- Email: [email protected]
NEW LABORATORY COURSE FOR CONTROL EDUCATION
NEW LABORATORY COURSE FOR CONTROL EDUCATION
Jakub Novák, Petr Chalupa, Vladimír Bobál
Department of Process Control Faculty of Applied Informatics, Tomas Bata University in Zlín Nad Stráněmi 4511, 76272 Zlín, Czech Republic Email: [email protected]
Abstract: This paper presents new control laboratory course designed at the Faculty of Applied Informatics for the undergraduate courses in Automatic control. Experience obtained during the building process of Control Laboratory and the organization of student assignments for laboratory course is described. The objectives of the laboratory course are to integrate the fundamental skills from theoretical courses to solve engineering problems in dynamics and control and to encourage the problem-based learning. Copyright 2006 IFAC Keywords: Laboratory education, Control education, Adaptive control, Educational aids, Engineering
1.
INTRODUCTION
This paper describes a new laboratory of Faculty of Applied Informatics and a new course which takes place in this laboratory. The aim of this laboratory and the course is to give students the opportunity to apply the theoretical knowledge they obtained in the courses of Identification, Control Theory and Modern Control Methods. In order to reduce the gap between the theory and practice the simulation based experiments can be used. There is a recent trend to provide virtual control laboratories using WWW and simulation models which is a very cost effective solution. However, nothing can replace the laboratory work. The recent development in hardware and software decreased the cost of computing, so that control hardware and software become affordable for universities.
The laboratory also provide ‘look and feel’ of realworld control situations. The expected results of the new laboratory course, is that students gain the basic practical skills considered essential for control education. 2. MOTIVATION The main motivation for using real plants in the educational process is the clear visibility of the controlled dynamic. Thus experimental work in laboratories is a requisite part of the engineering education. The other subjects, such as Identification or Modern Control, are mainly theoretical and exercises in these subject usually involves only simulation models in MATLAB/Simulink environment and so students have problems with interpretability of simulation examples. The real systems help to increase the transparency of these
solved examples. Students in the course have to face the real problems connected to control design, such as measurement noise, measurement quantization or control signal limitation. Student’s success or failure will be clearly recognizable because of the real system. The other motivation for using real plants is the necessity to complete all the steps of control design, starting from model building, identification and analysis, continuing with controller design and ending with control validation. For this whole process students have to integrate obtained knowledge from a number of prior courses. Control laboratory is also a typical place for problem-based learning and for training communication and cooperation skills, since students work in groups and have to communicate between each other and between the groups. 3.
equipped with two accurate pumps, driven by DC motor. The station’s equipment was supplied by AMIRA, a commercial supplier of test equipment for control education. This lab demonstrates control of the water level in a tank. The objective is to show a number of common control strategies so that insight into tuning of the individual controller parameters can be obtained as well as a demonstration how each affects the controller response.
DESCRIPTION OF THE COURSE AND LABORATORY
The course has been offered during a 14-week semester with 3-hours per week. The laboratory has 11 stations, each equipped with a PC, so that only 2 students can share one experiment. 10 stations are divided into 6 groups, so that one group consists of similar experiments such as three-tank system and four-tank system. During the course students have to complete 6 experiments, each from one group. Multifunctional cards with A/D and D/A converters from Humusoft and Advantech are installed in every PC. For solving the identification and design problems MATLAB/Simulink environment is used. The communication between the analog cards is provided by the Real-Time toolbox, which enables easy creation of Simulink blocks for writing and reading data from input and output channels. The eleven experiments are: - Three-tank system - Four-tank system - Inverted pendulum - Magnetic levitation - Twin rotor MIMO system - MIMO helicopter system - Servomotor system - Analog controller - Flow control system - Coupled drive system
Fig. 1. Three-tank laboratory system 3.2 Inverted pendulum The inverted pendulum is a classic plant designed for teaching advanced control systems theory in laboratory. Model of inverted pendulum from AMIRA Company is represented by a pendulum, connected to a cart which can be moved along a metal guiding bar. The cart is connected to a drive wheel. The wheel is driven by DC motor, which delivers a torque proportional to the acting control voltage. The objective of this plant is the understanding of stabilization of unstable plants. Typical real examples of systems that cannot operate without a controller are planes, missiles, nuclear reactor or all motors when rotation angle is to be controlled. In order of increasing difficulty the objectives we show only part of different control strategies that can be performed. - cart position control - simulating a crane on a construction site - balancing the pendulum in vertical position - swing up and balancing inverted pendulum
3.1 Three-tank system The three tank system belongs to the basic plants usually used in educational process. This apparatus consists of three interconnected tanks. Each tank is equipped with a static pressure sensor, which gives voltage proportional to the level of liquid in the tank. There are six ball valves, which gives many possibilities for configuration or can be used to introduce disturbances or faults. The apparatus is also
Fig. 2. Inverted pendulum model 3.3 Magnetic levitation The Magnetic levitation model consists of a steel ball hanging in the magnetic field of the coil. The
position of the ball is measured with magnetic positron sensor. The current in the coil is amplified and is proportional to the input voltage. Magnetic levitation is a typical example of an unstable nonlinear system with one input and one output. From dynamical point of view the levitation model can be approximated by system of order 3 with astatism of order 2. The plant was provided by HUMUSOFT Company.
consists of two identical motors connected with a clutch, tachogenerator and IRC sensor for angle measurement. The first motor is used as generator of variable load torque or as a disturbance and the second one is used for control. The test equipment was obtained from AMIRA.
Fig. 5. Servomechanism model 3.6 Analog controller
Fig. 3. Magnetic levitation model 3.4 Twin rotor MIMO system The twin rotor MIMO system provides high-order, nonlinear system, where significant coupling between the actions of the rotors can be observed. The angle of attack of the rotors is fixed and aerodynamic forces are controlled by varying the speeds of the motors. High resolution optical encoders provide feedback from vertical and horizontal angular position. Move in either vertical or horizontal angle can be fixed to simplify the control experiment. The goal of experiment is to control both the main and the tail rotor simultaneously.
Analog controller CE120 is a tool for testing P, I, PI and PID controllers. In this experiment, contrary to the rest of course, the controlled plant is realized by PC. In this experiment student’s goal is to control a stable, unstable and integral plants created in Simulink. The main objectives of this experiment are to set up PID controller parameters on the analog controller and to measure the behavior of the system. TQ Education and Training Ltd is a producer of this equipment.
Fig. 6. Analog controller CE120 Other models used in the laboratory course includes the four tank system, MIMO helicopter system from Humusoft, Flow control system from Leybold, where students have the chance to try other environment than Simulink and Coupled drive systems from TQ Education and Training Ltd for multivariable control. 4.
TYPICAL COURSE EXPERIMENT
The list of control design steps by Skogestad and Postlethwaithe (1996) was used as a basic template for creation of all of the course experiments. Fig. 4. MIMO Twin rotor model 3.5 Servomotor control This station provides DC motor for control and identification studies. The speed servomechanism
plant and model are used for validation of the obtained model. Unit R
Ω
ke
s.V-1 2 -1
km b mz J
kg.m .s kg.m2.s-1 N.m kg.m2.s-1
L
H
Description Armature resistance Electric constant of motor Motor constant Friction constant Load moment Moment of inertia Armature inductance
Value 3 0,8 2 0,2 0 0,5 0,003
Table 2. Example of parameters of the servomotor model 4.2 Controller synthesis
Table 1. Steps in control design The whole design process can be divided according to the Table 1 into 3 main phases: model building and analysis, controller synthesis and validation. 4.1 Model building and analysis During the first phase students have to apply their theoretical knowledge obtained in the courses of Identification and Modeling of Dynamical Systems. Their first task is to study the system, to find out about the linearity or nonlinearity of the system, signal limitations and to plot the static characteristic of the system. The lab assignment includes the system of differential equations describing the system (1) and a table with system parameters to provide information about laboratory model. di (t )
= − Ri (t ) − keω (t ) + um (t ) dt d ω (t ) J = km i (t ) − bω (t ) − mz (t ) dt d ϕ (t ) = ω (t ) dt
L
The choice of a control scheme is highly correlated with the objectives or requirements for robustness, speed accuracy etc., but it also depends on the type of the model, obtained in the identification phase. Students can choose any controller to satisfy the specifications but in some cases the type of the controller is defined beforehand. Typical example is a speed control with a P controller, where students learn how the proportional gain influences overshoot, speed and steady-state error. Students tune PID controller using the Ziegler-Nichols rules, poleplacement or dynamics inversion method. In this part of the design process students should realize the importance of accurate model and that consideration of all aspects of interest (robustness etc.) yields the best results. They also learn that that tuning rules can be most helpful, but one must understand whether the rules fits the problem. The Self-Tuning Controllers (STC) Simulink toolbox is widely used for control of nonlinear plants. The description of the toolbox and used algorithm with applications can be found in Bobál (2005, 2003). Students also learn how to quantify interactions by means of Relative Gain Array (RGA), from model or by measuring step responses. 4.3 Validation
(1)
Students’ aim involves derivation of state-space model, linearization in a working point if necessary, creation of the Simulink model, identification from step response using the least-squares method and identification of ARX model. Plot responses of the
The control objectives are set to challenge the students and where it is possible, the faults of sensors of disturbances are introduced and it is expected that the students’ designs will respond appropriately. The Simulink blocks of plants (Fig. 7), lab assignments for each experiment are accessible to students via Internet.
REFERENCES Bobál, V.,Bohm, J., Fessl, J. Machacek, J. (2005). Digital Self-tuning Controllers. Springer-Verlag, Germany. Bobál, V., Chalupa P., Kubalčík, M., Dostál P. (2003). Self-tuning Control: Laboratory RealTime Education. In. Proceeding of the 6th IFAC Symposium on Advances in Control Education, Oulu, Finland.
Fig. 8 Example of Simulink block of the servomotor model After each two weeks students must submit their lab report with all results, control schemes and measurement data. Students’ reports are uploaded to the course web pages, where all the reports are stored and where students also receive grades and comments from instructors. Students are awarded grades based on both individual and group contribution and activity. 5. CONCLUSIONS This paper presents brief overview of the new control lab and the new course at the department of Process control. This course has been offered once (Winter Semester 2005) for students of the department. Future plans include extension of the course for students of 3rd year and inclusion of new teaching equipment which is a miniature of continuous stirred tank reactor and new model of combustion motor. Integration of the laboratory equipment for other courses is also considered. The importance of control laboratory courses is widely recognized as necessary part of control education. The role of the laboratory is to improve student’s problem solving ability and team cooperation, which are considered crucial for their future career success. According the students’ impression and to the first outcomes, these goals are attained satisfactorily. ACKNOWLEDGMENT This work was supported by the Ministry of Education of the Czech Republic under grant 1M6840770004.
Skogestad S., Postlethwaite, I. (1996). Multivariable Feedback Control. John Wiley & Sons, Inc., New York.
Jakub Novák, Petr Chalupa, Vladimír Bobál
Department of Process Control Faculty of Applied Informatics, Tomas Bata University in Zlín Nad Stráněmi 4511, 76272 Zlín, Czech Republic Email: [email protected]
Abstract: This paper presents new control laboratory course designed at the Faculty of Applied Informatics for the undergraduate courses in Automatic control. Experience obtained during the building process of Control Laboratory and the organization of student assignments for laboratory course is described. The objectives of the laboratory course are to integrate the fundamental skills from theoretical courses to solve engineering problems in dynamics and control and to encourage the problem-based learning. Copyright 2006 IFAC Keywords: Laboratory education, Control education, Adaptive control, Educational aids, Engineering
1.
INTRODUCTION
This paper describes a new laboratory of Faculty of Applied Informatics and a new course which takes place in this laboratory. The aim of this laboratory and the course is to give students the opportunity to apply the theoretical knowledge they obtained in the courses of Identification, Control Theory and Modern Control Methods. In order to reduce the gap between the theory and practice the simulation based experiments can be used. There is a recent trend to provide virtual control laboratories using WWW and simulation models which is a very cost effective solution. However, nothing can replace the laboratory work. The recent development in hardware and software decreased the cost of computing, so that control hardware and software become affordable for universities.
The laboratory also provide ‘look and feel’ of realworld control situations. The expected results of the new laboratory course, is that students gain the basic practical skills considered essential for control education. 2. MOTIVATION The main motivation for using real plants in the educational process is the clear visibility of the controlled dynamic. Thus experimental work in laboratories is a requisite part of the engineering education. The other subjects, such as Identification or Modern Control, are mainly theoretical and exercises in these subject usually involves only simulation models in MATLAB/Simulink environment and so students have problems with interpretability of simulation examples. The real systems help to increase the transparency of these
solved examples. Students in the course have to face the real problems connected to control design, such as measurement noise, measurement quantization or control signal limitation. Student’s success or failure will be clearly recognizable because of the real system. The other motivation for using real plants is the necessity to complete all the steps of control design, starting from model building, identification and analysis, continuing with controller design and ending with control validation. For this whole process students have to integrate obtained knowledge from a number of prior courses. Control laboratory is also a typical place for problem-based learning and for training communication and cooperation skills, since students work in groups and have to communicate between each other and between the groups. 3.
equipped with two accurate pumps, driven by DC motor. The station’s equipment was supplied by AMIRA, a commercial supplier of test equipment for control education. This lab demonstrates control of the water level in a tank. The objective is to show a number of common control strategies so that insight into tuning of the individual controller parameters can be obtained as well as a demonstration how each affects the controller response.
DESCRIPTION OF THE COURSE AND LABORATORY
The course has been offered during a 14-week semester with 3-hours per week. The laboratory has 11 stations, each equipped with a PC, so that only 2 students can share one experiment. 10 stations are divided into 6 groups, so that one group consists of similar experiments such as three-tank system and four-tank system. During the course students have to complete 6 experiments, each from one group. Multifunctional cards with A/D and D/A converters from Humusoft and Advantech are installed in every PC. For solving the identification and design problems MATLAB/Simulink environment is used. The communication between the analog cards is provided by the Real-Time toolbox, which enables easy creation of Simulink blocks for writing and reading data from input and output channels. The eleven experiments are: - Three-tank system - Four-tank system - Inverted pendulum - Magnetic levitation - Twin rotor MIMO system - MIMO helicopter system - Servomotor system - Analog controller - Flow control system - Coupled drive system
Fig. 1. Three-tank laboratory system 3.2 Inverted pendulum The inverted pendulum is a classic plant designed for teaching advanced control systems theory in laboratory. Model of inverted pendulum from AMIRA Company is represented by a pendulum, connected to a cart which can be moved along a metal guiding bar. The cart is connected to a drive wheel. The wheel is driven by DC motor, which delivers a torque proportional to the acting control voltage. The objective of this plant is the understanding of stabilization of unstable plants. Typical real examples of systems that cannot operate without a controller are planes, missiles, nuclear reactor or all motors when rotation angle is to be controlled. In order of increasing difficulty the objectives we show only part of different control strategies that can be performed. - cart position control - simulating a crane on a construction site - balancing the pendulum in vertical position - swing up and balancing inverted pendulum
3.1 Three-tank system The three tank system belongs to the basic plants usually used in educational process. This apparatus consists of three interconnected tanks. Each tank is equipped with a static pressure sensor, which gives voltage proportional to the level of liquid in the tank. There are six ball valves, which gives many possibilities for configuration or can be used to introduce disturbances or faults. The apparatus is also
Fig. 2. Inverted pendulum model 3.3 Magnetic levitation The Magnetic levitation model consists of a steel ball hanging in the magnetic field of the coil. The
position of the ball is measured with magnetic positron sensor. The current in the coil is amplified and is proportional to the input voltage. Magnetic levitation is a typical example of an unstable nonlinear system with one input and one output. From dynamical point of view the levitation model can be approximated by system of order 3 with astatism of order 2. The plant was provided by HUMUSOFT Company.
consists of two identical motors connected with a clutch, tachogenerator and IRC sensor for angle measurement. The first motor is used as generator of variable load torque or as a disturbance and the second one is used for control. The test equipment was obtained from AMIRA.
Fig. 5. Servomechanism model 3.6 Analog controller
Fig. 3. Magnetic levitation model 3.4 Twin rotor MIMO system The twin rotor MIMO system provides high-order, nonlinear system, where significant coupling between the actions of the rotors can be observed. The angle of attack of the rotors is fixed and aerodynamic forces are controlled by varying the speeds of the motors. High resolution optical encoders provide feedback from vertical and horizontal angular position. Move in either vertical or horizontal angle can be fixed to simplify the control experiment. The goal of experiment is to control both the main and the tail rotor simultaneously.
Analog controller CE120 is a tool for testing P, I, PI and PID controllers. In this experiment, contrary to the rest of course, the controlled plant is realized by PC. In this experiment student’s goal is to control a stable, unstable and integral plants created in Simulink. The main objectives of this experiment are to set up PID controller parameters on the analog controller and to measure the behavior of the system. TQ Education and Training Ltd is a producer of this equipment.
Fig. 6. Analog controller CE120 Other models used in the laboratory course includes the four tank system, MIMO helicopter system from Humusoft, Flow control system from Leybold, where students have the chance to try other environment than Simulink and Coupled drive systems from TQ Education and Training Ltd for multivariable control. 4.
TYPICAL COURSE EXPERIMENT
The list of control design steps by Skogestad and Postlethwaithe (1996) was used as a basic template for creation of all of the course experiments. Fig. 4. MIMO Twin rotor model 3.5 Servomotor control This station provides DC motor for control and identification studies. The speed servomechanism
plant and model are used for validation of the obtained model. Unit R
Ω
ke
s.V-1 2 -1
km b mz J
kg.m .s kg.m2.s-1 N.m kg.m2.s-1
L
H
Description Armature resistance Electric constant of motor Motor constant Friction constant Load moment Moment of inertia Armature inductance
Value 3 0,8 2 0,2 0 0,5 0,003
Table 2. Example of parameters of the servomotor model 4.2 Controller synthesis
Table 1. Steps in control design The whole design process can be divided according to the Table 1 into 3 main phases: model building and analysis, controller synthesis and validation. 4.1 Model building and analysis During the first phase students have to apply their theoretical knowledge obtained in the courses of Identification and Modeling of Dynamical Systems. Their first task is to study the system, to find out about the linearity or nonlinearity of the system, signal limitations and to plot the static characteristic of the system. The lab assignment includes the system of differential equations describing the system (1) and a table with system parameters to provide information about laboratory model. di (t )
= − Ri (t ) − keω (t ) + um (t ) dt d ω (t ) J = km i (t ) − bω (t ) − mz (t ) dt d ϕ (t ) = ω (t ) dt
L
The choice of a control scheme is highly correlated with the objectives or requirements for robustness, speed accuracy etc., but it also depends on the type of the model, obtained in the identification phase. Students can choose any controller to satisfy the specifications but in some cases the type of the controller is defined beforehand. Typical example is a speed control with a P controller, where students learn how the proportional gain influences overshoot, speed and steady-state error. Students tune PID controller using the Ziegler-Nichols rules, poleplacement or dynamics inversion method. In this part of the design process students should realize the importance of accurate model and that consideration of all aspects of interest (robustness etc.) yields the best results. They also learn that that tuning rules can be most helpful, but one must understand whether the rules fits the problem. The Self-Tuning Controllers (STC) Simulink toolbox is widely used for control of nonlinear plants. The description of the toolbox and used algorithm with applications can be found in Bobál (2005, 2003). Students also learn how to quantify interactions by means of Relative Gain Array (RGA), from model or by measuring step responses. 4.3 Validation
(1)
Students’ aim involves derivation of state-space model, linearization in a working point if necessary, creation of the Simulink model, identification from step response using the least-squares method and identification of ARX model. Plot responses of the
The control objectives are set to challenge the students and where it is possible, the faults of sensors of disturbances are introduced and it is expected that the students’ designs will respond appropriately. The Simulink blocks of plants (Fig. 7), lab assignments for each experiment are accessible to students via Internet.
REFERENCES Bobál, V.,Bohm, J., Fessl, J. Machacek, J. (2005). Digital Self-tuning Controllers. Springer-Verlag, Germany. Bobál, V., Chalupa P., Kubalčík, M., Dostál P. (2003). Self-tuning Control: Laboratory RealTime Education. In. Proceeding of the 6th IFAC Symposium on Advances in Control Education, Oulu, Finland.
Fig. 8 Example of Simulink block of the servomotor model After each two weeks students must submit their lab report with all results, control schemes and measurement data. Students’ reports are uploaded to the course web pages, where all the reports are stored and where students also receive grades and comments from instructors. Students are awarded grades based on both individual and group contribution and activity. 5. CONCLUSIONS This paper presents brief overview of the new control lab and the new course at the department of Process control. This course has been offered once (Winter Semester 2005) for students of the department. Future plans include extension of the course for students of 3rd year and inclusion of new teaching equipment which is a miniature of continuous stirred tank reactor and new model of combustion motor. Integration of the laboratory equipment for other courses is also considered. The importance of control laboratory courses is widely recognized as necessary part of control education. The role of the laboratory is to improve student’s problem solving ability and team cooperation, which are considered crucial for their future career success. According the students’ impression and to the first outcomes, these goals are attained satisfactorily. ACKNOWLEDGMENT This work was supported by the Ministry of Education of the Czech Republic under grant 1M6840770004.
Skogestad S., Postlethwaite, I. (1996). Multivariable Feedback Control. John Wiley & Sons, Inc., New York.