- Email: [email protected]
Selftuning PID Control Based on the Closed-Loop Response Recognition
IFAC
Copyright © IFAC Control Systems Design, Bratislava, Slovak Republic, 2003
~
Publications www.elsevier.com/locate/ifac
SELFTU ING PIn
co
TROL BASED ON THE CLOSED-LOOP RESPONSE RECOGNITION Martin Foltin, Ivan Sekaj
Department ofAutomatic Control Systems, Faculty ofElectrical Engineering and Information Technology, Slovak University of Technology, l/kovicova 3. 812 19 Bratislava. Slovak Republic Tel: ++421 260291 506 E-mail :[email protected]. [email protected].
Abstract: A new type of knowledge adaptive control based on the closed-loop response recognition is proposed. This approach tries to mimic the behaviour of an expert, who has a lot of experience with the particular controlled system. The adaptive system updates the controller parameters according to the changes in system behaviour. The algorithm uses a rule-based system, which evaluates the closed-loop response shape after the decay of the transient mode, and computes the corrections of controller parameters. Because the main problem of such a control structure consists in designing of the rule-base, we focused our interest on the design of an automatic procedure for the rule-base generating. Copyright © 2003lFAC Keywords: Self tuning, PID controllers, MIMO, Step response
adaptation". The goal of the following proposed approach is to mimic the human behaviour and to update controller parameters with respect to the required closed-loop response. The underlying idea consists in that after the disturbance occurs we let the transient process decay and then evaluate the c1oseloop response (Fig. I.).
1. INTRODUCTION To control dynamic processes, which behaviour changes in time or which have nonlinear behaviour, adaptive control systems use to be used. In such cases for control algorithms design commonly exact mathematical models and stability and performance conditions are employed. The results obtained by such an approach are often very good, however sometimes problems may emerge e.g. when the complexity or non linearity degree of the model increases or if we have problems with inexact measurements or insufficient a priori information about the process (uncertainty). Thus, sometimes our "exact" mathematical approach and the resulting algorithms cannot be used to control the given process or some phases of it. In that moment it is the task for the human-operator to carry on and to control the process to the required state. The human works with his own model, based on his experience and estimations. He is able to deal with inexact, uncertain, nonnumeric and complex information (he exploits his "natural" intelligence), which in our case, he is able to apply for the process control. Using the operators "manual adaptation" of a complex or non-exactly described processes the results are sometimes better than using an "automatic
Adaptation supervisor Knowledgebased parameter tuning
e
w
+
«-
System
response
Ioil~f---
evaluation
Controller
u
Process f-I__>---,-Y---...
Fig. I. Block scheme of the rule-based adaptation system of a PlO controller. Using a rule-based mechanism, corrections of actual controller parameters are computed. The aim is to design a tuning algorithm, which will provide a good controller adaptation without any exact a-priori information about the process. Similar methods can be found in (Pfeiffer and Isermann, 1993; DeSilva
149
1991; Oliveira, et al., 1991). This method is based on a time-response shape recognition using the leastsquare-error method.
After a single-shot generating of such a database all data are ready for the application in the on-line adaptive system. The Adaptation mechanism is as follows. After the detection of some disturbance in the closed-loop we let decay the transient period. Next the acquired time response is normed and then there is searched for the "most similar" timeresponse from all records in the database, i.e. which minimize the criterion
2. THE ADAPTATION MECHANISM The recognition of the transient response shape is based on the comparison of the time-responses with a set of representative shapes using the least-squareerror method. A brief description of this method is as follows. Consider a "nominal system", which is located (when possible) in the centre of the area A in which the system parameters can move during the normal operation
n
J
= L(YJ.k -
Yk)~ ----). min
(4)
k=1
where Ydk is the closed-loop response from the database under the controller parameters Pd, Id, Dd, d is the ordinal number of the database record with the "most similar" time-response (Fig. 3.) and k is the simulation step.
(I)
where lp, h ID are the considered intervals for the PID parameters, or it is a system, which can be considered as a typical representative of a class of systems (from point of view system response shape). For such a system we design optimal PlO controller parameters p', D' with respect to selected requirements (performance index etc.) (Sekaj, 1999). Then we start to perform a cycle of systematic changes in the PlO controller parameters in a defined universe with defined steps Sp , SI and SD. For each set of actual parameters {Pd, Id, Dd} it is realized a simulation of the closed-loop system with the selected disturbance (set point step etc.). The obtained time-response is written into the database together with the corresponding controller parameters set. The number of such records in the database is
y
t.
"J
t
(2)
Fig. 3. Evaluation of the "most similar" response
where
After retrieving of the selected time-response there is loaded the appropriate set {Pd, I". Dd: from the database or it is interpolated between neighbour items in database.
(3)
The last step is the parameter corrections
For a PI controller the database represents a 2-D table, where each item of the table contains a record of a closed-loop time-response and the set of the corresponding parameters P and I. An example for a particular closed-loop is in the Fig.2, where the marked response represents the desired closed-loop response shape. For the PID case the table is by analogy 3-dimensional.
calculation
of controller
These corrections are used for the actual PlO controller updating ~,~ =
p
P.,,,,,,,, + !1P
1n.... = 1",,,,,f + !'11
Dn.~
=
(6)
D",,,,,,, + !lD
and the algorithm is waiting for new disturbances and then it is repeating. The main steps of the algorithm are as follows: I. 2. Fig. 2. Database of closed-loop time-responses 150
Detection of a disturbance and waiting for the closed-loop response decay Evaluation of the most similar time response from the database using (4)
3. 4.
Interpolation between neighbour PID parameter sets in the database Correction of the actual PID parameter set using (5) and (6)
7.
65·
,2
55
Despite the fact that this algorithm is not trivial for computation, the response evaluation and parameter correction is calculated only at the moment after decay of the transient period. Therefore there are no problems with the implementation in real-time control.
~
~
5
;.
35
30,-----:50~--'=OO--::::'50,.------=""~
3. CASE STUDY
250
DJ
tllIJ
An example of the adaptation process of a DC-drive speed is depicted in Fig. 4.
Fig. 6. Adaptation process of the TITO system control
66
4. CONCLUSION
64 •.
The described knowledge-based adaptation of a PI 1 PID controller mimic the tuning of a controller by an experienced human-operator. The advantage of this approach consists in, that it does not require a mathematical model of the controlled process. It is able to adapt the PI 1 PID controller parameters only after the closed-loop behaviour recognition, after the decay of the transient mode. Another advantage is the possibility to use designed rule-base for a class of similar systems, no matter their time constants are. Experiments in simulation and real-time has shown, that the mentioned adaptation approach is surprising robust and it is working reliable.
62 6
•• '-,.........., I
58.
I
54.
I h
-
r
I --.r'::---
48 46-----o 50
~
100
150
lis)
Fig. 4. Adaptation process of the PID controller of a DC-drive speed
Acknowledgement. This work has been supported by the grant No. 117630/20 "Intelligent methods of modeling and control" of the Slovak Grant Agency.
Another example in case of a more complex controlled object is as follows. The controlled system consists from two servomotors (two input and two output system - TITO). Between the two motors there are strong interactions. The goal is the independent speed control of both motors. The block scheme of the object with the considered control structure is in Fig.5.
e1
PI 1
DeSilva. C.W.: An Analytical Framework for Knowledge-Based Tuning ofServo Controllers, Eng.Applic.Artif.Intellig.. VolA. No.3. 177-189, 1991 Foltin. M.: Design of Knowledge-Based Adaptive Control, thesis. FEI STU Bratislava. 2000. (in slovak) Oliveira. P.. Lima. P, Sentineiro. 1.: Fuzzy Supervision on Intelligent Control Systems. ECC 9 I. Grenoble. France, 1991 PfeifTer. B.M., Isermann, R.,: Selftuning of classical controllers with fuzzy-logic. Proc. ofIMACS Symp. "Mathematical and Intelligent models in system Simulation", Brussels 1993 Sekaj, L Foltin. M.: Adaptive Control Based on the Closed-Loop Response Recognition. VDI Berichte, 2000. Nr. 1761-1805. 82-88. Sekaj. L Foltin, M.: Adaptive Control Based on the Closed-Loop Resposne Recognition. Process Control 2001, High Tatras. 188. Sekaj, I.: Genetic Algorithm-Based Control System Design and System Identification, Conferrence Mendel'99, Bmo, Czech Republic,june 91h -12'h 1999, pp. 139-144
+w1
~
-j.
u1
~
Y1
~
TITO
~
u2 - -
Y2 -T
PI 2
REFERENCES
4
~
.--+W 2
Fig. 5. Block scheme of the closed-loop with 2 servo systems For the speed control(r, and Y2) two independent PI controllers are used PI, and PI}, each with two parameters (P and I). An example of the adaptation process is depicted in Fig. 6.
151
Copyright © IFAC Control Systems Design, Bratislava, Slovak Republic, 2003
~
Publications www.elsevier.com/locate/ifac
SELFTU ING PIn
co
TROL BASED ON THE CLOSED-LOOP RESPONSE RECOGNITION Martin Foltin, Ivan Sekaj
Department ofAutomatic Control Systems, Faculty ofElectrical Engineering and Information Technology, Slovak University of Technology, l/kovicova 3. 812 19 Bratislava. Slovak Republic Tel: ++421 260291 506 E-mail :[email protected]. [email protected].
Abstract: A new type of knowledge adaptive control based on the closed-loop response recognition is proposed. This approach tries to mimic the behaviour of an expert, who has a lot of experience with the particular controlled system. The adaptive system updates the controller parameters according to the changes in system behaviour. The algorithm uses a rule-based system, which evaluates the closed-loop response shape after the decay of the transient mode, and computes the corrections of controller parameters. Because the main problem of such a control structure consists in designing of the rule-base, we focused our interest on the design of an automatic procedure for the rule-base generating. Copyright © 2003lFAC Keywords: Self tuning, PID controllers, MIMO, Step response
adaptation". The goal of the following proposed approach is to mimic the human behaviour and to update controller parameters with respect to the required closed-loop response. The underlying idea consists in that after the disturbance occurs we let the transient process decay and then evaluate the c1oseloop response (Fig. I.).
1. INTRODUCTION To control dynamic processes, which behaviour changes in time or which have nonlinear behaviour, adaptive control systems use to be used. In such cases for control algorithms design commonly exact mathematical models and stability and performance conditions are employed. The results obtained by such an approach are often very good, however sometimes problems may emerge e.g. when the complexity or non linearity degree of the model increases or if we have problems with inexact measurements or insufficient a priori information about the process (uncertainty). Thus, sometimes our "exact" mathematical approach and the resulting algorithms cannot be used to control the given process or some phases of it. In that moment it is the task for the human-operator to carry on and to control the process to the required state. The human works with his own model, based on his experience and estimations. He is able to deal with inexact, uncertain, nonnumeric and complex information (he exploits his "natural" intelligence), which in our case, he is able to apply for the process control. Using the operators "manual adaptation" of a complex or non-exactly described processes the results are sometimes better than using an "automatic
Adaptation supervisor Knowledgebased parameter tuning
e
w
+
«-
System
response
Ioil~f---
evaluation
Controller
u
Process f-I__>---,-Y---...
Fig. I. Block scheme of the rule-based adaptation system of a PlO controller. Using a rule-based mechanism, corrections of actual controller parameters are computed. The aim is to design a tuning algorithm, which will provide a good controller adaptation without any exact a-priori information about the process. Similar methods can be found in (Pfeiffer and Isermann, 1993; DeSilva
149
1991; Oliveira, et al., 1991). This method is based on a time-response shape recognition using the leastsquare-error method.
After a single-shot generating of such a database all data are ready for the application in the on-line adaptive system. The Adaptation mechanism is as follows. After the detection of some disturbance in the closed-loop we let decay the transient period. Next the acquired time response is normed and then there is searched for the "most similar" timeresponse from all records in the database, i.e. which minimize the criterion
2. THE ADAPTATION MECHANISM The recognition of the transient response shape is based on the comparison of the time-responses with a set of representative shapes using the least-squareerror method. A brief description of this method is as follows. Consider a "nominal system", which is located (when possible) in the centre of the area A in which the system parameters can move during the normal operation
n
J
= L(YJ.k -
Yk)~ ----). min
(4)
k=1
where Ydk is the closed-loop response from the database under the controller parameters Pd, Id, Dd, d is the ordinal number of the database record with the "most similar" time-response (Fig. 3.) and k is the simulation step.
(I)
where lp, h ID are the considered intervals for the PID parameters, or it is a system, which can be considered as a typical representative of a class of systems (from point of view system response shape). For such a system we design optimal PlO controller parameters p', D' with respect to selected requirements (performance index etc.) (Sekaj, 1999). Then we start to perform a cycle of systematic changes in the PlO controller parameters in a defined universe with defined steps Sp , SI and SD. For each set of actual parameters {Pd, Id, Dd} it is realized a simulation of the closed-loop system with the selected disturbance (set point step etc.). The obtained time-response is written into the database together with the corresponding controller parameters set. The number of such records in the database is
y
t.
"J
t
(2)
Fig. 3. Evaluation of the "most similar" response
where
After retrieving of the selected time-response there is loaded the appropriate set {Pd, I". Dd: from the database or it is interpolated between neighbour items in database.
(3)
The last step is the parameter corrections
For a PI controller the database represents a 2-D table, where each item of the table contains a record of a closed-loop time-response and the set of the corresponding parameters P and I. An example for a particular closed-loop is in the Fig.2, where the marked response represents the desired closed-loop response shape. For the PID case the table is by analogy 3-dimensional.
calculation
of controller
These corrections are used for the actual PlO controller updating ~,~ =
p
P.,,,,,,,, + !1P
1n.... = 1",,,,,f + !'11
Dn.~
=
(6)
D",,,,,,, + !lD
and the algorithm is waiting for new disturbances and then it is repeating. The main steps of the algorithm are as follows: I. 2. Fig. 2. Database of closed-loop time-responses 150
Detection of a disturbance and waiting for the closed-loop response decay Evaluation of the most similar time response from the database using (4)
3. 4.
Interpolation between neighbour PID parameter sets in the database Correction of the actual PID parameter set using (5) and (6)
7.
65·
,2
55
Despite the fact that this algorithm is not trivial for computation, the response evaluation and parameter correction is calculated only at the moment after decay of the transient period. Therefore there are no problems with the implementation in real-time control.
~
~
5
;.
35
30,-----:50~--'=OO--::::'50,.------=""~
3. CASE STUDY
250
DJ
tllIJ
An example of the adaptation process of a DC-drive speed is depicted in Fig. 4.
Fig. 6. Adaptation process of the TITO system control
66
4. CONCLUSION
64 •.
The described knowledge-based adaptation of a PI 1 PID controller mimic the tuning of a controller by an experienced human-operator. The advantage of this approach consists in, that it does not require a mathematical model of the controlled process. It is able to adapt the PI 1 PID controller parameters only after the closed-loop behaviour recognition, after the decay of the transient mode. Another advantage is the possibility to use designed rule-base for a class of similar systems, no matter their time constants are. Experiments in simulation and real-time has shown, that the mentioned adaptation approach is surprising robust and it is working reliable.
62 6
•• '-,.........., I
58.
I
54.
I h
-
r
I --.r'::---
48 46-----o 50
~
100
150
lis)
Fig. 4. Adaptation process of the PID controller of a DC-drive speed
Acknowledgement. This work has been supported by the grant No. 117630/20 "Intelligent methods of modeling and control" of the Slovak Grant Agency.
Another example in case of a more complex controlled object is as follows. The controlled system consists from two servomotors (two input and two output system - TITO). Between the two motors there are strong interactions. The goal is the independent speed control of both motors. The block scheme of the object with the considered control structure is in Fig.5.
e1
PI 1
DeSilva. C.W.: An Analytical Framework for Knowledge-Based Tuning ofServo Controllers, Eng.Applic.Artif.Intellig.. VolA. No.3. 177-189, 1991 Foltin. M.: Design of Knowledge-Based Adaptive Control, thesis. FEI STU Bratislava. 2000. (in slovak) Oliveira. P.. Lima. P, Sentineiro. 1.: Fuzzy Supervision on Intelligent Control Systems. ECC 9 I. Grenoble. France, 1991 PfeifTer. B.M., Isermann, R.,: Selftuning of classical controllers with fuzzy-logic. Proc. ofIMACS Symp. "Mathematical and Intelligent models in system Simulation", Brussels 1993 Sekaj, L Foltin. M.: Adaptive Control Based on the Closed-Loop Response Recognition. VDI Berichte, 2000. Nr. 1761-1805. 82-88. Sekaj. L Foltin, M.: Adaptive Control Based on the Closed-Loop Resposne Recognition. Process Control 2001, High Tatras. 188. Sekaj, I.: Genetic Algorithm-Based Control System Design and System Identification, Conferrence Mendel'99, Bmo, Czech Republic,june 91h -12'h 1999, pp. 139-144
+w1
~
-j.
u1
~
Y1
~
TITO
~
u2 - -
Y2 -T
PI 2
REFERENCES
4
~
.--+W 2
Fig. 5. Block scheme of the closed-loop with 2 servo systems For the speed control(r, and Y2) two independent PI controllers are used PI, and PI}, each with two parameters (P and I). An example of the adaptation process is depicted in Fig. 6.
151