CA2656235C - Methods and devices for the discrete self-adjusting controllers - Google Patents
Methods and devices for the discrete self-adjusting controllers Download PDFInfo
- Publication number
- CA2656235C CA2656235C CA2656235A CA2656235A CA2656235C CA 2656235 C CA2656235 C CA 2656235C CA 2656235 A CA2656235 A CA 2656235A CA 2656235 A CA2656235 A CA 2656235A CA 2656235 C CA2656235 C CA 2656235C
- Authority
- CA
- Canada
- Prior art keywords
- controller
- control
- state parameters
- parameters
- vector
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 14
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 22
- 239000013598 vector Substances 0.000 claims description 31
- UBOXGVDOUJQMTN-UHFFFAOYSA-N 1,1,2-trichloroethane Chemical compound ClCC(Cl)Cl UBOXGVDOUJQMTN-UHFFFAOYSA-N 0.000 claims 1
- 230000010354 integration Effects 0.000 claims 1
- 230000003044 adaptive effect Effects 0.000 abstract description 9
- 230000006870 function Effects 0.000 description 4
- 238000003491 array Methods 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- ZMJBYMUCKBYSCP-UHFFFAOYSA-N Hydroxycitric acid Chemical compound OC(=O)C(O)C(O)(C(O)=O)CC(O)=O ZMJBYMUCKBYSCP-UHFFFAOYSA-N 0.000 description 1
- 206010047531 Visual acuity reduced Diseases 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000004886 process control Methods 0.000 description 1
- 230000001105 regulatory effect Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/0205—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric not using a model or a simulator of the controlled system
- G05B13/024—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric not using a model or a simulator of the controlled system in which a parameter or coefficient is automatically adjusted to optimise the performance
- G05B13/0245—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric not using a model or a simulator of the controlled system in which a parameter or coefficient is automatically adjusted to optimise the performance not using a perturbation signal
Landscapes
- Engineering & Computer Science (AREA)
- Health & Medical Sciences (AREA)
- Artificial Intelligence (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Evolutionary Computation (AREA)
- Medical Informatics (AREA)
- Software Systems (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Automation & Control Theory (AREA)
- Feedback Control In General (AREA)
Abstract
Methods to adjust the controller gains of discrete controllers are suggested. The adjustment relies on a set of parameters called the state parameters. These parameters are combinations of modes, which propagate the deviation from minimum variance control and contribute to more variability of the error variable. The state parameters are re-estimated on-line to portray the real current behavior of the control system, and this re-estimation establishes the self-adjusting algorithm. The algorithm can be used for both adaptive and self-tuning controls. In a nonadaptive environment, the state parameters converge to constant values. In an adaptive environment, the state parameters adapt to new values.
Description
Field of the Invention This invention relates to adaptive and self-tuning controllers for the control of processes, machines and systems. The invention presents algorithms to adjust the controller gains of a discrete controller. The controllers are called self-adjusting controllers because they can be, depending on the environment of the control system, either an adaptive controller or a self-tuning controller.
Background of the Invention The control of a stochastic regulating control is a difficult problem with no satisfactory solution yet. The difficulty in the problem is the model of the disturbance must be modeled in real-time and on-line. An adaptive or self-tuning controller is the correct approach to the solution. The existing algorithms are, however, not adequate because of poor vision. From the first paper in self-tuning control of Astrom, K.J. and Wittenmark, B. ("On Self-tuning Regulators", Automatica, No. 9, 185-189, 1973) to the relatively recent paper of Vu, K. et al ("Recursive Least Determinant Self-tuning Regu-lator", IEE Proceedings - Control Theory and Applications, Vol. 147, No. 3, 285-292, 2000), the algorithms are poor. In the domain of intellectual prop-erty, we see that neither the patent An Improved Self-tuning Controller of the FoxBoro Company (Canadian Patent CA 2,122,472, US Patent 5,587,896) nor the patent Self-tuning process control system of West Instr Limited (UK
Patent GB2279777A) is a good self-tuning algorithm. The reason for these poor performances is the poor choice of the self-tuning parameters.
It turns out that not all the parameters of a controller at one time have clear relations with those at the immediate past. Only a selective set of pa-rameters, called the state parameters, can have these simple relations, which establish the self-tuning algorithm. The rest of the parameters are calculated from these parameters. These parameters are called the state parameters be-cause they represent the state of the dynamics of a process or machine. If these parameters do not change after some tuning period, we have a non-adaptive environment and the algorithm is a self-tuning control algorithm.
On the contrary, if the state parameters constantly change, we have an adap-tive environment and the algorithm is an adaptive control algorithm. For a common name, the algorithm is called a self-adjusting control algorithm.
Summary of the Invention It is the object of this invention to introduce an effective self-adjusting control algorithm to adjust the controller gains of a discrete controller for corrective control of a feedback control system.
It is a further object of this invention to introduce an effective self-adjusting control algorithm to adjust the controller gains of a discrete con-troller for corrective control of a feedforward-feedback control system.
Brief Description of the Drawings Figure I. Block diagram of a self-adjusting discrete feedforward-feedback control system.
Figure 2. Block diagram of the controller part of a digital control chip.
Description of the Preferred Embodiment The possibility to express the output or controlled variable as a function of the controller parameters is the idea behind a self-tuning control algorithm.
In the following, the approach to adjust the parameters of a controller is dis-cussed and the device to implement the self-adjusting algorithm is described.
Method Consider the control system depicted in Figure I. With dt = 0 and yr = 0, the control system is a stochastic feedback control system and is described by the equation yt =
w(z1) 0(z-1) ___________________ ut-f-i + __ at, w(z1) ___________________ llt_f_i 11)(z-1) at or w(z-1)0(z-1)0(z-1)11t + 6(z-1)7(z-1)Yt Yt+ f +1 =
ti(z-1)6)(z-1) 0(z-1)at+f +1, a(z-1)ut b(z-1)yt c(z1) __ + et+ f+11 [ut ut-1 = ' ' Yt Yt-1 " *JO , 'T et+ f +1) c(z1) .
X f+1 1 + + = = = +
+ et+ f +1 =
CLZ-"
When the set point variable yr is not zero, the variable yt can be defined as the deviation of the output variable Yt from the set point. A nonzero dis-turbance (it will give a feedforward-feedback control system and the variable vector Xt+f+i will contain this variable in addition to the other variables ut and yt.
The equation t+ f +1N
is the equation of the minimum variance controller. Such a controller can be used for an industrial process to control the quality of a product. An illustrative example is the control of a paper machine in the paper industry.
The variable yt in Xt+f+1 can be the deviation of the paper sheet moisture from its set point, and the control variable ut is the steam pressure to the dryer of the paper machine.
The parameters ci's are the state parameters. Each state parameter is a combination of the modes that propagate the deviation from minimum variance control and contribute to more variation of the variable ,yt. The controller parameter vector 0 and the state parameters cz's are obtained by minimizing a finite sum of squares of the residual et. The minimization with respect to the controller parameter vector 0 gives, for a finite control horizon at the time t, the following equation CT ¨ tX XT1 Min lim. yT 1 +C2CT2 ______ [C1 C2]Yt (1) t oT
with E as a small positive constant indicating closeness of optimality and the controller parameter vector Ot _ Fr 0 0 XT
1+ [ t ](C2CT2)-1[Xt C]-1 CT
XT
(C2C2T)-1[C1 Cbtt.
Background of the Invention The control of a stochastic regulating control is a difficult problem with no satisfactory solution yet. The difficulty in the problem is the model of the disturbance must be modeled in real-time and on-line. An adaptive or self-tuning controller is the correct approach to the solution. The existing algorithms are, however, not adequate because of poor vision. From the first paper in self-tuning control of Astrom, K.J. and Wittenmark, B. ("On Self-tuning Regulators", Automatica, No. 9, 185-189, 1973) to the relatively recent paper of Vu, K. et al ("Recursive Least Determinant Self-tuning Regu-lator", IEE Proceedings - Control Theory and Applications, Vol. 147, No. 3, 285-292, 2000), the algorithms are poor. In the domain of intellectual prop-erty, we see that neither the patent An Improved Self-tuning Controller of the FoxBoro Company (Canadian Patent CA 2,122,472, US Patent 5,587,896) nor the patent Self-tuning process control system of West Instr Limited (UK
Patent GB2279777A) is a good self-tuning algorithm. The reason for these poor performances is the poor choice of the self-tuning parameters.
It turns out that not all the parameters of a controller at one time have clear relations with those at the immediate past. Only a selective set of pa-rameters, called the state parameters, can have these simple relations, which establish the self-tuning algorithm. The rest of the parameters are calculated from these parameters. These parameters are called the state parameters be-cause they represent the state of the dynamics of a process or machine. If these parameters do not change after some tuning period, we have a non-adaptive environment and the algorithm is a self-tuning control algorithm.
On the contrary, if the state parameters constantly change, we have an adap-tive environment and the algorithm is an adaptive control algorithm. For a common name, the algorithm is called a self-adjusting control algorithm.
Summary of the Invention It is the object of this invention to introduce an effective self-adjusting control algorithm to adjust the controller gains of a discrete controller for corrective control of a feedback control system.
It is a further object of this invention to introduce an effective self-adjusting control algorithm to adjust the controller gains of a discrete con-troller for corrective control of a feedforward-feedback control system.
Brief Description of the Drawings Figure I. Block diagram of a self-adjusting discrete feedforward-feedback control system.
Figure 2. Block diagram of the controller part of a digital control chip.
Description of the Preferred Embodiment The possibility to express the output or controlled variable as a function of the controller parameters is the idea behind a self-tuning control algorithm.
In the following, the approach to adjust the parameters of a controller is dis-cussed and the device to implement the self-adjusting algorithm is described.
Method Consider the control system depicted in Figure I. With dt = 0 and yr = 0, the control system is a stochastic feedback control system and is described by the equation yt =
w(z1) 0(z-1) ___________________ ut-f-i + __ at, w(z1) ___________________ llt_f_i 11)(z-1) at or w(z-1)0(z-1)0(z-1)11t + 6(z-1)7(z-1)Yt Yt+ f +1 =
ti(z-1)6)(z-1) 0(z-1)at+f +1, a(z-1)ut b(z-1)yt c(z1) __ + et+ f+11 [ut ut-1 = ' ' Yt Yt-1 " *JO , 'T et+ f +1) c(z1) .
X f+1 1 + + = = = +
+ et+ f +1 =
CLZ-"
When the set point variable yr is not zero, the variable yt can be defined as the deviation of the output variable Yt from the set point. A nonzero dis-turbance (it will give a feedforward-feedback control system and the variable vector Xt+f+i will contain this variable in addition to the other variables ut and yt.
The equation t+ f +1N
is the equation of the minimum variance controller. Such a controller can be used for an industrial process to control the quality of a product. An illustrative example is the control of a paper machine in the paper industry.
The variable yt in Xt+f+1 can be the deviation of the paper sheet moisture from its set point, and the control variable ut is the steam pressure to the dryer of the paper machine.
The parameters ci's are the state parameters. Each state parameter is a combination of the modes that propagate the deviation from minimum variance control and contribute to more variation of the variable ,yt. The controller parameter vector 0 and the state parameters cz's are obtained by minimizing a finite sum of squares of the residual et. The minimization with respect to the controller parameter vector 0 gives, for a finite control horizon at the time t, the following equation CT ¨ tX XT1 Min lim. yT 1 +C2CT2 ______ [C1 C2]Yt (1) t oT
with E as a small positive constant indicating closeness of optimality and the controller parameter vector Ot _ Fr 0 0 XT
1+ [ t ](C2CT2)-1[Xt C]-1 CT
XT
(C2C2T)-1[C1 Cbtt.
The parameter matrices and vectors in these equations are defined as below CI = = ' 1 = = 1=
C1 C1 = = = 1 c1= , c2=
=
= =
=
0 =
= =
Ci = = = 1 Xto Yto¨t xto+1 Cl = Yto C = , Xt == Yt =
_ci_ = =
xt Yt and xt = [ Veint_f_i = " f -7n Yt- f -1 = " lit- f -n for a feedback controller, xt = [Vdutf -1 = Yt- f -1 ' ' ' dt- f -1- k ' dt-f-p-k for a feedforward-feedback controller with k > 0 as zero or the difference between the dead time of the measured disturbance and that of the plant dynamics and xt = [ Vdnt-f-i Yt-f- 1 Yt- f -2 Yt- f -3 for a three-mode PID (Proportional, Integral and Derivative) controller.
The integer parameters 1, m, n, p and d are the appropriate orders of the controller.
In the conventional approach of self-tuning and adaptive controls, the controller parameter vector at a particular time N, 13N (optimal value of ON), is obtained as a function of the controller parameter vector 13N-1. In this invention, it is the vector of the state parameters c = [c1 c2 = = r at the time N, which is obtained as a function of that at the time N ¨ 1.
C1 C1 = = = 1 c1= , c2=
=
= =
=
0 =
= =
Ci = = = 1 Xto Yto¨t xto+1 Cl = Yto C = , Xt == Yt =
_ci_ = =
xt Yt and xt = [ Veint_f_i = " f -7n Yt- f -1 = " lit- f -n for a feedback controller, xt = [Vdutf -1 = Yt- f -1 ' ' ' dt- f -1- k ' dt-f-p-k for a feedforward-feedback controller with k > 0 as zero or the difference between the dead time of the measured disturbance and that of the plant dynamics and xt = [ Vdnt-f-i Yt-f- 1 Yt- f -2 Yt- f -3 for a three-mode PID (Proportional, Integral and Derivative) controller.
The integer parameters 1, m, n, p and d are the appropriate orders of the controller.
In the conventional approach of self-tuning and adaptive controls, the controller parameter vector at a particular time N, 13N (optimal value of ON), is obtained as a function of the controller parameter vector 13N-1. In this invention, it is the vector of the state parameters c = [c1 c2 = = r at the time N, which is obtained as a function of that at the time N ¨ 1.
The controller for the control criterion Al in E { yt2+ f +1 AVditt2lyt, Yt-1, = ' A > 0 vrdut gives the controller equation T
A I
, f +113t Ecivdut_i =0 cto iO
with ao as the first element of the vector f3t.
The state parameters in c are obtained from Eq. (1) and the controller gains are calculated from these two sets of parameters as given by the last equation. The initial values of these state parameters can be obtained directly from a block of data in the beginning of a control period, from an initial estimate of the controller gains or an estimate for their values. With the arrival of new data, the state parameters in c are re-estimated from Eq. (1).
The methods to adjust the parameters and the controller equation are set forth in the claims. The device to implement the self-adjusting algorithms is described next.
Device The self-adjusting controllers are implemented as a digital chip. On this chip, the controller part of the chip consists of an analog-to-digital converter (ADC), a multiplexer, some read-only memory (ROM) and some random-access memory (RAM). The execution program of the self-adjusting algo-rithms resides in the ROM of the chip. The controller parameters and the variables reside in the RAM. The variable to be controlled along with other variables such as the set point yr and measured disturbance dt, must be fed through the ADC for discretization. The control variable Vdut is out-putted as the width of a pulse. The orders of the controller and the sizes of the arrays for the variables in the self-adjusting algorithms are specified together with the code for the execution program when it is loaded into the ROM of the chip. The configuration of the controller part of the chip is depicted in Figure 2. The operation of the chip is described as follows.
At the time of control, the operating system software of the chip reads the signals provided by the variables Yt, dt if any, and yr. These signals are then multiplexed to the ADC. The execution program of the self-adjusting controller is then invoked to read in these signals and store them in arrays in RAM. The self-adjusting control algorithms are then invoked to operate on these data in RAM to produce a new set of values for the state parameters ci's. The controller gain vector :ji\I is then calculated from these state param-eters. The control variable is then computed from these sets of parameters.
The control action, Vdut - the realization of the control variable, is given by the width of a pulse.
In applications with larger apparatus, the whole controller part can be replaced by a function subroutine in the software of the control computer.
A I
, f +113t Ecivdut_i =0 cto iO
with ao as the first element of the vector f3t.
The state parameters in c are obtained from Eq. (1) and the controller gains are calculated from these two sets of parameters as given by the last equation. The initial values of these state parameters can be obtained directly from a block of data in the beginning of a control period, from an initial estimate of the controller gains or an estimate for their values. With the arrival of new data, the state parameters in c are re-estimated from Eq. (1).
The methods to adjust the parameters and the controller equation are set forth in the claims. The device to implement the self-adjusting algorithms is described next.
Device The self-adjusting controllers are implemented as a digital chip. On this chip, the controller part of the chip consists of an analog-to-digital converter (ADC), a multiplexer, some read-only memory (ROM) and some random-access memory (RAM). The execution program of the self-adjusting algo-rithms resides in the ROM of the chip. The controller parameters and the variables reside in the RAM. The variable to be controlled along with other variables such as the set point yr and measured disturbance dt, must be fed through the ADC for discretization. The control variable Vdut is out-putted as the width of a pulse. The orders of the controller and the sizes of the arrays for the variables in the self-adjusting algorithms are specified together with the code for the execution program when it is loaded into the ROM of the chip. The configuration of the controller part of the chip is depicted in Figure 2. The operation of the chip is described as follows.
At the time of control, the operating system software of the chip reads the signals provided by the variables Yt, dt if any, and yr. These signals are then multiplexed to the ADC. The execution program of the self-adjusting controller is then invoked to read in these signals and store them in arrays in RAM. The self-adjusting control algorithms are then invoked to operate on these data in RAM to produce a new set of values for the state parameters ci's. The controller gain vector :ji\I is then calculated from these state param-eters. The control variable is then computed from these sets of parameters.
The control action, Vdut - the realization of the control variable, is given by the width of a pulse.
In applications with larger apparatus, the whole controller part can be replaced by a function subroutine in the software of the control computer.
Claims (8)
1. A method to design and set up variables for the self-adjusting control al-gorithms of a single-input-single-output feedback, feedforward-feedback or PID controller, which comprises of the following steps:
(a) accepting, from the design of a control engineer, the con-troller type of said controllers and its corresponding or-ders l, m, n and p, (b) accepting, from the design of a control engineer, the de-gree of integration d = 1 for integral action and d = 0 otherwise, (c) accepting, from the design of a control engineer, the penalty constant .lambda. as a small positive constant for smooth control actions, (d) setting up the appropriate matrices and vectors of the variables, in the beginning and at each control time, for the said controllers as below and x t = [ .gradient.d u t-.function.-1 .multidot. .gradient.d u t-.function.-m y t-.function.1 .multidot. y t-.function.-n ]
for a feedback controller, X t = [~ d U t-f-1 .cndot..cndot..cndot. Y t -f-1 .cndot..cndot..cndot. d t- f-1-k .cndot..cndot..cndot. d t-f-p-k ]
for a feedforward-feedback controller with k >= 0 as zero or the difference between the dead time of the measured disturbance and that of the plant dynamics and X t = [ ~ d U t-f-1 Y t-f-1 Y t-f-2 Y t-f-3 ]
for a PID controller.
(a) accepting, from the design of a control engineer, the con-troller type of said controllers and its corresponding or-ders l, m, n and p, (b) accepting, from the design of a control engineer, the de-gree of integration d = 1 for integral action and d = 0 otherwise, (c) accepting, from the design of a control engineer, the penalty constant .lambda. as a small positive constant for smooth control actions, (d) setting up the appropriate matrices and vectors of the variables, in the beginning and at each control time, for the said controllers as below and x t = [ .gradient.d u t-.function.-1 .multidot. .gradient.d u t-.function.-m y t-.function.1 .multidot. y t-.function.-n ]
for a feedback controller, X t = [~ d U t-f-1 .cndot..cndot..cndot. Y t -f-1 .cndot..cndot..cndot. d t- f-1-k .cndot..cndot..cndot. d t-f-p-k ]
for a feedforward-feedback controller with k >= 0 as zero or the difference between the dead time of the measured disturbance and that of the plant dynamics and X t = [ ~ d U t-f-1 Y t-f-1 Y t-f-2 Y t-f-3 ]
for a PID controller.
2. A method to determine the initial values of the state parameters in c for the self-adjusting control algorithms of a discrete control system with a feedback, feedforward-feedback or PID controller, which comprises of the following steps:
(a) choosing the state parameters in c for the following quan-tity to have the minimal value where all the matrices and vectors are set up as shown in step (d) of claim 1 for the appropriate controller and if the initial controller gains are not given, (b) choosing the state parameters in c for the following quan-tity to have the minimal value where all the matrices and vectors are set up as shown in step (d) of claim 1 for the appropriate controller and if the initial controller gain vector .beta. t i , is given, (c) accepting the initial state parameters in c if they are given.
(a) choosing the state parameters in c for the following quan-tity to have the minimal value where all the matrices and vectors are set up as shown in step (d) of claim 1 for the appropriate controller and if the initial controller gains are not given, (b) choosing the state parameters in c for the following quan-tity to have the minimal value where all the matrices and vectors are set up as shown in step (d) of claim 1 for the appropriate controller and if the initial controller gain vector .beta. t i , is given, (c) accepting the initial state parameters in c if they are given.
3. A method to tune the controller gains and calculate the control action of a discrete feedback controller at the control time N, which comprises of the following steps:
(a) determining the parameter µ, with the available values of the state parameters of the last control time in c N-1, for the sum of squares given by the following equation to have the minimal value where all the matrices and vectors are set up as shown in step (d) of claim 1 for a feedback controller and the state parameters in C1 and C2 are set to c = c N1 ¨ µg(c N-1) with g(c N-1) as the vector of the derivatives of S N(c) evaluated at the value C N-1, (b) setting c N = c N-1 if no positive value of µ can be found in step (a) and setting c N = c N-1 ¨ µg(c N-1) otherwise, (c) obtaining the controller parameters from the vector given by with the state parameters in C1 and C2 obtained from step (b), (d) calculating the control action ~ d U N from the following equation with a0 as the first element of the vector ~N.
(a) determining the parameter µ, with the available values of the state parameters of the last control time in c N-1, for the sum of squares given by the following equation to have the minimal value where all the matrices and vectors are set up as shown in step (d) of claim 1 for a feedback controller and the state parameters in C1 and C2 are set to c = c N1 ¨ µg(c N-1) with g(c N-1) as the vector of the derivatives of S N(c) evaluated at the value C N-1, (b) setting c N = c N-1 if no positive value of µ can be found in step (a) and setting c N = c N-1 ¨ µg(c N-1) otherwise, (c) obtaining the controller parameters from the vector given by with the state parameters in C1 and C2 obtained from step (b), (d) calculating the control action ~ d U N from the following equation with a0 as the first element of the vector ~N.
4. A method to adapt the controller gains and calculate the control action of a discrete feedback controller at the control time N, which comprises of the following steps:
(a) determining the state parameter vector c for the sum of squares given by the following equation to have the minimal value where all the matrices and vectors are set up as shown in step (d) of claim 1 for a feedback controller, (b) comparing the two sums of squares S N(c) and S N(c N-1) and accepting the new values of the state parameters c N = c if S N(c) < S N(c N-1) or c N = c N-1 otherwise, (c) obtaining the controller parameters as shown in step (c) of claim 3, (d) calculating the control action ~ d U N as shown in step (d) of claim 3.
(a) determining the state parameter vector c for the sum of squares given by the following equation to have the minimal value where all the matrices and vectors are set up as shown in step (d) of claim 1 for a feedback controller, (b) comparing the two sums of squares S N(c) and S N(c N-1) and accepting the new values of the state parameters c N = c if S N(c) < S N(c N-1) or c N = c N-1 otherwise, (c) obtaining the controller parameters as shown in step (c) of claim 3, (d) calculating the control action ~ d U N as shown in step (d) of claim 3.
5. A method to tune the controller gains and calculate the control action of a discrete feedforward-feedback controller at the control time N, which comprises of the following steps:
(a) determining the parameter µ, with the available values of the state parameters of the last control time in c N-1, for the sum of squares given by the following equation to have the minimal value where all the matrices and vectors are set up as shown in step (d) of claim 1 for a feedforward-feedback controller and the state parameters in C1 and C2 are set to c = c N-1 ¨ µg(c N-1) with g(c N-1) as the vector of the derivatives of S N(c) evaluated at the value c N-1, (b) setting c N = c N-1 if no positive value of µ can be found in step (a) and setting c N = c N-1 ¨ µg(c N-1) otherwise, (c) obtaining the controller parameters and from the vector given by with the state parameters in C1 and C2 obtained from step (b), (d) calculating the control action ~ d U N from the following equation with a0 as the first element of the vector ~ N.
(a) determining the parameter µ, with the available values of the state parameters of the last control time in c N-1, for the sum of squares given by the following equation to have the minimal value where all the matrices and vectors are set up as shown in step (d) of claim 1 for a feedforward-feedback controller and the state parameters in C1 and C2 are set to c = c N-1 ¨ µg(c N-1) with g(c N-1) as the vector of the derivatives of S N(c) evaluated at the value c N-1, (b) setting c N = c N-1 if no positive value of µ can be found in step (a) and setting c N = c N-1 ¨ µg(c N-1) otherwise, (c) obtaining the controller parameters and from the vector given by with the state parameters in C1 and C2 obtained from step (b), (d) calculating the control action ~ d U N from the following equation with a0 as the first element of the vector ~ N.
6. A method to adapt the controller gains and calculate the control action of a discrete feedforward-feedback controller at the control time N, which comprises of the following steps:
(a) determining the state parameter vector c for the sum of squares given by the following equation to have the minimal value where all the matrices and vectors are set up as shown in step (d) of claim 1 for a feedforward-feedback controller, (b) comparing the two sums of squares S N(c) and S N(c N-1) and accepting the new values of the state parameters c N = c if S N(c) < S N(c N-1) or c N = c N-1 otherwise, (c) obtaining the controller parameters as shown in step (c) of claim 5, (d) calculating the control action ~ d U N as shown in step (d) of claim 5.
(a) determining the state parameter vector c for the sum of squares given by the following equation to have the minimal value where all the matrices and vectors are set up as shown in step (d) of claim 1 for a feedforward-feedback controller, (b) comparing the two sums of squares S N(c) and S N(c N-1) and accepting the new values of the state parameters c N = c if S N(c) < S N(c N-1) or c N = c N-1 otherwise, (c) obtaining the controller parameters as shown in step (c) of claim 5, (d) calculating the control action ~ d U N as shown in step (d) of claim 5.
7. A method to tune the controller gains and calculate the control action of a discrete PID controller at the control time N , which comprises of the following steps:
(a) determining the parameter p, with the available values of the state parameters of the last control time cN_1, for the sum of squares given by the following equation to have the minimal value where all the matrices and vectors are set up as shown in step (d) of claim 1 for a PID controller and the state parameters in C1 and C2 are set to c = c N-1 ¨ µg(c N-1) with g(c N-1) as the vector of the derivatives of S N(c) evaluated at the value c N-1, (b) setting c N = c N-1 if no positive value of µ can be found in step (a) and setting c N = c N-1 ¨ µg(c N-1) otherwise, (c) obtaining the gain vector given by the following equation and calculating the controller gains as below with the state parameters in C1 and C2 obtained from step (b), (d) calculating the control action ~ d U N from the following equation ~ d U N = (k p, N + k i, N + K d, N)Y N ¨ (k p, N + 2k d, N) Y N-1 + k d, NYN-2.
(a) determining the parameter p, with the available values of the state parameters of the last control time cN_1, for the sum of squares given by the following equation to have the minimal value where all the matrices and vectors are set up as shown in step (d) of claim 1 for a PID controller and the state parameters in C1 and C2 are set to c = c N-1 ¨ µg(c N-1) with g(c N-1) as the vector of the derivatives of S N(c) evaluated at the value c N-1, (b) setting c N = c N-1 if no positive value of µ can be found in step (a) and setting c N = c N-1 ¨ µg(c N-1) otherwise, (c) obtaining the gain vector given by the following equation and calculating the controller gains as below with the state parameters in C1 and C2 obtained from step (b), (d) calculating the control action ~ d U N from the following equation ~ d U N = (k p, N + k i, N + K d, N)Y N ¨ (k p, N + 2k d, N) Y N-1 + k d, NYN-2.
8. A method to adapt the controller gains and calculate the control action of a discrete PID controller at the control time N, which comprises of the following steps:
(a) determining the state parameter vector c for the sum of squares given by the following equation to have the minimal value where all the matrices and vectors are set up as shown in step (d) of claim 1 for a PID controller, (b) comparing the two sums of squares S N(c) and S N(c N-1) and accepting the new values of the state parameters c N = c if S N(c) < S N(c N-1) or c N = c N-1 otherwise, (c) obtaining the controller gains as shown in step (c) of claim 7, (d) calculating the control action .gradient.d u N as shown in step (d) of claim 7 with the controller gains obtained from the last step (c).
(a) determining the state parameter vector c for the sum of squares given by the following equation to have the minimal value where all the matrices and vectors are set up as shown in step (d) of claim 1 for a PID controller, (b) comparing the two sums of squares S N(c) and S N(c N-1) and accepting the new values of the state parameters c N = c if S N(c) < S N(c N-1) or c N = c N-1 otherwise, (c) obtaining the controller gains as shown in step (c) of claim 7, (d) calculating the control action .gradient.d u N as shown in step (d) of claim 7 with the controller gains obtained from the last step (c).
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA2656235A CA2656235C (en) | 2009-02-16 | 2009-02-16 | Methods and devices for the discrete self-adjusting controllers |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA2656235A CA2656235C (en) | 2009-02-16 | 2009-02-16 | Methods and devices for the discrete self-adjusting controllers |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CA2656235A1 CA2656235A1 (en) | 2010-08-16 |
| CA2656235C true CA2656235C (en) | 2013-12-24 |
Family
ID=42634733
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA2656235A Active CA2656235C (en) | 2009-02-16 | 2009-02-16 | Methods and devices for the discrete self-adjusting controllers |
Country Status (1)
| Country | Link |
|---|---|
| CA (1) | CA2656235C (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108983703A (en) * | 2018-07-06 | 2018-12-11 | 清华大学 | Ultraprecise kinematic system feedforward controller parameter tuning method |
-
2009
- 2009-02-16 CA CA2656235A patent/CA2656235C/en active Active
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108983703A (en) * | 2018-07-06 | 2018-12-11 | 清华大学 | Ultraprecise kinematic system feedforward controller parameter tuning method |
Also Published As
| Publication number | Publication date |
|---|---|
| CA2656235A1 (en) | 2010-08-16 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| EP0159103B1 (en) | Process control apparatus | |
| Zervos et al. | On PID controller tuning using orthonormal series identification | |
| JP4993820B2 (en) | An adaptive estimation model in process control systems. | |
| EP0139243B1 (en) | Process control apparatus | |
| JP5697899B2 (en) | Adaptive controller based on continuously scheduled model parameters | |
| JP4639821B2 (en) | Target value processing device, temperature controller and control process execution system | |
| EP0384437B1 (en) | Method and system for changing control parameters in accordance with state of process in process control | |
| JP2002523821A (en) | Controller for determining optimal tuning parameters used in a process control system and method of operating the controller | |
| WO2007001252A1 (en) | Apparatuses, systems, and methods utilizing adaptive control | |
| JP2015076024A (en) | Plant-control-device control gain optimization system | |
| JP2009510606A (en) | On-demand automatic tuner for plant control systems | |
| CA2656235C (en) | Methods and devices for the discrete self-adjusting controllers | |
| Partanen et al. | The application of an iterative identification and controller design to a sugar cane crushing mill | |
| CN109964180B (en) | Device and method for determining parameters of a control device | |
| JP4982905B2 (en) | Control method and control apparatus | |
| Hess et al. | Industrial Application to a PID Selftuner Used for System Start-Up | |
| WO1998012611A1 (en) | Method and apparatus for automated tuning of pid controllers | |
| Ammar | Tuning model predictive controllers for cross-direction processes | |
| Pathiran | Improving the regulatory response of PID controller using Internal Model Control principles | |
| Prokop et al. | Algebraic principles as a tool for energy saving | |
| Silva et al. | Auto tuning applied to distillation column based on Armax model parameter estimation | |
| JP4119358B2 (en) | Control method and control apparatus | |
| JP7517874B2 (en) | Control device and control method | |
| Ammar | An LMI tuning technique for robust constrained cross-direction controllers | |
| RU159833U1 (en) | SYSTEM OF AUTOMATIC REGULATION OF THE WATER LEVEL IN THE BOILER DRUM |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| EEER | Examination request |