GB2514412A

GB2514412A - Auto-tuning for non-parametric convolution model-based predictive functional controller

Info

Publication number: GB2514412A
Application number: GB1309357.0A
Authority: GB
Inventors: Dejan Dovzan; Igor Skrjanc
Original assignee: Individual
Current assignee: Individual
Priority date: 2013-05-24
Filing date: 2013-05-24
Publication date: 2014-11-26
Anticipated expiration: 2033-05-24
Also published as: GB2514412B; GB201309357D0

Abstract

A method of tuning, preferably auto-tuning (fig.1), of a predictive functional controller 3. The method is based on a non-parametric convolution model of the process 4. It can be used only for stable processes. The method may include the classical PFC control law being altered in a way that only a recorded step response reference 1 can be used for tuning. Such a modification may lower the number of parameters for PFC tuning and simplifies the retuning procedure by skipping a conventional step of identifying the process model parameters. Preferably the method enables the control law to be modified in order to implement anti-windup protection and include an exponential decay of future control signals in the minimization process called implicit filtering 10 of the control signals.

Description

Title: Auto-tuning for non-parametric convolution model-based predictive functional controller

Field of invention

This invention relates to the control systems and, more particularly, to the methods of tuning and auto-tuning for predictive functional controller.

Background of the invention

The predictive functional controller (PEC) is a simple jet effective model predictive control algorithm based on the model of the process. Because of its simplicity and performance it was widely implemented in the industry (see: J. Richalet, A. Rault, J. L. Testud, J. Papon: Model predictive heuristic control: Application to industrial processes. Autornatica, Vol. 14, No. 5, pp.413-428, 1978.; D. Dovan, I. krjanc: Control of mineral wool thickness using predictive functional control. Robot. corn put.-integr.

manuf., Vol. 28, No. 3, pp. 344-350, 2012.).

The PEC has two tuning parameters and the internal process model, which is also a part of the controller. User defined tuning parameters are: the time constant of the reference response and the prediction horizon. The designer must identify the model of the controlled process, its structure and the model parameters, the time constant, gain and process delay must be determined. The determination of model structure is particularly difficult and very important for the quality and robustness of control. The model parameters are usually determined by classical methods such as tangent method, area method, method of moments or any other method. Methods for determining the parameters are presented in K. Aström, 1. I-Iagglund: P1D Controllers: Theory. Design and Tuning.

Instrument Society of America, North Carolina, 1995. The main advantage of proposed invention is the fact that this step can be abandoned.

Since the process parameters usually change during its aging, the controller should be tuned periodically during the process lifespan to insure efficiency of the control loop. The tuning should be done by an expert. However this can be costly and time consuming task, which can be avoided by using auto-tuning methods that do this automatically. The procedure must be also simple from computational aspect to be programed on a low level hardware.

An object of the presented invention is to provide simple tuning procedure of the PFC controller that can be either used by the operator or it can be programmed for automatic tuning. With this invention the step of identifyingthe model parameters can be abandoned. Further invention object is the windup protection of the PFC tuned by a step response model and implicit filtering of the control signal.

Summary of the invention

The invention relates to the auto-tuning procedure of PFC. The presented procedure is based on a non-parametric convolution model of the process. It can be used only for stable processes. According to the invention the classical PFC control law is altered in a way that only the recorded step response can be used for tuning. This lowers the number of parameters for PFC tuning and simplifies the retuning procedure.

The invention is also directed to the realization of exponential future control signal decay that is included in the minimization process. This invention explains how to implement the exponential decay of future control signal change in the minimization procedure.

Further invention aspect is also the implementation of the PFC windup protection, which is integrated directly into control law. The integrated protection is able to constrain the controller output and protect the controlled process against damages, that could happen due to high controller outputs.

The invention is based on modifying the classical PFC control law in order to receive a step response as a tuning parameter. Further the control law is modified to implement the anti-windup protection and include the exponential decay of future control signal in the minimization process called implicit filtering of the control signal. The presented tuning procedure may be done off-line manually or programmed for on-line automatic tuning.

Brief description of the drawings

In the following, the object of the invention will be explained in detail on the basis of the accompanying drawings. For all drawings applies that doubled lines represent a multiple-value data flow, while single lines represent a single-value data flow.

The list of figures: Figure 1: A block diagram illustrating the structure of the PFC automatic tuning.

Figure 2: A block diagram illustrating the structure of the PFC manual tuning.

Figure 3: Graphs representing the signals during the tuning procedure.

Figure 4: Graphical representation of transforming the recorded response of the model to the step response used for tuning the PEC.

Figure 5: Representation of vector &that holds the data about the step response.

Figure 6: Graphical representation of automatic process delay definition.

Figure 7: Graphical representation of the constant future control assumption.

Figure 8: Graphical representation of future control exponential decay assumption (implicit filtering of the control signal).

Detailed description of the invention

Here we present a detailed description of the invention. This invention is not specifically limited to embodiment in either analogue or digital hardware, or software. The following description is generally valid for either implementation.

The tuning procedure as one of the object of invention can be done manually, or can be implemented parallel to controller as automatic tuning procedure. The typical implementation of automatic tuner is shown on Figure 1. Block 1 represents the reference, which the process output must follow. Block 2 represents the error calculation. Block 3 represents the PFC controller, where the controller output is calculated. The user inputs to this block are t5, H and 0r* H denotes the prediction horizon Ur denotes the reference trajectory and t5 denotes the sampling time. The user inputs are given trough user interface represented by block 9. when using the control law that assumes the exponential decay of the future control signal the user must also specify the parameter a. If the windup protection is used the maximal and minimal output of the controller must be defined (Umm, Umax) and anti-windup gain (I<). If there are no process constraints the minimal controller output can be chosen as Umox to reduce the number of user input parameters. Block 4 represents the real plant (process). The output of the process (block 4) is fed back to the switching mechanism (block 7). BlockS represents the tuning mechanism. This mechanism will be described later on. The user inputs to this block are the height of the step dU and the START input. The user inputs them trough user interface represented by block 6.

The input START triggers the recording of process step response, which is in this case also the tuning procedure. The tuner (block 5) is also responsible for switching the switches, represented by block 7 and 8. The switch position a, connects the tuner to the process. Position b connects the PFC controller to the process. Block 10 represents the filter. If the process output is very noisy the filter may be applied on the input of the tuner unit, to smoothen the process output.

The scheme for manual tuning is presented on Figure 2. Here we have only blocks representing the control loop. Block 1 represents the reference input to the system; block 2 calculates the error of the system; block 3 represents the PFC controller and block 4 represents the process. The inputs to the PFC controller (block 5) are the same as with automatic tuner with addition that the user must provide the step response of the process that he recorded manually.

The detailed description of the auto tuning procedure will be given next. The auto tuning procedure can be best described by Figure 3. The tuning procedure is triggered by signal START. The signal is triggered by the user through the user interface (block 6). The way that this signal is triggered depends on the realization of the tuner and the controller. For example if they are both realized in a PLC or microcontroller, the signal can be triggered by a button press. If the tuner is realised in SCADA system, the signal can be triggered by clicking the start button in tuner's SCADA menu. The tuning procedure should be started when the controlled process is in a steady state. The reference must not be changed during the tuning procedure. To prevent changes of the reference during the tuning procedure, simple logic could be implemented that delays the reference changes or discards them while the tuning state (Figure 3, graph 3c) is on. The tuning state 3c should also be displayed in the user interface (Figure 1, block 6). The tuning state 3c is turned on when the user triggers the start of the tuning procedure.

The first ksamples (k= 10) are used to calculate the mean of the controller output (uo). The tuner then switches the position of switches, represented by block 7 and 8 on Figure 1, into position a. The signals are shown on Figure 3, graph 3d. The tuner (block 5 on Figure 1) then outputs the value u0 and tracks the process output for kd samples (kd = 20). The mean of kd samples is then calculated to determine the current working point (yo) of the process. Also the variance of the process output U2Qise is calculated to determine the noise of the process output measurement. Next the tuner outputs the step change seen on Figure 3, graph 3b. The step height is dU, the output of the tuner is u0i-dU. When the step change is applied to the process, the tuner starts recording the process output presented in graph 3a. After 1<5 (k5 = 100) recorded samples the tuner starts tracking mean of the process output.

Two mean values are calculated m1 and m2: m1= ks m2= where k is the current sample and y0isthe process output. When the difference between mean values m1 and m2 is lower than a certain thresholds (s = 0.0001) the recording stops.

if m1 < then STOP the recording According to Figure 3, the sample when recording stops is denoted as kN. Figure 4 represents the procedure after the step response is recorded. The recorded step is shown on graph 4a. From the recorded step response the previously calculated working point (ya) is subtracted. The result is shown on graph 4b. Next the division by the height of the step du is done. The result is shown on graph 4d.

The transformed step response (g) and the noise variance (a2noe) are then transferred to the PFC controller. According to Figure 5, the step response is recorded and transferred to the PFC as a vector of values. The length of the vector g is N. The elements of vector iare the values of transformed step response g at each sample. The time between two samples is defined by sampling time t3.

The tuning signal is turned off (3c) and switches 7 and 8 are turned into position a (3d).

The described tuning procedure can also be done manually. If so the step response and the delay of the process Dare given to F'FC controller through the user interface (Figure 1, block 9).

When the step response is transferred to the PFC, the controller uses this step response as a tuning parameter. In order for the PFC to receive the step response as a tuning parameter its control law must be modified. In the following paragraphs the modification of the control law will be given.

The PFC controller based on the step response model and using convolution can be realized by implementing the following equations:

N

1-a'! ic-' u(k) = (w(k) -y(k)) --y)4u(k -I), YH YH11 where g is the recorded step response gH is the value of step response in H-th sample, N is the length of the recorded step response and Llu is the change of the control signal. The control signal is then calculated as: u(k) = u(k -1) + Au(k) The control law that considers the process delays is given with the following equations: 1 N u(k) = (w(k) -y(k)) -____ --i) -A, YH+D YH+D 1 -jH+D N A = _______ -g3Au(k -1) 9H+D 1=1 u(k) = u(k -1) + Au(k) With the given revision of the standard PFC equations, we can tune the PFC controller with step response, without having to identify the parametric model of the process.

If the PFC is tuned manually the parameters Tr, H and 0 must be specified by the user along with the step response vector g. When auto tuning is used the delay D is calculated from the transferred step response and the noise variance. According to Figure 6, the delay is defined as time from the first sample of the recorded step response to the sample to the sample kN-3. The kN is determined when at least 3 consequent samples of the step response are above the value. The 0r parameter is calculated from the given Tr parameter as: ts a,. = e Ti-, To improve the performance of the base control law we can consider the exponential decaying of the control signal change (Figure 8) in the minimization process (implicit filtering of the control signal). If this is done the denominator gK and of the control law change. The PFC control law is derived from the following equation: Am = Ap, where Am is the model change and Ap is the process change. With the convolution theorem the Am can be written as: Am = y11(k+ H) -y(k) = g1Au(k + H -o +(9D+i -g)u(k -1) and Ap as: Ap = (i -a)(w(k) -Yp(k)) When constant future control is assumed the >r=1 g1Au(k + H -i) is simplified to gAu(k), since the change of the future control action is considered to be zero. If the exponential decay of the control change is considered the Am can be written as: Am = y11(k + H) -y1(k) = ag_1Au(k) + -g1)u(k -I) Here the future samples of the control law were weighted with a: Au(k + 1) = crtAu(k) When using exponential decay assumption, the control laws for the PFC step tuning controller can be written as:

N

1-at' 1 iu(k) = H-i 1 (w(k) -y(k)) - -g,)u(k -I), a gH1 i=o a gn_i 1=1 u(k) = u(k -1) + iu(k), for control when not considering the process delay and as: 1 N 4u(k) = (w(k) -y(k)) -H-i -gD1)u(k -i) -A, 1=0 a gH÷D-i gH+D-i i=i 1* N A = H-I ar -g,)Au(k -0' j= agfl÷ 1=1 u(k) = u(k -1) + iiu(k), for control when considering the process delay. The parameter a is specified bythe user and is defined according to the dominant time constant of the process and has the function of the control signal filtering.

Additional the anti-windup protection may be implemented. The equation u(k) = u(k -1) + zlu(k) is then transformed into: u(k) = u(k -1) + Au(k) -where is the user defined constant and e is calculated as: fO; Iu(k-1)I «=Umax -lu(k -1) -Umax; Iu(k -1)1 > Uniax where is the maximal allowed controller output that is specified by the user.

Claims

Claims: 1. The non-parametric model-based predictive functional control method for stable processes of arbitrary order with or without dead-time and phase non-minimal behavior.
2. The procedure of implicit filtering of control signal for the control method from claimi.
3. The implementation of control signal constraint to prevent controller windup for the control method from claimi.
4. The step response tuning and auto-tuning procedure for the non-parametric model-based predictive functional control method from claimi.