- Email: [email protected]
Teaching advanced process control to undergraduates
Pergamon
Computers chem. Engng Vol. 20, Suppl., pp. SI347-S1352, 1996 Copyright © 1996 Elsevier Science Lid S0098-1354(96)00231-1 Printed in Great Britain. All rights reserved 0098-1354/96 $15.00+0.00
Teaching Advanced Process Control to Undergraduates Daniel R. Lewin*, Joav Rockman and Ram Lavie Department of Chemical Engineering, Technion, Haifa 32000, Israel phone: +972 48292 006 fax: +972 4 8230 476 emall: [email protected]
ABSTRACT This paper describes the advanced process control course sequence offered to undergraduates at the Technion's Department of Chemical Engineering. Presented here are the educational objectives of the sequence, as well as the format of the three courses involved. The paper will focus on the methods used, and in particular in the computer aided design and analysis tools utilized. As it turns out, the elective courses tend to attract the more capable and motivated of our students. The unreserved enthusiasm expressed by the students indicates that we seem to be on the right track.
KEYWORDS Process control education, computer aided instruction, computer aided design, real time control. 1. INTRODUCTION Process control is often taught to undergraduates in the form of a single, analysis oriented course, where relatively little emphasis is placed on the design aspects of the curriculum. The subjects coveted are typically dynamic modelling, linearization and stability analysis of chemical processes (usually using very simple examples) and that of simple control systems (usually limited to simple PID SISO designs). Such a course, if well defined, will give the student sufficient background to be able to understand the dynamic nature of processes. This is justly considered to be a necessary part of the education of chemical engineers in general, whatever facet of chemical engineering they will be practicing. However, the analytical focus of the typical undergraduate course will not adequately prepare students for practical work in process control in industry, since such activity involves synthesis skills which they will not have acquired. Real-life control system design involves a trade-off between robustness and performance (Morari and Zafiriou, 1989). The term robustness implies that the control system, usually linear, should be relatively insensitive to modelling inaccuracies, which arise as a result of approximating the true process by a linear model, from which the controller is derived. Most of the available undergraduate text books (e.g. Stephanopouios (1984), Seborg et al (1989), Luyben, 1990) do not deal with the quantitative aspects of robust process control design adequately, nor do they explicitly deal with the controllability implications of process design. Indeed, the significance of quantitative performatw~ specifications have been Iraditionally ignored by educators in chemical process control design. In order to prepare for their careers as process control engineers, students should therefore be armed with a toolbox containing the relevant theory and sharpen their skills by solving non-trivial, cl~en-ended problems.
* Author to whom all correspondance should be addressed. si347
S1348
European Symposium on Computer Aided Process Engineering---6. Part B
This paper describes our experiences in teaching process control to undergraduates at the Technlon's Chemical Engineering Department. The paper is organized as follows. First, the complete sequence is briefly described, with special emphasis made on the kinds of instructional objectives we are seeking to satisfy. Next follows a description of the computational tools, some of which were developed in our laboratory for teaching purposes. One of the highlights of the sequence are two parallel courses covering continuous process control system design theory and practice. These will be described in greater detail.
2. THE PROCESS CONTROL SEQUENCE AT THE TECHNION Undergraduate ChemE students at the Technion are offered a sequence of four courses, each of 40 credit hours, of which only the first is compulsory. This course concentrates on dynamic process modelling, but it also covers basic feedback control, including some design and performance specification issues. The three other courses are electives: two courses on control system design (one covers continuous systems and the other discrete systems) and a control laboratory, which is offered in parallel with the continuous design course. The three elective courses are designed to expose the students to advanced concepts such as dealing with model uncertainty, process interactions in multivariable systems, and digital control system implementation. The laboratory course exposes the students to practical issues while implementing the methods covered up to the advance continuous systems course. The connection between the courses is illustrated by the block diagram in Figure 1.
Introduction to ] Process Dynamics and Control
II L,
I
Continuous Process Control System Design
Process
Control Laboratory
II I Discxete Process Control System Design
Figure 1: Process Control Courses at the Technion
The theoretical courses are structured into units, each preceded by a motivating statement or problem, as well as clearly stated instructional objectives. For example, in the unit which presents IMC (Internal Model Control) design principles, the inslructional objectives are: At the end of this section, the student should be able to: 1. Formulate a given SISO control problem in the IMC framework. 2. Design a robust feedback controller for an arbitrary uncertain SISO process using the IMC method. 3. Translate a control system from the classical to the IMC form (and vice versa). 4. Design a PI/PID/IMC controller for an arbitrary uncertain SISO system, and be able to guarantee closed stability despite the process uncertainty. 5. To be able to select and tune the most suitable controller for a given control problem, posed in terms of an uncertain process model, and desired control performance (e.g. closed loop bandwidth, and setpoint tracking). These instructional objectives define what the student has to be able to achieve to show us that the design principles have been understood.
3. SOFTWARE TOOLS. Matlab ®and Simulink~ have been introduced as standard tools in the control courses for the past three years (the first introductory course on process dynamics and control stresses analysis and avoids the use of computers). Matlab ® is used for controller design (in the Laplace, frequency and Z domains) while Simulink* is used for time domain simulation. Students not familiar with Matlab ~ (it is also used
European Symposiumon ComputerAided ProcessEngineering---6.Part B
S1349
in other elective courses), are '~rought up to speed" in the first two exercise period of the Continuous Process Control System Design course. Students enjoy working with this software, and we have noted a marked increase in the level of competence in the material as a result. The process control laboratory module, taught in parallel to the continuous control system design module, has been recently drastically changed by assimilating Matlab/Simulink® as the sole simulation and process control implementation software. This has involved modifying the software in a modular fashion to enable it to communicate with an A/D interface card to a PC-486 computer. A real time application library, called LabLib, was written for use with Simulink® and students, already familiar with Matlab ~ and Simulink* learn the use of LabLib in 15 to 30 minutes. Obviously, employing the same software for both design and implementation of control is a great advantage. It facilitates learning on the part of the student by reducing the overhead of having to acquaint with different software. More importantly, it permits the intuitive reflection of analysis on implementation and vice-versa. This has proven to be a significant asset, speeding up the understanding of the course work. 4. I N T E G R A T I N G THEORY & PRACTICE As indicated in Figure 1, the continuous process control system design course is offered in parallel with the process control lab. Most students who opt for the control sequence enroll for both courses, making it possible to fully integrate progress in the two courses. Thus, laboratory experiments have been designed to reinforce theoretical concepts covered in the design course, and are appropriately synchronized as shown in Table I. Table 1: The sequence of topics covered in the design course and in the laboratory. Week 1-3
4 5-9
10-13
Design Course Linear systems analysis Frequency domain Model identification Classical frequency domain design IMC design principles IMC PID tuning Cascade and feedforward (FF) Introduction to MIMO Systems Interaction RGA matrix Decentralized Control RIM Plant-wide control
Laboratory Experiment 1. Process modelling 2. System identification 3. Single loop feedback & cascade control 4. Model-based control (IMC and FF) 5. MIMO control (Decentralized and nonlinear decoupling)
The discrete course, which follows the continuous course chronologically, exposes the students to sampling theory, discrete filtering techniques, Z-transforms, discrete time response, stability of discrete systems, discrete IMC design principles (with the focus being placed here on what is different to what the students have learned in the continuous course) and pole placement design. The course concludes by covering Model Predictive Control (MPC) and Dynamic Matrix Control (DMC). Students are taught to visualize a DMC scheme as an MPC slave driven by an Linear Programming (LP) master. Since we cannot assume that the students are familiar with constrained optimization, some background material is offered on LP techniques. In covering MPC/DMC, the emphasis is on getting the students to grasp what is Involved in the design and tuning of these controllers and to be able to quantify under which situations this approach is superior to a decentralized control system (e.g. diagonal PID's). Since MPC/DMC incorporate both multivariable feedforward action and because of implicit decoupling, actuators driven by these controllers will anlicipate the required action in advance of those driven by SISO PID's. However, the advanced schemes will in general be more sensitive to modelling error than
S1350
European Symposium on Computer Aided Process Engineering---6. Part B
decentalized schemes. In any case, simple comparison of the Ixrformance of SISO PID with SISO DMC (e.g. Seborg et al, 1989) misses the point altogether[.
5. EXAMPLE: DESIGNING AND IMPLEMENTING PID AND IMC CONTROLLERS In order to illustrate the degree to which the continuous design course and the lab are integrated, we shall now describe a typical experiment and the appropriate thetxetical support furnished by the design course. Consider the fourth experiment, which is intended to cover model-based control design and implementation. For this experiment, the students work on the mixing process, illustrated by the flow diagram in Figure 2. Continuous flows of fresh and salty water are fed via control valves CV. and CV. to a well mixed tank incorporating a constant orifice at the outlet, CVT, thereby causing the level to be a function of the combined flow rates. Level, h, is measured by a differential pressure transducer, concentration, C, is measured by a conductivity meter a certain distance downstream from the mixing tank, creating the required delay in output measurement. Fresh and salty water flow rates are measured by flow meters and marked as q~ and qs respectively. Control valves CVw and CV, are regulated by electrical signals, Vw and Vs respectively. Fresh and salty water supply tanks are kept at constant level.
O. roofof build~
Dead Tira~
Figure 2: Flow diagram of the mixing process. l~
[lie
Cliplmod
Edit Options •imulaiton Slyio
IMI CJmlr.lh'r IM.,
Block name: CC Block type:
IMC Controller [Mask]
Enter the Mode, Lombda Ilite¢ value, p~p, Teu, Thete], k~faeo and MVmln end MVmox. Mode [0 - MAN, 1 - AUTO. 2 - CASC] 0
-
j
]
kombdo '
l
I Kp. Tea, There J I-.e,s.3,1 al
]
MVee
30
]
Saturation limits pdVIow.MVhlgh I
IO.lOOl
Figure 3: Simulink ®model used to model and control the process.
]
Figure 4: Example of parameter input table for a Smart IMC controller.
The fourth experiment involves the design of regulatory control of the tank effluent salt concentration using imxlel-based techniques. Figure 3 shows the Simulink® model, "mimol", used to control the system. This model is used also for the fifth control lab where MIMO control issues are analyzed. Shown are the two supervisory loops that are responsible for level and concentration regulation The model "Real Mixing Tank" incorporates the A/D and D/A blocks which interface with the teal process, together with the lower level flow control PI loops. Also, the IMC controller is "waiting" at the bottom to replace the PID, by simply exchanging the PID with the IMC block using standard, mouse
European Symposiumon ComputerAided ProcessEngineering--6. Part B
S1351
controlled, cut and paste operations. Each block is an icon that can he "double clicked" so as to reveal a parameter input table that allows user input of relevant data As an example, the "Smart IMC" parameter input table is shown in Figure 4. As preparation, the students are asked to identify the plant based upon knowledge of the model (obtained from the first lab), For this purpose, we have modelled the real mixing tank as a Simulink* model (the "Simulated Mixing Tank" block shown in figure 3). As preparation for the experiment, the students are asked to formulate an uncertain linear approximation of the process, using this block. The typical model generated by the students takes the form: 1 e_O,(Kpq,+K~q,) [1] ~s+l where x is the time constant of the system, 0 is the dead time and Kp and Ka are the gains of the process and disturbance respectively. The linear model parameters must be subject to uncertainty in order that the linear model will reasonably approximate the non-linear process: Kp = --0.8+ 0.16 K d = 0.8 + 0.10 x = 5.3 + 0.2[s] 0 = 14.6 + 4.0[s] [2] C(s)=
In parallel with this lab, the students have been exposed to robust control system design using IMC principles in the design course. They are therefore aware that for a full order IMC controller, the model corresponds to the nominal process, and any stability limitations are due to parametric uncertainty. The multipUcative uncertainty, lm(o3), which is used to compute the closed loop stability limit, is defitied as.
~..
IP~(ito)-~(i(o)
to))=I ~
[3]
where Pw is the worst plant (in terms of instability), derived by taking the maximum gain, minimum time constant and maximum delay time, and /;(i(o)is the corresponding plant evaluated for nominal conditions. For the PID controller, a first order Pad6 approximation is performed so that the controller is based upon the plant model:
+1)
P=KP (OI2s+l~Es+l)"
[4]
Potentially, the PID controller is subject to greater stability limitations than the IMC controller, since the former incorporates structural uncertainty (due to model reduction) over and above the already existing parametric uncertainty. Using model [4], one can derive the PID parameters based upon the nominal values of the process parameters (Rivera et al, 1986). To ensure stability, the following condition must be met: if(ito)l _<..~-=. 1 ,vto _>o.
[5]
lm(co)
where f(io~) is a first order lag, with filter time constant k, used to augment the IMC controller (structurally identical for both the IMC and PID designs). Figure 5 shows condition [5] graphically for both designs. Stability is ensured for 3. values greater than 2.75 and 7.5 s for the IMC and PID designs respectively. In order to obtain a gain margin of 2, one may detune the controller by increasing the value of 3. to 3." according to the following equation:
x'=
I 2V~(~=,
l
..--r -._-r fl)c ) (l)~
[6]
101 . . . . . . . . .
0 lO
tI
.^-q
1u10-2
''`
--:
.
.
.
.
.
.
.
.
.
.
* i i i , i
i,
'l iI ,
. .
'* iI ,,
¢1| II tlI 4
'""
.
.
.
il '
"
".
10-1 10 ° Frequency [llsec]
.
\
. . . .
I
10 !
Figure 5: Robust stability limits for IMC and PID designs
S1352
European S y m p o s i u m on C o m p u t e r Aided Process E n g i n e e r i n g ~ 6 . Part B
where L, and t~ are respectively the critical X value that brings the system to the verge of instability and the frequency at which the If(ito~ and ~(t0) -1 curves tangentially meet (0.55 and 0.25 rad/s for the IMC and PID designs, respectively). ~.* values for the controllers are therefore set at 6.3 and 16.5 s for the IMC and PID controllers, respectively. Figure 6 shows the simulated responses to set point changes in concentration that the students obtained for these settings using the "Simulated Mixing Tank" block. Clearly, the performance of the two control schemes are virtually identical, with both settling in under 80 s with very little overshoot. Thus, the students are made aware, a priori by simulation, that they should not expect to see a big difference between the two schemes. This is important since it reduces the amount of frustration the students would experience during the lab had they not been exposed to this before hand. Having prepared themselves for the lab, the students substitute the "Real Mixing Tank" block for the simulation, start up the process, and are ready to start testing in minutes. Figure 7 shows concentration control as implemented experimentally with each of the designed controllers, using the same parameters set in the simulation. Again, the difference between the performance of the controllers is clearly marginal. Note that the time scales and responses are very similar to those obtained in the simulations, thus allowing for the students to gain confidence in the theory. This has always been a stumbling point in the lab in the past, and we believe this has finally been solved by modifying Simulink®to allow for real time control. 5 5 ¢ 1 . 5 ~
- - IMC Control - - PID Control
6£ ~
r 5C
~r
,J
C,p
- - IMC Control - - PID Control ~
L k;...#. ~,;,~_ • * .t-~"
3C
~
~
-
-
-
-
-
"71
0~
t-
25 20 " " _ L . _
2C 50
*.
, ~ . . .......
I00
150 Time [s~]
20O
250
Figure 6: Simulated response of the process to set point change, comparison between PID and flff C.
15~[
, 150
200
250 Time [s¢¢]
300
350
Figure 7: Experimental response of the process to se~ooint change, comparing PID and IMC.
6. CONCLUSIONS The advanced process control course sequence objectives, of developing the student's analytical, design and problem-solving skills in process control have been met. This has been partially achieved through the extensive experimentation that is now achievable at the students own initiative due to the ease of exploration. The study program exposes the students to process control issues in a gradually increasing degree of complexity, experimenting along the way with most of the topics taught in theory. Throughout the course, the students are encouraged to explore on their own. They do so with great enthusiasm. REFERENCES Luyben, W. L. (1990). Process Modelling, Simulation and Control for Chemical Engineers, 2rid Ed., McGraw-Hill Morari, M. and Zafiriou, E. (1989). Robust Process Control, Prentice-Hall Rivera, D.E., Morari, M. and Skogestad, S. (1986). "Internal Model Control 4. PID Controller Design", I.&E.C. Proc. Des. Dev., 25, 252 Seborg, D. E., Edgar, T. F., Mellichamp, D. A. (1989). Process Dynamics and Control, Wiley Step~ulos, G. (1984). Chemical Process Control, Prentice-Hall
Computers chem. Engng Vol. 20, Suppl., pp. SI347-S1352, 1996 Copyright © 1996 Elsevier Science Lid S0098-1354(96)00231-1 Printed in Great Britain. All rights reserved 0098-1354/96 $15.00+0.00
Teaching Advanced Process Control to Undergraduates Daniel R. Lewin*, Joav Rockman and Ram Lavie Department of Chemical Engineering, Technion, Haifa 32000, Israel phone: +972 48292 006 fax: +972 4 8230 476 emall: [email protected]
ABSTRACT This paper describes the advanced process control course sequence offered to undergraduates at the Technion's Department of Chemical Engineering. Presented here are the educational objectives of the sequence, as well as the format of the three courses involved. The paper will focus on the methods used, and in particular in the computer aided design and analysis tools utilized. As it turns out, the elective courses tend to attract the more capable and motivated of our students. The unreserved enthusiasm expressed by the students indicates that we seem to be on the right track.
KEYWORDS Process control education, computer aided instruction, computer aided design, real time control. 1. INTRODUCTION Process control is often taught to undergraduates in the form of a single, analysis oriented course, where relatively little emphasis is placed on the design aspects of the curriculum. The subjects coveted are typically dynamic modelling, linearization and stability analysis of chemical processes (usually using very simple examples) and that of simple control systems (usually limited to simple PID SISO designs). Such a course, if well defined, will give the student sufficient background to be able to understand the dynamic nature of processes. This is justly considered to be a necessary part of the education of chemical engineers in general, whatever facet of chemical engineering they will be practicing. However, the analytical focus of the typical undergraduate course will not adequately prepare students for practical work in process control in industry, since such activity involves synthesis skills which they will not have acquired. Real-life control system design involves a trade-off between robustness and performance (Morari and Zafiriou, 1989). The term robustness implies that the control system, usually linear, should be relatively insensitive to modelling inaccuracies, which arise as a result of approximating the true process by a linear model, from which the controller is derived. Most of the available undergraduate text books (e.g. Stephanopouios (1984), Seborg et al (1989), Luyben, 1990) do not deal with the quantitative aspects of robust process control design adequately, nor do they explicitly deal with the controllability implications of process design. Indeed, the significance of quantitative performatw~ specifications have been Iraditionally ignored by educators in chemical process control design. In order to prepare for their careers as process control engineers, students should therefore be armed with a toolbox containing the relevant theory and sharpen their skills by solving non-trivial, cl~en-ended problems.
* Author to whom all correspondance should be addressed. si347
S1348
European Symposium on Computer Aided Process Engineering---6. Part B
This paper describes our experiences in teaching process control to undergraduates at the Technlon's Chemical Engineering Department. The paper is organized as follows. First, the complete sequence is briefly described, with special emphasis made on the kinds of instructional objectives we are seeking to satisfy. Next follows a description of the computational tools, some of which were developed in our laboratory for teaching purposes. One of the highlights of the sequence are two parallel courses covering continuous process control system design theory and practice. These will be described in greater detail.
2. THE PROCESS CONTROL SEQUENCE AT THE TECHNION Undergraduate ChemE students at the Technion are offered a sequence of four courses, each of 40 credit hours, of which only the first is compulsory. This course concentrates on dynamic process modelling, but it also covers basic feedback control, including some design and performance specification issues. The three other courses are electives: two courses on control system design (one covers continuous systems and the other discrete systems) and a control laboratory, which is offered in parallel with the continuous design course. The three elective courses are designed to expose the students to advanced concepts such as dealing with model uncertainty, process interactions in multivariable systems, and digital control system implementation. The laboratory course exposes the students to practical issues while implementing the methods covered up to the advance continuous systems course. The connection between the courses is illustrated by the block diagram in Figure 1.
Introduction to ] Process Dynamics and Control
II L,
I
Continuous Process Control System Design
Process
Control Laboratory
II I Discxete Process Control System Design
Figure 1: Process Control Courses at the Technion
The theoretical courses are structured into units, each preceded by a motivating statement or problem, as well as clearly stated instructional objectives. For example, in the unit which presents IMC (Internal Model Control) design principles, the inslructional objectives are: At the end of this section, the student should be able to: 1. Formulate a given SISO control problem in the IMC framework. 2. Design a robust feedback controller for an arbitrary uncertain SISO process using the IMC method. 3. Translate a control system from the classical to the IMC form (and vice versa). 4. Design a PI/PID/IMC controller for an arbitrary uncertain SISO system, and be able to guarantee closed stability despite the process uncertainty. 5. To be able to select and tune the most suitable controller for a given control problem, posed in terms of an uncertain process model, and desired control performance (e.g. closed loop bandwidth, and setpoint tracking). These instructional objectives define what the student has to be able to achieve to show us that the design principles have been understood.
3. SOFTWARE TOOLS. Matlab ®and Simulink~ have been introduced as standard tools in the control courses for the past three years (the first introductory course on process dynamics and control stresses analysis and avoids the use of computers). Matlab ® is used for controller design (in the Laplace, frequency and Z domains) while Simulink* is used for time domain simulation. Students not familiar with Matlab ~ (it is also used
European Symposiumon ComputerAided ProcessEngineering---6.Part B
S1349
in other elective courses), are '~rought up to speed" in the first two exercise period of the Continuous Process Control System Design course. Students enjoy working with this software, and we have noted a marked increase in the level of competence in the material as a result. The process control laboratory module, taught in parallel to the continuous control system design module, has been recently drastically changed by assimilating Matlab/Simulink® as the sole simulation and process control implementation software. This has involved modifying the software in a modular fashion to enable it to communicate with an A/D interface card to a PC-486 computer. A real time application library, called LabLib, was written for use with Simulink® and students, already familiar with Matlab ~ and Simulink* learn the use of LabLib in 15 to 30 minutes. Obviously, employing the same software for both design and implementation of control is a great advantage. It facilitates learning on the part of the student by reducing the overhead of having to acquaint with different software. More importantly, it permits the intuitive reflection of analysis on implementation and vice-versa. This has proven to be a significant asset, speeding up the understanding of the course work. 4. I N T E G R A T I N G THEORY & PRACTICE As indicated in Figure 1, the continuous process control system design course is offered in parallel with the process control lab. Most students who opt for the control sequence enroll for both courses, making it possible to fully integrate progress in the two courses. Thus, laboratory experiments have been designed to reinforce theoretical concepts covered in the design course, and are appropriately synchronized as shown in Table I. Table 1: The sequence of topics covered in the design course and in the laboratory. Week 1-3
4 5-9
10-13
Design Course Linear systems analysis Frequency domain Model identification Classical frequency domain design IMC design principles IMC PID tuning Cascade and feedforward (FF) Introduction to MIMO Systems Interaction RGA matrix Decentralized Control RIM Plant-wide control
Laboratory Experiment 1. Process modelling 2. System identification 3. Single loop feedback & cascade control 4. Model-based control (IMC and FF) 5. MIMO control (Decentralized and nonlinear decoupling)
The discrete course, which follows the continuous course chronologically, exposes the students to sampling theory, discrete filtering techniques, Z-transforms, discrete time response, stability of discrete systems, discrete IMC design principles (with the focus being placed here on what is different to what the students have learned in the continuous course) and pole placement design. The course concludes by covering Model Predictive Control (MPC) and Dynamic Matrix Control (DMC). Students are taught to visualize a DMC scheme as an MPC slave driven by an Linear Programming (LP) master. Since we cannot assume that the students are familiar with constrained optimization, some background material is offered on LP techniques. In covering MPC/DMC, the emphasis is on getting the students to grasp what is Involved in the design and tuning of these controllers and to be able to quantify under which situations this approach is superior to a decentralized control system (e.g. diagonal PID's). Since MPC/DMC incorporate both multivariable feedforward action and because of implicit decoupling, actuators driven by these controllers will anlicipate the required action in advance of those driven by SISO PID's. However, the advanced schemes will in general be more sensitive to modelling error than
S1350
European Symposium on Computer Aided Process Engineering---6. Part B
decentalized schemes. In any case, simple comparison of the Ixrformance of SISO PID with SISO DMC (e.g. Seborg et al, 1989) misses the point altogether[.
5. EXAMPLE: DESIGNING AND IMPLEMENTING PID AND IMC CONTROLLERS In order to illustrate the degree to which the continuous design course and the lab are integrated, we shall now describe a typical experiment and the appropriate thetxetical support furnished by the design course. Consider the fourth experiment, which is intended to cover model-based control design and implementation. For this experiment, the students work on the mixing process, illustrated by the flow diagram in Figure 2. Continuous flows of fresh and salty water are fed via control valves CV. and CV. to a well mixed tank incorporating a constant orifice at the outlet, CVT, thereby causing the level to be a function of the combined flow rates. Level, h, is measured by a differential pressure transducer, concentration, C, is measured by a conductivity meter a certain distance downstream from the mixing tank, creating the required delay in output measurement. Fresh and salty water flow rates are measured by flow meters and marked as q~ and qs respectively. Control valves CVw and CV, are regulated by electrical signals, Vw and Vs respectively. Fresh and salty water supply tanks are kept at constant level.
O. roofof build~
Dead Tira~
Figure 2: Flow diagram of the mixing process. l~
[lie
Cliplmod
Edit Options •imulaiton Slyio
IMI CJmlr.lh'r IM.,
Block name: CC Block type:
IMC Controller [Mask]
Enter the Mode, Lombda Ilite¢ value, p~p, Teu, Thete], k~faeo and MVmln end MVmox. Mode [0 - MAN, 1 - AUTO. 2 - CASC] 0
-
j
]
kombdo '
l
I Kp. Tea, There J I-.e,s.3,1 al
]
MVee
30
]
Saturation limits pdVIow.MVhlgh I
IO.lOOl
Figure 3: Simulink ®model used to model and control the process.
]
Figure 4: Example of parameter input table for a Smart IMC controller.
The fourth experiment involves the design of regulatory control of the tank effluent salt concentration using imxlel-based techniques. Figure 3 shows the Simulink® model, "mimol", used to control the system. This model is used also for the fifth control lab where MIMO control issues are analyzed. Shown are the two supervisory loops that are responsible for level and concentration regulation The model "Real Mixing Tank" incorporates the A/D and D/A blocks which interface with the teal process, together with the lower level flow control PI loops. Also, the IMC controller is "waiting" at the bottom to replace the PID, by simply exchanging the PID with the IMC block using standard, mouse
European Symposiumon ComputerAided ProcessEngineering--6. Part B
S1351
controlled, cut and paste operations. Each block is an icon that can he "double clicked" so as to reveal a parameter input table that allows user input of relevant data As an example, the "Smart IMC" parameter input table is shown in Figure 4. As preparation, the students are asked to identify the plant based upon knowledge of the model (obtained from the first lab), For this purpose, we have modelled the real mixing tank as a Simulink* model (the "Simulated Mixing Tank" block shown in figure 3). As preparation for the experiment, the students are asked to formulate an uncertain linear approximation of the process, using this block. The typical model generated by the students takes the form: 1 e_O,(Kpq,+K~q,) [1] ~s+l where x is the time constant of the system, 0 is the dead time and Kp and Ka are the gains of the process and disturbance respectively. The linear model parameters must be subject to uncertainty in order that the linear model will reasonably approximate the non-linear process: Kp = --0.8+ 0.16 K d = 0.8 + 0.10 x = 5.3 + 0.2[s] 0 = 14.6 + 4.0[s] [2] C(s)=
In parallel with this lab, the students have been exposed to robust control system design using IMC principles in the design course. They are therefore aware that for a full order IMC controller, the model corresponds to the nominal process, and any stability limitations are due to parametric uncertainty. The multipUcative uncertainty, lm(o3), which is used to compute the closed loop stability limit, is defitied as.
~..
IP~(ito)-~(i(o)
to))=I ~
[3]
where Pw is the worst plant (in terms of instability), derived by taking the maximum gain, minimum time constant and maximum delay time, and /;(i(o)is the corresponding plant evaluated for nominal conditions. For the PID controller, a first order Pad6 approximation is performed so that the controller is based upon the plant model:
+1)
P=KP (OI2s+l~Es+l)"
[4]
Potentially, the PID controller is subject to greater stability limitations than the IMC controller, since the former incorporates structural uncertainty (due to model reduction) over and above the already existing parametric uncertainty. Using model [4], one can derive the PID parameters based upon the nominal values of the process parameters (Rivera et al, 1986). To ensure stability, the following condition must be met: if(ito)l _<..~-=. 1 ,vto _>o.
[5]
lm(co)
where f(io~) is a first order lag, with filter time constant k, used to augment the IMC controller (structurally identical for both the IMC and PID designs). Figure 5 shows condition [5] graphically for both designs. Stability is ensured for 3. values greater than 2.75 and 7.5 s for the IMC and PID designs respectively. In order to obtain a gain margin of 2, one may detune the controller by increasing the value of 3. to 3." according to the following equation:
x'=
I 2V~(~=,
l
..--r -._-r fl)c ) (l)~
[6]
101 . . . . . . . . .
0 lO
tI
.^-q
1u10-2
''`
--:
.
.
.
.
.
.
.
.
.
.
* i i i , i
i,
'l iI ,
. .
'* iI ,,
¢1| II tlI 4
'""
.
.
.
il '
"
".
10-1 10 ° Frequency [llsec]
.
\
. . . .
I
10 !
Figure 5: Robust stability limits for IMC and PID designs
S1352
European S y m p o s i u m on C o m p u t e r Aided Process E n g i n e e r i n g ~ 6 . Part B
where L, and t~ are respectively the critical X value that brings the system to the verge of instability and the frequency at which the If(ito~ and ~(t0) -1 curves tangentially meet (0.55 and 0.25 rad/s for the IMC and PID designs, respectively). ~.* values for the controllers are therefore set at 6.3 and 16.5 s for the IMC and PID controllers, respectively. Figure 6 shows the simulated responses to set point changes in concentration that the students obtained for these settings using the "Simulated Mixing Tank" block. Clearly, the performance of the two control schemes are virtually identical, with both settling in under 80 s with very little overshoot. Thus, the students are made aware, a priori by simulation, that they should not expect to see a big difference between the two schemes. This is important since it reduces the amount of frustration the students would experience during the lab had they not been exposed to this before hand. Having prepared themselves for the lab, the students substitute the "Real Mixing Tank" block for the simulation, start up the process, and are ready to start testing in minutes. Figure 7 shows concentration control as implemented experimentally with each of the designed controllers, using the same parameters set in the simulation. Again, the difference between the performance of the controllers is clearly marginal. Note that the time scales and responses are very similar to those obtained in the simulations, thus allowing for the students to gain confidence in the theory. This has always been a stumbling point in the lab in the past, and we believe this has finally been solved by modifying Simulink®to allow for real time control. 5 5 ¢ 1 . 5 ~
- - IMC Control - - PID Control
6£ ~
r 5C
~r
,J
C,p
- - IMC Control - - PID Control ~
L k;...#. ~,;,~_ • * .t-~"
3C
~
~
-
-
-
-
-
"71
0~
t-
25 20 " " _ L . _
2C 50
*.
, ~ . . .......
I00
150 Time [s~]
20O
250
Figure 6: Simulated response of the process to set point change, comparison between PID and flff C.
15~[
, 150
200
250 Time [s¢¢]
300
350
Figure 7: Experimental response of the process to se~ooint change, comparing PID and IMC.
6. CONCLUSIONS The advanced process control course sequence objectives, of developing the student's analytical, design and problem-solving skills in process control have been met. This has been partially achieved through the extensive experimentation that is now achievable at the students own initiative due to the ease of exploration. The study program exposes the students to process control issues in a gradually increasing degree of complexity, experimenting along the way with most of the topics taught in theory. Throughout the course, the students are encouraged to explore on their own. They do so with great enthusiasm. REFERENCES Luyben, W. L. (1990). Process Modelling, Simulation and Control for Chemical Engineers, 2rid Ed., McGraw-Hill Morari, M. and Zafiriou, E. (1989). Robust Process Control, Prentice-Hall Rivera, D.E., Morari, M. and Skogestad, S. (1986). "Internal Model Control 4. PID Controller Design", I.&E.C. Proc. Des. Dev., 25, 252 Seborg, D. E., Edgar, T. F., Mellichamp, D. A. (1989). Process Dynamics and Control, Wiley Step~ulos, G. (1984). Chemical Process Control, Prentice-Hall