 otherwise:
ð6Þ
ð7aÞ
ð7bÞ
The backlash model in Eq. (4) can be rewritten as T vðtÞ ¼ y# jðtÞ;
ð8Þ
where dc T ; dr m# mc y# ðtÞ ¼ ½mc jðtÞ ¼ w# r ðtÞ
z#ðtÞ w# c ðtÞ
ð9Þ T
:
ð10Þ
For the tracking error eðtÞ ¼ z#ðtÞ zm ðtÞ; estimation error eðtÞ can be defined as eðtÞ ¼ eðtÞ þ y# ðtÞjðt 1Þ y# ðt 1Þeðt 1Þ: T
T
ð11Þ
By using Eq. (6) the update law for y# ðtÞ based on a gradient-type algorithm is given by Gjðt 1ÞeðtÞ y# ðt þ 1Þ ¼ y# ðtÞ ; ð12Þ I þ jT ðt 1Þjðt 1Þ where G is the adaptation gain with proper dimension. 3.3.2. Actuator dynamic characteristic estimation It is important to have detailed information on the dynamic characteristics of the actuator since it influences the control loop transfer function. By assuming that the actuator is being compensated and controlled properly by the actuator position controller and the adaptive nonlinearity-inverse model, and is only operating within the attainable range, the closed-loop relation between demand position (ud ) and actual position (ua ) can be represented by a first order model: Ua ðsÞ Ka ¼ : ð13Þ Ga ðsÞ ¼ Ud ðsÞ 1 þ Ta s The parameters of Eq. (13) are estimated using a recursive least-squares algorithm. 3.4. Actuator condition data The actuator condition data is defined to make the PID controller retuning strategy more efficient. In addition to the actuator actual position, the actuator condition data set involves: *
Fig. 5. Backlash and backlash-inverse models.
Estimates of the actuator input–output relationship (Eq. (13)): These estimates can be directly used in
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*
*
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calculating a new transfer function for the control system. The resulting transfer function is applied to the redesign of a new controller to counteract the degraded actuator performance. Estimates of noninvertible nonlinearities: Since noninvertible nonlinearities, such as saturation limits, cannot be self-compensated within the actuator, they must be reported to either the loop controller or the system operator to be dealt with. Actuation status: The SEVA interface (Yang & Clarke, 1999) is employed to describe the actuation status.
3.5. Fieldbus interface More than 50 different kinds of fieldbuses have appeared during the last decade (Thomesse, 1999). In this paper, a CAN bus is employed. CAN is a real-time communication bus developed by Bosch for use in automotive systems. A key advantage of using CAN is that a variety of actuators and sensors fitted with CAN interface are available on the market. Recent research highlighted that the CAN bus is also applicable to aeroengine control systems (Thompson et al., 1999).
4. On-line PID controller retuning As described in Sections 2 and 3, smart actuators are capable of providing a set of condition data, as well as self-diagnosis and compensation. As shown in Fig. 6, using the actuator condition data set, more efficient online retuning strategies can be obtained for a PID controller which can accommodate undesirable actuator characteristics. The retuning procedure based on the actuator condition data are depicted in Fig. 7. If retuning of the PID controller is needed due to changes in the plant and/or the actuator characteristics, then the retuning algorithm will assess the actuator condition data in order to locate the source of degradation before initiating the retuning procedure. The control loop degradation may be caused by change in either: *
plant (load conditions or disturbances),
Fig. 6. PID controller retuning based on a smart actuator.
Fig. 7. Actuator condition data-based monitoring and PID-controller retuning procedure.
* *
actuator, or both actuator and plant.
If the control performance has been degraded due to changes in load condition, then the process controller can easily determine that it is not caused by the actuator, as the condition data still reports normal operation of the actuator. In fact, research on automatic tuning has mostly focused on this case. Thus a conventional automatic tuning technique can be used to obtain a new set of parameters. When both the plant and actuator are changed, more careful consideration is needed even if a smart actuator is employed, unless there is a measure to identify if the plant is secure or not. As discussed before, if a ‘dumb’ actuator is used and its characteristics become nonlinear (even though they are compensable), then it may not be possible to obtain suitable parameters using a conventional tuning method. On the other hand, if the undesirable properties are compensated within the actuator by smart technology, so that the resulting actuator can still provide linear characteristics, then conventional tuning methods may still supply acceptable parameters. By developing a routine utilizing the
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actuator condition data to diagnose precisely the plant status, it may be possible to achieve a much better retuning algorithm. In the case of degradation of the actuator performance, if the process involves ‘dumb’ actuators, conventional automatic tuning methods may not provide appropriate control parameters. In contrast, the use of a smart actuator gives an increased capability to deal with the control system degradation, including the retuning of control parameters, without interruption of the closed-loop operation. 4.1. On-line retuning using a smart actuator as the actuator characteristics change In a control system containing a smart actuator, the PID controller retuning problem caused by undesirable actuator characteristics can be classified into three categories: *
*
*
Undesirable actuator characteristics uncompensated: In the case of uncompensable actuator faults, such as stuck, no retuning or reconfiguration is possible unless the system contains certain degree of redundancy. The actuator should warn the system operator so that appropriate maintenance can take place. Undesirable actuator characteristics compensated and the original performance attained: No controller retuning is needed in this case. For instance, actuator backlash does not initiate the retuning procedure, since it can be compensated within the smart actuator. Undesirable actuator characteristics compensated but performance degraded: In this case, the actuator no longer provides its original performance although it is still linear, and this will deteriorate the control loop performance. Examples in this category are the change in actuator time constant or noninvertable nonlinearity (e.g., saturation). A proper retuning based on the actuator status and parameters needs to be performed to provide the control system with a graceful degradation of performance.
¼
Ka 1 þ sTa
Kp ð1 þ sTz;1 Þ?ð1 þ sTz;n1 Þ est : ð1 þ sTp;1 Þð1 þ sTp;2 Þ?ð1 þ sTp;n Þ
ð14Þ
Since many of the design methods for a PID controller are based on simple models, it is often convenient to approximate the complex system into a lower order model. A first order approximation for Eq. (14) can be given by K ; ð15Þ Go ðsÞE 1 þ sT where T ¼ Tp;1 þ ? þ Tp;n Tz;1 ? Tz;n1 t > 0 and it is assumed that t5T (Astrom & Hagglund, 1995). With the simplified model, the closed-loop transfer function obtained with error feedback is Gc ðsÞ ¼
Go ðsÞGc ðsÞ ; 1 þ Go ðsÞGc ðsÞ
ð16Þ
where Gc is transfer function of a PID controller. If the closed-loop function Gc is specified, Gp is known, and Ga is estimated within the smart actuator, then it is possible to calculate a set of PID parameters for Gc : By applying a well-established standard pole-placement technique to the process of Eq. (16), a PID controller Gc that gives the desired closed-loop characteristics can be obtained.
5. Experiments on a distributed architecture demonstrator In order to experimentally validate the schemes for smart actuator and PID controller retuning, a distributed architecture demonstrator was used as shown in Fig. 8. The demonstrator consists of a dual-channel CAN bus network, an actuator rig, and a set of PCs on which various simulation tasks can be implemented. The demonstrator is capable of fault injections including adjustable actuator hardware conditions, such as
If controller retuning is needed due to changes in actuator properties, then the retuning algorithm will assess the actuator condition data to obtain the new actuator parameters before retuning the process controller. An on-line retuning method for a PID controller coping with the degraded actuator performance, as highlighted in the third case, is as below. Let Ga and Gp be the transfer functions of the actuator and the nth order plant, then the open-loop process can be represented by Go ðsÞ ¼ Ga ðsÞGp ðsÞ
Fig. 8. Picture of the CAN-based distributed architecture demonstrator.
D. Lee et al. / Control Engineering Practice 9 (2001) 1235–1244
operating range limits, load conditions, motor stepping rate, and backlash width. For more details on the demonstrator, see (Thompson et al., 1999). 5.1. Experimental set-up In this paper, two cases are considered as below: *
*
Actuator output backlash compensation using a smart actuator add-on intelligence. Retuning of PI control parameters to accommodate degraded actuator performance.
The former case is to validate the capability of local compensation that retains the normal actuator characteristics, and keeps the process controller operating without retuning. In the latter case, to investigate the proposed retuning strategy, increased actuator time constant is introduced, which results in the degradation of actuation performance. Fig. 9 describes the demonstrator set-up for these experiments. The simulation tasks are partitioned into five nodes: the PI controller, the plant, the sensor behaviour, and the actuator rig with the add-on intelligence. The PI controller node performs the closed-loop feedback control, and does online retuning as required. The output from the controller is the actuator position demand, which is passed to the actuator add-on intelligence node. The LVDT signal in the actuator rig, which in this experiment has a noise amplitude of 2.7%, is passed through a first-order low-
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pass filter before it is fed into the add-on intelligence. The sampling frequency of the control loop is chosen as 5 Hz. The plant node and the smart actuator run at 50 Hz. All the nodes in the demonstrator have built-in local clocks, which are synchronised based on the time references generated by the PI controller node. The CAN bus data transmission speed is chosen to be 1 Mbit/s. 5.2. Actuator backlash compensation results The actuator rig has an output backlash of width 4.5%, which is unknown. However, it is assumed that the backlash slope is known as m ¼ 1; and the left and right boundaries of the backlash width have the same magnitude, that is, c ¼ cr ¼ cc ¼ 2:25%: The backlash width is also assumed to be constant over the operating range. These assumptions are made based on the fact that not only the actuator used has a unity steady state gain between its demand and actual position, but also the output backlash in this experiment is caused by the mechanical clearance between the actuator shaft and the LVDT. The adaptive output backlash estimation algorithm described in Sections 3 is applied to estimation of the backlash width and adaption of the inverse-model. Fig. 10a indicates that the estimates of output backlash width c#ðtÞ converge to the true value. In Fig. 10b, the tracking errors for demand position ud (t)¼ sin(0:126t) are compared. The compensated actuator output tracks
Fig. 9. Experimental set-up.
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Fig. 10. Results for compensation of the actuator output backlash: (a) estimates of backlash width (true value c ¼ cr ¼ cc ¼ 2:25%) and (b) tracking errors for ud ðtÞ ¼ sinð0:126tÞ:
the demand position very closely. Fig. 11a shows the actuator characteristics without compensation, which are thus seen to follow a different path in the forward and backward directions. In Fig. 11b, the compensated actuator input-output relationship shows nearly unity gain. In this case, thus, controller retuning has not taken place. A difficulty with the adaptive estimation method in Tao and Kokotovic (1996) is its sensitivity to noise. The variations in the LVDT output signal due to noise introduced problems in identifying the correct direction, and this has been avoided applying a low pass filter along with a deadband (Shinskey, 1996). Since the stepper-motor-based actuator used in the experiments has a slow dynamic characteristic, the effects of phase lag caused by the low pass filter were not significant. However, this is generally not the case in many industrial actuators. Therefore, for further applications it will be essential to improve the backlash estimation algorithm so as to achieve robustness against the measurement noise. 5.3. PI controller retuning results As an illustrative example for the proposed retuning strategy a PI controller is used:
1 Gc ðsÞ ¼ Kp 1 þ : ð17Þ sTi The plant model is assumed to be a first order pure time delay model: 20 0:1s e : ð18Þ Gp ðsÞ ¼ 1 þ 5s By applying a standard pole-placement design technique (see for example, Astrom & Hagglund, 1995), PI parameters for Eq. (17) can be given by Kp ¼ ð2zon T 1Þ=K;
ð19Þ
Ti ¼ ð2zon T 1Þ=o2n T;
ð20Þ
where z and on are relative damping and frequency, and K and T are gain and time constant of the approximated open-loop process. Parameters for the PI controller are initialized with Kp ¼ 0:023 and Ti ¼ 3:77:
Fig. 11. Static characteristics of the actuator with output backlash: (a) without; and (b) with compensation.
5.3.1. Abrupt change of the actuator time constant At t=100 s, the time constant of the actuator is changed from 0.5 to 1.0 s by decreasing the motor stepping rate. Such an abrupt change can be caused by faults. Plant and actuator outputs without controller retuning are illustrated in Fig. 12. An excessive overshoot appears due to actuator velocity saturation. In Fig. 13, better results are obtained by applying the smart actuator and the PI retuning approach proposed in this paper. The smart actuator provides the PI controller retuning algorithm with the time constant as estimated
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in Fig. 13a, with which a new set of control parameters is calculated using Eqs. (19) and (20). Figs. 13b and c show that the retuned PI controller retains control performance although settling time is seen to increase. It is seen that estimates of the actuator time constant converge slowly to the true value. The capability of selfdiagnosis, including estimation of the actuator time constant, can be improved by employing model-based fault diagnosis techniques based on extra information which is available inside the actuator.
Fig. 12. Plant and actuator outputs without PI controller retuning as actuator time constant changes from 0.5 to 1.0 s at t ¼ 100 s.
5.3.2. Drift of the actuator time constant In addition to the abrupt large change of the actuator time constant, drifts are also likely to happen since control actuators undergo wear and aging. In this experiment, the actuator time constant has been gradually increased by 20% (i.e., 0.5–0.6 s) for 3000 s. Table 1 and Fig. 14 indicate that, using the retuning strategy based on the smart actuator results in the integrated absolute error (IAE) being decreased by 3.4%, as well as in significant reduction in the overshoot.
Table 1 Setpoint responses with actuator time constant drifts of 20% (0.5–0.6 s)
Fig. 13. Results of PI controller with retuning as actuator time constant changes from 0.5 to 1.0 s at t ¼ 100 s: (a) estimates of actuator time constant; (b) plant output; and (c) actuator output.
Trial
IAE
Maximum overshoot
Maximum settling time
With retuning Without retuning
1790.7 1853.9
1.38% 5.39%
21.5 s 35.8 s
Fig. 14. Results of PI controller retuning as actuator time constant drifts from 0.5 to 0.6 s.
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6. Conclusions In this paper, it is highlighted that, by adopting a smart actuator technology, standard PID control techniques can be used successfully in the presence of undesirable actuator characteristics. Main contributions from this work are summarized as follows. Firstly, a smart actuator scheme that can maintain the control performance in the presence of undesirable actuator characteristics has been identified. The proposed smart actuator scheme focuses on the adaptive diagnosis and compensation of the actuator static and dynamic characteristics, as well as bi-directional communication to the process controller. The scheme was implemented using a PC-based add-on intelligence and a low-cost actuator rig. It has been highlighted that the smart actuator could be applied to on-line PID controller retuning using a standard pole-placement technique to counteract degraded actuator performance. The advantages of using the proposed smart actuator and on-line retuning approaches were examined on a distributed architecture demonstrator. The experimental results indicate that, the actuator output backlash and the degraded actuator performance can be compensated successfully by combining a relatively simple retuning strategy based on a standard technique with the proposed smart actuator scheme. The PI controller retuning was performed without either an excitation signal or interruption of the system operation. Several subjects for further work are identified as follows: *
*
*
Retuning technique for a large distributed control system: A different approach will be required for applying the smart actuator based tuning technique to a large distributed control system, such as a chemical process having multiple control loops and actuators. Combining anti-windup schemes: The information on the actuator limits of achievable velocity and position can be used for integrator anti-windup (e.g. a PI controller with actuator feedback, Alsop, 1995). Combining the proposed tuning approach with an anti-windup technique may improve the control performance in the presence of uncompensable actuator characteristics. Reconfigurable control system based on extra information provided by the smart actuator: The proposed smart actuator scheme can be used for reconfigurable control systems so as to tolerate actuator faults. For example, a reconfiguration strategy based on constrained model-based predictive control (Maciejowski, 1997) indicates that knowledge of the
actuator rate and/or range limits may be exploited in reconfiguring the control laws.
Acknowledgements The authors would like to acknowledge the financial support of Rolls–Royce plc.
References Alsop, P. (1995). The self-validating actuator. Ph.D. thesis, Oxford University, UK. Astrom, K. J., & Hagglund, T. (1995). PID controllers: Theory, design and tuning. USA: Instrument Society of America. Astrom, K.J. (1996). Tuning and adaptation. Proceedings of the 13th IFAC world congress. San Francisco, USA (pp. 1–18). Bosch (1991). CAN specification version 2.0. Robert Bosch GmbH, Postbach 50, D-7000 Stuttgart 1. Clarke, D. W. (1995). Sensor, actuator and loop validation. IEEE Control Systems Magazine, 15(4), 39–45. Harrold, D. (1999). Select and size control valves properly to save money. Control Engineering, 55–60. Isermann, R., & Raab, U. (1993). Intelligent actuators-ways to autonomous actuating systems. Automatica, 29(5), 1315–1331. Liu, G. P., & Daley, S. (1999). Optimal-tuning PID controller design in the frequency domain with application to a rotary hydraulic system. Control Engineering Practice, 7, 821–830. Maciejowski, J.M. (1997). Reconfigurable control using constrained optimization. Proceedings of the European control conference, Brussels, Belgium (pp.107–130). Masten, M.K. (1997). Electronics: The intelligence in intelligent control. Proceedings of the IFAC intelligent components and instruments for control application, Annecy, France (pp.1–11). McCormack, A. S., & Godfrey, K. R. (1998). Rule-based autotuning based on frequency domain identification. IEEE Transactions on Control Systems Technology, 6(1), 43–61. Peng, Y., Vrancic, D., & Hanus, R. (1996). Anti-windup, bumpless, and conditioned transfer techniques for PID controllers. IEEE Control Systems Magazine, 16(4), 48–57. Shinskey, F. G. (1996). Process control systems: Application, design, and tuning (4th Ed.). New York: McGraw-Hill. Sun, L., Liu, W., & Sano, A. (1999). Identification of a dynamical system with input nonlinearity. IEE Proceedings, PartD, 146(1), 41–51. Tao, G., & Kokotovic, P. V. (1996). Adaptive control of systems with actuator and sensor nonlinearities. USA: Wiley. Thompson, H. A., Benitez-Perez, H., Lee, D., Ramos-Hernandez, D. N., Fleming, P. J., & Legge, C. G. (1999). A CANbus-based safetycritical distributed aeroengine control systems architecture demonstrator. Microprocessors and Microsystems, 23, 345–355. Thomesse, J. P. (1999). Fieldbuses and interoperability. Control Engineering Practice, 7, 81–94. Yang, J. C., & Clarke, D. W. (1999). The self-validating actuator. Control Engineering Practice, 7, 249–260. Xie, C., Pu, J. S., & Moore, P. R. (1998). A case study on the development of intelligent actuator components for distributed control systems using LONWORK neuron chips. Mechatronics, 8, 103–119.
PID control for a distributed system with a smart actuator Dongik Lee*, Jeff Allan, Haydn A. Thompson, Stuart Bennett Rolls-Royce University Technology Centre in Control and Systems Engineering, Department of Automatic Control and Systems Engineering, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK Received 6 April 2001; accepted 6 April 2001
Abstract The emergence of distributed architectures based on smart components and fieldbus networks is promoting changes in proportional-integral-derivative (PID) controller design issues. This paper explores how PID control can benefit from smart actuator and fieldbus technologies. Firstly, this paper discusses a smart actuator scheme to improve the efficiency of PID controller retuning, as well as an implementation using a low-cost stepper-motor. Then, the smart actuator is applied to on-line adaptation of PID parameters using a standard pole-placement design method. Finally, experimental validation of the proposed approach is conducted using a controller area network (CAN) bus-based distributed architecture demonstrator. r 2001 Elsevier Science Ltd. All rights reserved. Keywords: PID control; Actuators; Nonlinearity; Fieldbus; Distributed control
1. Introduction Distributed architectures based on smart component and fieldbus technologies are becoming more common in modern control systems. Not only does a distributed architecture offer reduced wiring and simplified maintenance, it also provides the opportunity to implement more sophisticated control laws. Consequently, the emergence of distributed control systems leads to changes in process controller design issues (Clarke, 1995). From the viewpoint of PID controller design, one of the issues that is most significantly affected is antiwindup. Anti-windup algorithms (for example, Alsop, 1995; Peng, Vrancic, & Hanus, 1996) can be designed more efficiently if the actuator position and/or rate saturation limits are known. By employing a ‘smart’ actuator that can provide the process controller with this information through a fieldbus network it is possible to adapt the anti-windup parameters. For example, in Alsop (1995), a PI configuration with actuator feedback using the information from the smart
*Corresponding author. Tel.: +44-114-222-5236; fax: +44-114-2731729. E-mail address: cop97dl@sheffield.ac.uk (D. Lee).
actuator has been used to resolve integrator windup caused by the actuator saturation. Another key area where benefit may be derived is in automatic tuning, on which this paper focuses. The automatic tuning of PID control parameters has attracted significant interest (Astrom & Hagglund, 1995; Astrom, 1996; McCormack & Godfrey, 1998; Liu & Daley, 1999). Unfortunately, most of the automatic tuning techniques suffer from two drawbacks: (a) interruption of the normal closed-loop operation; and (b) poor results caused by undesirable actuator characteristics. The former is introduced because many automatic tuning techniques rely on a pre-defined test, such as relay test, for which disconnection of the closedloop control is needed. Such interruption is often undesirable. For example, an on-line approach without the closed-loop interruption is usually required when the automatic tuning technique is applied to adaptation of the controller to cope with time-varying disturbances. The latter drawback is introduced by the assumption that an actuator is an ideal element having unity gain, instantaneous response and no steady-state offset. However, actuators in reality are nonlinear, slow, and limited in their operation. In practice, actuator faults are the largest source of control system degradation. For instance, an analysis in a pulp and paper mill revealed that 70% of the actuators had significant operating
0967-0661/01/$ - see front matter r 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 7 - 0 6 6 1 ( 0 1 ) 0 0 0 6 9 - 7
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problems (Harrold, 1999). Undesirable actuator characteristics result in many problems, such as large overshoot for set-point changes, limit cycles, and stickslip motions. If automatic tuning techniques are to be effective for industrial processes, then, as Astrom and Hagglund (1995) have emphasized, the actuators must be checked carefully before tuning the controller. As actuator properties change with time it is necessary to monitor on-line the actuator characteristic during normal operation. Unfortunately, this is not easy with a conventional ‘dumb’ actuator. However, by employing a distributed architecture based on a smart actuator and a fieldbus network, on-line monitoring can be obtained. A ‘smart’ actuator (or ‘intelligent’ actuator) has a builtin microprocessor and a standard fieldbus interface, so that it has the capability for local computation and thus intelligent functionality with bi-directional communications to the ‘higher-level’ process controller (Clarke, 1995). This paper aims to show how standard PID control techniques, especially with regard to on-line retuning, can benefit from smart actuator and fieldbus technologies. A smart actuator scheme suitable for PID controller retuning is identified and implemented. In order to make the PID controller retuning more efficient, the proposed smart actuator scheme focuses on developing the capability for self-diagnosis, selfcompensation, and bi-directional communications to the process controller. Then, the smart actuator is applied to on-line retuning of PID parameters based on a standard pole-placement design method. Finally, experimental validation of the proposed approach is conducted using a distributed architecture demonstrator which consists of a set of PCs, a stepper-motor-based smart actuator, and a CAN (Bosch, 1991) bus network.
2. The smart actuator concept Before developing a PID controller retuning strategy, it is necessary to identify the content of intelligent functionality which can be embedded in a smart actuator. Several researchers have suggested schemes for smart actuators (Isermann & Raab, 1993; Xie, Pu, & Moore, 1998; Yang & Clarke, 1999), which provide decision on the actuator health status and information on the changes of physical parameters. However, this information is not of direct use in PID controller retuning. Controller retuning or reconfiguration requires static and dynamic actuator characteristics, such as saturation limits and time constant, which have a direct influence on the control system performance. The proposed smart actuator scheme focuses on selfdiagnosis and self-compensation of the actuator characteristics, and on a digital communication interface for exchange of extra information with the process con-
troller. Key features of the suggested smart actuator scheme are given below: *
*
*
*
Self-compensation: Actuators may have undesirable static and dynamic characteristics introducing many problems for the PID control loop. For instance, limit cycles caused by actuator backlash cannot be removed by adjusting PID parameters (Astrom & Hagglund, 1995). Therefore, a nonlinearity compensation algorithm using an inverse model and a simple position controller are implemented in order to maintain the actuator characteristics to be as linear as possible within the attainable actuation range. Self-diagnosis: An adaptive nonlinearity estimation algorithm (Tao & Kokotovic, 1996) is employed since actuator nonlinearities vary with time. In addition to the nonlinearity estimation, on-line estimation of the actuator input-output dynamic characteristic is also implemented. Condition data: A set of condition data describing the actuator characteristics is defined, with which the PID controller retuning will be performed. Fieldbus interface: For data exchanges between the smart actuator and the process controller, a CAN bus interface is employed.
3. Smart actuator implementation based on a low-cost stepper-motor 3.1. System overview A smart actuator can be implemented with either integrated intelligence or add-on intelligence (Masten, 1997). In the integrated intelligence type implementation, actuator intelligence and actuation are combined into a single material. A piezoceramic actuator is a typical example of this type. However, the integrated intelligence is still not commonly used due to technological difficulties. On the other hand, in the add-on intelligence type of implementation, a smart unit based on a microprocessor or DSP, is added to a ‘dumb’ actuator. A benefit of the add-on intelligence approach is that a low-cost device can be used instead of a high precision manufactured device. Enhanced capabilities are obtained with embedded microprocessor power. As shown in Fig. 1, for experimental purposes, the smart actuator concept described in Section 2 is implemented using an add-on intelligence, CAN bus, and an actuator rig. A PC provides local computation to achieve the add-on intelligence described in Section 2. The actuator rig consists of a 4-phase hybrid steppermotor and a linear variable differential transformer (LVDT). The rotary torque of the stepper-motor is transferred through a gear train to the leadscrew which generates back-and-forth straight line motion. The
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stepper-motor runs with constant stepping rate. The LVDT measures the position of the leadscrew, which is fed back to the add-on intelligence through the CAN bus. To generate an output backlash a clearance between the LVDT and the leadscrew is inserted. A simplified model of the smart actuator implementation with output backlash is depicted in Fig. 2. Details on the implementation are given below. 3.2. Self-compensation 3.2.1. Actuator nonlinearity compensation An inverse model-based approach is a powerful tool to compensate for process input or output nonlinearity (Tao & Kokotovic, 1996). For an input nonlinearity, N; the output of its inverse model N# * is given by vðtÞ ¼ N# * ðud ðtÞÞ;
ð1Þ
where ud is the actuator demand position and the argument t denotes discrete time. If the inverse model estimated is exact, then the actuator output ðua Þ follows the demand, and Eq. (2) can be achieved: ua ðtÞ ¼ NðN# * ðud ðtÞÞÞ ¼ ud ðtÞ:
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The output nonlinearity shown in Fig. 3 is difficult to deal with because the output of the unknown linear part GðsÞ is not completely observable from ua ðtÞ; which results in a bounded error even if the parameter estimate is equal to the true value. For achieving ua ðtÞ ¼ ud ðtÞ; a more complicated control algorithm is needed. In this work, the scheme shown in Fig. 4 is adopted. If the tracking error eðtÞ ¼ zm ðtÞ z#ðtÞ goes to zero, then the actuator output ua ðtÞ converges to the demand ud ðtÞ with a bounded error in finite time steps.
3.2.2. Actuator position control A three-state position controller, along with pulsewidth modulation (PWM), is exploited for the actuator position control since the stepper-motor is driven at a constant stepping rate. A deadband (d) between two active states is added so as to prevent frequent changes of the motor direction due to measurement noise. The width of the deadband is chosen as the amount of measurement noise. Since the controller has only proportional action, actual position of the actuator will come to rest somewhere around the active zone (i.e.,
ð2Þ
Fig. 3. Output nonlinearity (N) compensation using its inverse model (N# * ).
Fig. 1. Schematic of a smart actuator implementation using actuator rig and add-on intelligence. Fig. 4. Block diagram of the output backlash compensation scheme.
Fig. 2. Simplified model of the smart actuator implementation with an output backlash.
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around 7d), so that offset at the actual position will appear. This offset is reduced by employing a feedforward compensation wðtÞ as 8 if zm ðtÞ > zm ðt 1Þ; >
3.3.1. On-line output backlash estimation As indicated in Section 3.1, the ‘dumb’ actuator rig is configured with output backlash. To identify such nonlinearities, an off-line estimation approach, which collects steady-state data through testing over the full range, is usually used (e.g., Sun, Liu, & Sano, 1999). However, the off-line estimation methods are not very realistic because nonlinearities typically change with time. In Alsop (1995) a recursive least squares (RLS) algorithm was used to estimate actuator nonlinearities. In particular, the nonlinearity model is represented with a set of straight line functions, so that the parameters of each line are estimated by applying linear least-squares algorithm based on only steady-state data. However, it may be difficult to obtain the steady-state data when the actuator demand values vary continuously (e.g., ramp input), so that convergence of the estimates can be delayed. In this paper, an adaptive estimation method (Tao & Kokotovic, 1996) based on transient data is applied to on-line estimation of the output backlash. A discrete-time model for output backlash is given by 8 > < mðzðtÞ cc Þ if zðtÞpzc ; vðtÞ ¼ NðzðtÞÞ ¼ mðzðtÞ cr Þ if zðtÞXzr ; ð4Þ > : vðt 1Þ if zc ozðtÞozr ;
ð5aÞ
vðt 1Þ þ cr : ð5bÞ m The meaning of m; cc and cr is depicted in Figs. 4 and 5 where m is the backlash slope and cr > 0 is the right crossing, whilst cc o0, is the left crossing. The backlash width is given by (cr cc ). For this backlash model,
zr ¼
z#ðtÞ ¼
w# r w# c r Þ þ c ðvðtÞ þ mc c c Þ; ðvðtÞ þ mc m# m#
where ( w# r ¼
3.3. Self-diagnosis
where vðt 1Þ þ cc ; zc ¼ m
estimated output of the unknown linear part GðsÞ using the backlash inverse model is represented by
( w# c ¼
1 if z#ðtÞ ¼ vðtÞ=m# þ c#r ; 0 otherwise 1
if z#ðtÞ ¼ vðtÞ=m# þ c#c ;
0 otherwise:
ð6Þ
ð7aÞ
ð7bÞ
The backlash model in Eq. (4) can be rewritten as T vðtÞ ¼ y# jðtÞ;
ð8Þ
where dc T ; dr m# mc y# ðtÞ ¼ ½mc jðtÞ ¼ w# r ðtÞ
z#ðtÞ w# c ðtÞ
ð9Þ T
:
ð10Þ
For the tracking error eðtÞ ¼ z#ðtÞ zm ðtÞ; estimation error eðtÞ can be defined as eðtÞ ¼ eðtÞ þ y# ðtÞjðt 1Þ y# ðt 1Þeðt 1Þ: T
T
ð11Þ
By using Eq. (6) the update law for y# ðtÞ based on a gradient-type algorithm is given by Gjðt 1ÞeðtÞ y# ðt þ 1Þ ¼ y# ðtÞ ; ð12Þ I þ jT ðt 1Þjðt 1Þ where G is the adaptation gain with proper dimension. 3.3.2. Actuator dynamic characteristic estimation It is important to have detailed information on the dynamic characteristics of the actuator since it influences the control loop transfer function. By assuming that the actuator is being compensated and controlled properly by the actuator position controller and the adaptive nonlinearity-inverse model, and is only operating within the attainable range, the closed-loop relation between demand position (ud ) and actual position (ua ) can be represented by a first order model: Ua ðsÞ Ka ¼ : ð13Þ Ga ðsÞ ¼ Ud ðsÞ 1 þ Ta s The parameters of Eq. (13) are estimated using a recursive least-squares algorithm. 3.4. Actuator condition data The actuator condition data is defined to make the PID controller retuning strategy more efficient. In addition to the actuator actual position, the actuator condition data set involves: *
Fig. 5. Backlash and backlash-inverse models.
Estimates of the actuator input–output relationship (Eq. (13)): These estimates can be directly used in
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*
*
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calculating a new transfer function for the control system. The resulting transfer function is applied to the redesign of a new controller to counteract the degraded actuator performance. Estimates of noninvertible nonlinearities: Since noninvertible nonlinearities, such as saturation limits, cannot be self-compensated within the actuator, they must be reported to either the loop controller or the system operator to be dealt with. Actuation status: The SEVA interface (Yang & Clarke, 1999) is employed to describe the actuation status.
3.5. Fieldbus interface More than 50 different kinds of fieldbuses have appeared during the last decade (Thomesse, 1999). In this paper, a CAN bus is employed. CAN is a real-time communication bus developed by Bosch for use in automotive systems. A key advantage of using CAN is that a variety of actuators and sensors fitted with CAN interface are available on the market. Recent research highlighted that the CAN bus is also applicable to aeroengine control systems (Thompson et al., 1999).
4. On-line PID controller retuning As described in Sections 2 and 3, smart actuators are capable of providing a set of condition data, as well as self-diagnosis and compensation. As shown in Fig. 6, using the actuator condition data set, more efficient online retuning strategies can be obtained for a PID controller which can accommodate undesirable actuator characteristics. The retuning procedure based on the actuator condition data are depicted in Fig. 7. If retuning of the PID controller is needed due to changes in the plant and/or the actuator characteristics, then the retuning algorithm will assess the actuator condition data in order to locate the source of degradation before initiating the retuning procedure. The control loop degradation may be caused by change in either: *
plant (load conditions or disturbances),
Fig. 6. PID controller retuning based on a smart actuator.
Fig. 7. Actuator condition data-based monitoring and PID-controller retuning procedure.
* *
actuator, or both actuator and plant.
If the control performance has been degraded due to changes in load condition, then the process controller can easily determine that it is not caused by the actuator, as the condition data still reports normal operation of the actuator. In fact, research on automatic tuning has mostly focused on this case. Thus a conventional automatic tuning technique can be used to obtain a new set of parameters. When both the plant and actuator are changed, more careful consideration is needed even if a smart actuator is employed, unless there is a measure to identify if the plant is secure or not. As discussed before, if a ‘dumb’ actuator is used and its characteristics become nonlinear (even though they are compensable), then it may not be possible to obtain suitable parameters using a conventional tuning method. On the other hand, if the undesirable properties are compensated within the actuator by smart technology, so that the resulting actuator can still provide linear characteristics, then conventional tuning methods may still supply acceptable parameters. By developing a routine utilizing the
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actuator condition data to diagnose precisely the plant status, it may be possible to achieve a much better retuning algorithm. In the case of degradation of the actuator performance, if the process involves ‘dumb’ actuators, conventional automatic tuning methods may not provide appropriate control parameters. In contrast, the use of a smart actuator gives an increased capability to deal with the control system degradation, including the retuning of control parameters, without interruption of the closed-loop operation. 4.1. On-line retuning using a smart actuator as the actuator characteristics change In a control system containing a smart actuator, the PID controller retuning problem caused by undesirable actuator characteristics can be classified into three categories: *
*
*
Undesirable actuator characteristics uncompensated: In the case of uncompensable actuator faults, such as stuck, no retuning or reconfiguration is possible unless the system contains certain degree of redundancy. The actuator should warn the system operator so that appropriate maintenance can take place. Undesirable actuator characteristics compensated and the original performance attained: No controller retuning is needed in this case. For instance, actuator backlash does not initiate the retuning procedure, since it can be compensated within the smart actuator. Undesirable actuator characteristics compensated but performance degraded: In this case, the actuator no longer provides its original performance although it is still linear, and this will deteriorate the control loop performance. Examples in this category are the change in actuator time constant or noninvertable nonlinearity (e.g., saturation). A proper retuning based on the actuator status and parameters needs to be performed to provide the control system with a graceful degradation of performance.
¼
Ka 1 þ sTa
Kp ð1 þ sTz;1 Þ?ð1 þ sTz;n1 Þ est : ð1 þ sTp;1 Þð1 þ sTp;2 Þ?ð1 þ sTp;n Þ
ð14Þ
Since many of the design methods for a PID controller are based on simple models, it is often convenient to approximate the complex system into a lower order model. A first order approximation for Eq. (14) can be given by K ; ð15Þ Go ðsÞE 1 þ sT where T ¼ Tp;1 þ ? þ Tp;n Tz;1 ? Tz;n1 t > 0 and it is assumed that t5T (Astrom & Hagglund, 1995). With the simplified model, the closed-loop transfer function obtained with error feedback is Gc ðsÞ ¼
Go ðsÞGc ðsÞ ; 1 þ Go ðsÞGc ðsÞ
ð16Þ
where Gc is transfer function of a PID controller. If the closed-loop function Gc is specified, Gp is known, and Ga is estimated within the smart actuator, then it is possible to calculate a set of PID parameters for Gc : By applying a well-established standard pole-placement technique to the process of Eq. (16), a PID controller Gc that gives the desired closed-loop characteristics can be obtained.
5. Experiments on a distributed architecture demonstrator In order to experimentally validate the schemes for smart actuator and PID controller retuning, a distributed architecture demonstrator was used as shown in Fig. 8. The demonstrator consists of a dual-channel CAN bus network, an actuator rig, and a set of PCs on which various simulation tasks can be implemented. The demonstrator is capable of fault injections including adjustable actuator hardware conditions, such as
If controller retuning is needed due to changes in actuator properties, then the retuning algorithm will assess the actuator condition data to obtain the new actuator parameters before retuning the process controller. An on-line retuning method for a PID controller coping with the degraded actuator performance, as highlighted in the third case, is as below. Let Ga and Gp be the transfer functions of the actuator and the nth order plant, then the open-loop process can be represented by Go ðsÞ ¼ Ga ðsÞGp ðsÞ
Fig. 8. Picture of the CAN-based distributed architecture demonstrator.
D. Lee et al. / Control Engineering Practice 9 (2001) 1235–1244
operating range limits, load conditions, motor stepping rate, and backlash width. For more details on the demonstrator, see (Thompson et al., 1999). 5.1. Experimental set-up In this paper, two cases are considered as below: *
*
Actuator output backlash compensation using a smart actuator add-on intelligence. Retuning of PI control parameters to accommodate degraded actuator performance.
The former case is to validate the capability of local compensation that retains the normal actuator characteristics, and keeps the process controller operating without retuning. In the latter case, to investigate the proposed retuning strategy, increased actuator time constant is introduced, which results in the degradation of actuation performance. Fig. 9 describes the demonstrator set-up for these experiments. The simulation tasks are partitioned into five nodes: the PI controller, the plant, the sensor behaviour, and the actuator rig with the add-on intelligence. The PI controller node performs the closed-loop feedback control, and does online retuning as required. The output from the controller is the actuator position demand, which is passed to the actuator add-on intelligence node. The LVDT signal in the actuator rig, which in this experiment has a noise amplitude of 2.7%, is passed through a first-order low-
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pass filter before it is fed into the add-on intelligence. The sampling frequency of the control loop is chosen as 5 Hz. The plant node and the smart actuator run at 50 Hz. All the nodes in the demonstrator have built-in local clocks, which are synchronised based on the time references generated by the PI controller node. The CAN bus data transmission speed is chosen to be 1 Mbit/s. 5.2. Actuator backlash compensation results The actuator rig has an output backlash of width 4.5%, which is unknown. However, it is assumed that the backlash slope is known as m ¼ 1; and the left and right boundaries of the backlash width have the same magnitude, that is, c ¼ cr ¼ cc ¼ 2:25%: The backlash width is also assumed to be constant over the operating range. These assumptions are made based on the fact that not only the actuator used has a unity steady state gain between its demand and actual position, but also the output backlash in this experiment is caused by the mechanical clearance between the actuator shaft and the LVDT. The adaptive output backlash estimation algorithm described in Sections 3 is applied to estimation of the backlash width and adaption of the inverse-model. Fig. 10a indicates that the estimates of output backlash width c#ðtÞ converge to the true value. In Fig. 10b, the tracking errors for demand position ud (t)¼ sin(0:126t) are compared. The compensated actuator output tracks
Fig. 9. Experimental set-up.
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Fig. 10. Results for compensation of the actuator output backlash: (a) estimates of backlash width (true value c ¼ cr ¼ cc ¼ 2:25%) and (b) tracking errors for ud ðtÞ ¼ sinð0:126tÞ:
the demand position very closely. Fig. 11a shows the actuator characteristics without compensation, which are thus seen to follow a different path in the forward and backward directions. In Fig. 11b, the compensated actuator input-output relationship shows nearly unity gain. In this case, thus, controller retuning has not taken place. A difficulty with the adaptive estimation method in Tao and Kokotovic (1996) is its sensitivity to noise. The variations in the LVDT output signal due to noise introduced problems in identifying the correct direction, and this has been avoided applying a low pass filter along with a deadband (Shinskey, 1996). Since the stepper-motor-based actuator used in the experiments has a slow dynamic characteristic, the effects of phase lag caused by the low pass filter were not significant. However, this is generally not the case in many industrial actuators. Therefore, for further applications it will be essential to improve the backlash estimation algorithm so as to achieve robustness against the measurement noise. 5.3. PI controller retuning results As an illustrative example for the proposed retuning strategy a PI controller is used:
1 Gc ðsÞ ¼ Kp 1 þ : ð17Þ sTi The plant model is assumed to be a first order pure time delay model: 20 0:1s e : ð18Þ Gp ðsÞ ¼ 1 þ 5s By applying a standard pole-placement design technique (see for example, Astrom & Hagglund, 1995), PI parameters for Eq. (17) can be given by Kp ¼ ð2zon T 1Þ=K;
ð19Þ
Ti ¼ ð2zon T 1Þ=o2n T;
ð20Þ
where z and on are relative damping and frequency, and K and T are gain and time constant of the approximated open-loop process. Parameters for the PI controller are initialized with Kp ¼ 0:023 and Ti ¼ 3:77:
Fig. 11. Static characteristics of the actuator with output backlash: (a) without; and (b) with compensation.
5.3.1. Abrupt change of the actuator time constant At t=100 s, the time constant of the actuator is changed from 0.5 to 1.0 s by decreasing the motor stepping rate. Such an abrupt change can be caused by faults. Plant and actuator outputs without controller retuning are illustrated in Fig. 12. An excessive overshoot appears due to actuator velocity saturation. In Fig. 13, better results are obtained by applying the smart actuator and the PI retuning approach proposed in this paper. The smart actuator provides the PI controller retuning algorithm with the time constant as estimated
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in Fig. 13a, with which a new set of control parameters is calculated using Eqs. (19) and (20). Figs. 13b and c show that the retuned PI controller retains control performance although settling time is seen to increase. It is seen that estimates of the actuator time constant converge slowly to the true value. The capability of selfdiagnosis, including estimation of the actuator time constant, can be improved by employing model-based fault diagnosis techniques based on extra information which is available inside the actuator.
Fig. 12. Plant and actuator outputs without PI controller retuning as actuator time constant changes from 0.5 to 1.0 s at t ¼ 100 s.
5.3.2. Drift of the actuator time constant In addition to the abrupt large change of the actuator time constant, drifts are also likely to happen since control actuators undergo wear and aging. In this experiment, the actuator time constant has been gradually increased by 20% (i.e., 0.5–0.6 s) for 3000 s. Table 1 and Fig. 14 indicate that, using the retuning strategy based on the smart actuator results in the integrated absolute error (IAE) being decreased by 3.4%, as well as in significant reduction in the overshoot.
Table 1 Setpoint responses with actuator time constant drifts of 20% (0.5–0.6 s)
Fig. 13. Results of PI controller with retuning as actuator time constant changes from 0.5 to 1.0 s at t ¼ 100 s: (a) estimates of actuator time constant; (b) plant output; and (c) actuator output.
Trial
IAE
Maximum overshoot
Maximum settling time
With retuning Without retuning
1790.7 1853.9
1.38% 5.39%
21.5 s 35.8 s
Fig. 14. Results of PI controller retuning as actuator time constant drifts from 0.5 to 0.6 s.
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6. Conclusions In this paper, it is highlighted that, by adopting a smart actuator technology, standard PID control techniques can be used successfully in the presence of undesirable actuator characteristics. Main contributions from this work are summarized as follows. Firstly, a smart actuator scheme that can maintain the control performance in the presence of undesirable actuator characteristics has been identified. The proposed smart actuator scheme focuses on the adaptive diagnosis and compensation of the actuator static and dynamic characteristics, as well as bi-directional communication to the process controller. The scheme was implemented using a PC-based add-on intelligence and a low-cost actuator rig. It has been highlighted that the smart actuator could be applied to on-line PID controller retuning using a standard pole-placement technique to counteract degraded actuator performance. The advantages of using the proposed smart actuator and on-line retuning approaches were examined on a distributed architecture demonstrator. The experimental results indicate that, the actuator output backlash and the degraded actuator performance can be compensated successfully by combining a relatively simple retuning strategy based on a standard technique with the proposed smart actuator scheme. The PI controller retuning was performed without either an excitation signal or interruption of the system operation. Several subjects for further work are identified as follows: *
*
*
Retuning technique for a large distributed control system: A different approach will be required for applying the smart actuator based tuning technique to a large distributed control system, such as a chemical process having multiple control loops and actuators. Combining anti-windup schemes: The information on the actuator limits of achievable velocity and position can be used for integrator anti-windup (e.g. a PI controller with actuator feedback, Alsop, 1995). Combining the proposed tuning approach with an anti-windup technique may improve the control performance in the presence of uncompensable actuator characteristics. Reconfigurable control system based on extra information provided by the smart actuator: The proposed smart actuator scheme can be used for reconfigurable control systems so as to tolerate actuator faults. For example, a reconfiguration strategy based on constrained model-based predictive control (Maciejowski, 1997) indicates that knowledge of the
actuator rate and/or range limits may be exploited in reconfiguring the control laws.
Acknowledgements The authors would like to acknowledge the financial support of Rolls–Royce plc.
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