CA1125414A - Adaptive predictive control system - Google Patents
Adaptive predictive control systemInfo
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- CA1125414A CA1125414A CA286,253A CA286253A CA1125414A CA 1125414 A CA1125414 A CA 1125414A CA 286253 A CA286253 A CA 286253A CA 1125414 A CA1125414 A CA 1125414A
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Abstract
ABSTRACT OF THE DISCLOSURE:
In summary the adaptive-predictive control system described uses a digital computer to accomplish the adaptive control of single-input single-output or multivariable time-variant processes with known or unknown parameters and with or without time delays, in such a way that the dynamic output vector of the process is predicted and the control vector, to be applied to the process, is computed with the objective that the predicted dynamic output vector becomes equal to the desired dynamic process output vector.
In summary the adaptive-predictive control system described uses a digital computer to accomplish the adaptive control of single-input single-output or multivariable time-variant processes with known or unknown parameters and with or without time delays, in such a way that the dynamic output vector of the process is predicted and the control vector, to be applied to the process, is computed with the objective that the predicted dynamic output vector becomes equal to the desired dynamic process output vector.
Description
11254~4 The invention concerns an adaptive control system for single-input single-output or multivariable time-variant processes with known or unknown parameters and with or without time delays. The field of applications is unlimited, for example it can be applied to systems in such diverse fields as aeronau-tics, electrotechnics, chemical engineering, etc.
Examples of processes in which the adaptive-predic-tive control system has been applied are single-input single-output control of an aircraft, where the pitch angle is control-led by the elevator position and the multivariable control of adistillation column, where top and bottom composition are control-led by reflux and steam flow rates It is known that the control perfomance of a system with a control structure based on constant parameters deterio-rates when the dynamic parameters of the process vary in an u~foreseen way which can not be measured directly or indirectly.
In recent years control techniques have been devel-oped to try to solve this problem, the most noteworthy of which have been based on the model reference adaptive systems theory, which basically operates in one of the following ways :
(1) Performs a real time adaptive estimation of the parameters and state variables of the process, from which an adaptive regulator computes the control to be applied to the process, or
Examples of processes in which the adaptive-predic-tive control system has been applied are single-input single-output control of an aircraft, where the pitch angle is control-led by the elevator position and the multivariable control of adistillation column, where top and bottom composition are control-led by reflux and steam flow rates It is known that the control perfomance of a system with a control structure based on constant parameters deterio-rates when the dynamic parameters of the process vary in an u~foreseen way which can not be measured directly or indirectly.
In recent years control techniques have been devel-oped to try to solve this problem, the most noteworthy of which have been based on the model reference adaptive systems theory, which basically operates in one of the following ways :
(1) Performs a real time adaptive estimation of the parameters and state variables of the process, from which an adaptive regulator computes the control to be applied to the process, or
(2) Computes the control to be applied to the process through an adaptive control scheme in order to make the process output follow a model reference output. In general in both of the above cases the control structure requires the design of a corrector and the difficulties encountered in the computation of the parameters of this corrector as the order of the process in-creases, severely restricts the field of applications of thesetechniques.
- l -'?!' ~.,, li25414 According to the present invention there is provided a method for generating a control vector during each of a plurality of sampling instants k, said control vector to be applied to an electromechanical apparatus which carries out a process having at least one input variable and at least one output variable, at least one of said input variab~es defining a process input vector, said apparatus varying said process input vector in accordance with the value of said control vector, said method comprising the steps of: storing a model which is capable of predicting the dynamic value of a process output vector, which vector is composed of at least one of said process output variables, at a future sampling instant k+r+l as a function of said control vector; generating a desired dynamic process output vector, independently of said stored model, at each of said sampling instants k, said desired dynamic process output vector being representative of a desired value of said process output vector at said future instant k+r+l; generating, at each of said sampling instants k, that control vector whlch said model predicts will cause said dynamic process output vector to be equal to said desired dynamic process output vector at said future sampling instant k+r+l; and applying said control vector to said apparatus whereby said apparatus varies said process input vector accordingly.
According to the present invention, there i5 also provided a control system for controlling an electromechanlcal apparatus carrying out a process having at least one input variable and at least one output variable, said control system comprising: an electromechanical device for adjusting said at least one input variable as a function of a control vector applied thereto, driver block means responsive to a set point vector v(k) and an instantaneous process output vector ~.~
11;~5~
yp(k) for generating a desired incremental process output vector dl ~k~r+l) during each of a plurality of sampling intervals k, said desired incremental output vector dl (k+r+l) corresponding to the desired incremental change in an output vector of said process between the sampling interval k and the sampling interval k+r+l; control block means responsive to said desired incremental output vector dl (k+r~l) for generating an incre-mental control vector u(k) during each said sampling inter-val k in accordance with an adaptive-predictive model, said adaptive-predictive model serving to predict the process output vector and to determine the incremental control vector u(k) which must be applied to the process during sampling interval k to make the predicted process output vector equal to the desired process output vector during sampling interval k+r+l as determined by said incremental desired output vector dl (k+r+l); said driver block means generating said desired incremental process output vector dl (k+r+l) independently of said adaptive-predictive model; identification block means responsive to said incremental control vector u(kJ and an incremental process output vector y(k) for generating an estimated incremental process output vector d(k) during each said sampling interval k in accordance with said adaptive-predictive model, said estimated incremental process output vector d(k) being representative of the incremental process output which the adaptive-predictive model, as updapted during a sampling interval prior to sampling interval k, predicts should occur during interval k as a result of the generation of the incremental control vector u(k-r-l) during sampling interval k-r-l; means for generating an estimated error vector e(k) during each of said sampling intervals k, said estimated error vector e(k) being representative of the difference between said estimated incremental process output 2a-112S~
vector d(k) and said incremental output vector _(k); feedback means responsive to said estimated error vector e(k) for modifying the parameters of said adaptive-predictive model during each said sampling interval k, said feedback means to modify the parameters of said adaptive-predictive model in such a manner that said estimated error vector e(k~ is reduced towards zero; and means for applying said incremental control u(k) vector to said electromechanical device.
, . .~,.
~ 2b-11~5~
The present invention uses a digital computer to accomplish the adaptive control of single-input sinyle-output or m~ltivariable time-variant processes with known or unknown parameters and with or without time delays, in such a way that the b,ynamic output vector of the process is predicted and the control vector, to be applied to the process, is computed with the objective that the predicted dynamic output vector becomes equal to the desired dynamic output vector, and this is done at every sampling or control instant by a number of simple and specific operations.
The implementation of the invention will be described in a general way with reference to the accompanying figures, followinf this the results of a particular application od the control system will be shown~.
Fig. 1 shows the general and conceptual structure - of the adaptive-predictive control system.
Fig. 2 shows the distillation column on which the adaptive-predictive control system was implemented to carry out a multivariable control of the top and battom compositions as outputs with reflux and steam flow rates as inputs.
Fig. 3 shows results of one such experiment on the adaptive-predictive control of a distillation column..
At any sampling instant K, two modes of operation of the control system are possible; an identification mode and a control mode. Which mode is employed is determined by either a human or an automatic operator 2. In either case, the modes are as shown in Figure 1 :
1)~ Identification mode: In the identification mode, the control vector u (K) is directly applied from the operator 2 to both the apparatus 10 carrying out the process being control-led and the identi~ication block 3 as known by path 1. The iden-tification block 4 uses an adaptive-predictive model stored in 11~5~1~
the computation block 5 to compute an estimated incremental process output vector d(k). An error vector e(k) which re-presents the difference between the actual and estimated in-cremental process output vectory(k) and d(K), respectively, is used to update the parameters of the previously-mentioned adaptive-predictive model through an adaptive feedback machanism 6. The control vector u(k) is delayed by r+l sampling periods in delay block 11 before being acted upon by computation block 5.
2) Control mode: In this mode, the parameters of the adaptive-predictive model are updated as explained above.
The control vector u(K) to be applied to the apparatus 10 being controlled is computed by the control block 8, using the same updated adaptive-p~edictive model as identification block 4, in such a manner that the desired incremental output vector of the process dl(k+r+l), at the sampling instant k+r+l, will be equal to the predicted incremental process output vector at the same instant k+r+l, where r is the number of sampling time delays observed or conveniently considered in the process.
dl(k~r+l) is computed at the instant k by the driver block 9 in reponse to the operator 2 inputs.
The input of driver block 9 is set by the operator of the control system and represents the desired set point value of the output of the process. Driver block 9 generates the desired output trajectory which is desired dynamic trajectory over which the process output reaches the desired static output. dl(k~r+l) is the value of this trajectory at time k+r+l, i.e., the desired process output at instant k+r+l. This value is computed at instant k by the driver block 9 in response to the operator input ~(k) as set forth in some detail of the description of operation on (f) later in he application. As u~k) does not act on the process output until the lnstant k+r+l, the desired output vector ~.:1259~
of the process dl (k+r+l) at instant k must be known in order tocompute u(k). r is the number of sampling delays considered in the process.
~ o properly control the process being carried out by apparatus 10, the adaptive-predictive control system will always use incremental values of the output, input and meas-urable disturbance vectors of the process. Additionally, the control vector can be limit checked. The specifia operations that the control system will carry out, with the help of a digital computer, at every sampling instant k during the control mode are described as follows :
a) Measurement`(by sensor 12) and, if it is considered con-venient, filtering of the output variables of the process carried out to obtain the process output vector yp(k)l the dimension of which is considered to be n.
b) Computation of the incremental process output vector y(k) by:
X(k) = ~p(k) - yp(k-y) (equ.l) Where ~is an integer that can be conveniently chosen and represents the increment of the incremental process output vector ~(k).
c) Computation (in identification block 4) of the estimated incremental process output vector d(k) by the adaptive-pre-dictive model, which can be defined by :
h f d(k) = ~ Ai (k-l) y(k-i-rl) + ~ Biu~k 1-- i--+ ~ Ci(k-l~ w(k-i-r2) tequ. 2) i=l Where the vector u(k-i-r) and w(k-i-r2)are obtaine~ by :
u (k-i-r) = up ~k-i-r) - up(k-i-r-~) (equ. 3) w(k-i-r2) = wp(k-i-r2) - wp(k-i-r2-r) (equ.`h 11254~4 Where up(k-i-r) and wp(k-i-r2) are control and the measurable disturbance vector, respectively, of dimensions nl and m, at the sampling instants k-i-r and k-i-r2, respectively. In equation 2 the integers h, f and g can be conveniently chosen, and like-wise the integers rl and r2 can also be conveniently chosen taking into account the available or forecasted measurements of the output and disturbance vectors, respectively. The matrices Ai(k-l), Bi(k-l) and Ci(k-l~ of the adaptive-predictive model dimensions and their values correspond to a past value before being updated at the instant k. If the dimension of the control vector is bigger than the dimension of the output vector then, in most of the cases, supplementary conditions should be added to obtain a unique control solution, or simply some of the control vector components can be included in the disturbance vector; as a particular case it will be considered that nl=n.
d) Computation of the incremental estimation error vector by :
e(k) = ~(k) _ d(k) (equ.5) e) Computation (in adaptive feedback mechanism 6) of the updated values at instant k of the parameters aijq(k), bijq(k), and cijq(k), that are the elements in the jth row and qth column of the matrices Ai(k), Bi(k) and Ci(k), respectively, by means of the following algorithms :
aijq(k) = ~aijq4j(k) ej(k) yq(k-i-rl) + aijq(k-l) (equ.6) bijq(k) = ~bijq~ (k) ej(k) uq(k-i-r) + bijq~k~l) (equ.7 - - cijq(k) = ~cijq ~ (k) ej(k) wq(k-i~r2) + cijq(k~l) (equ.8) Where ej(k), yq(k-i-rl), uq(k-i-r) and wq(k-i-r2) are the corresponding components of the vectors e(k), ~(k-i-r), u(k-i-r) and w(k-i-r), reQpectively ~aijq' ~bijqand ~cijq are coefficients that ca~ be conveniently tuned, and aj(k) (j=l,n) are variable 112S4~4 gains that can be easely chosen among the wide range of possi-bilities that the well known gradient parameter identification techniques permit. A particular choice of these variable gains can be the following : h n aj(k) = 1/~1+ ~ ~ ~aijq Yp~k~i-rl)2 i=l q=1 f n g m + ~ ~ ~bijq Uq(k-i-r)2 + ~ ~ ~cijq wq~k-i-r2) i=j q=l i=j q=l ~ n) (equ. g) f) Computation (in driver block gk of the desired incremental output vector dl(k+r+l), which can be carried out as follows:
1. Computation of the desired process output vector dp(k+r+l) of dimension (nxl) which can be done in various ways, such as using a model reference with desired dynamics or using any other design that will take into account the desired dynamics and also the previously measured or forecasted process out-puts. For example, this last type of design can be defined by the following equation :
t s dp(k+r+l) = ~ F; yp(k+r+l-rl-i) +'~ Hj v(k+l-i) (equ. 10) i=l ,~=1 Where yp ~k+~+l-rl-i) and v(k+l-i) are the process output vector and the driver block input vector at the sampling instant k+r+l-rl-i and k+l-i, respectively. v~k+1-1) is a vector of dimension n, that is generated directly by the -- operator; and the matrices Fi(i = 1, t) and Hj(j = 1, s) as well as the integers t and s, can be chosen freely, to take - into account the desired dynamics. An illustration of this choice is given in the Experimental Example, below.
2. From the value of the desired output vector of the process dp~k+r+l), the desired incremental output vector dl~k+r+l) can be easely computed in various manners; a particular one, ~: ' ll~S~i~
usually convenient when y~r, is given by the following equation:
dl(k+r+l) = dp(k+r+l) - ~p(k+r+l-~) teqU. 11) IE found necessary the value of dl(k+r+l) can be limit checked.
g) Computation (in control block 8) of the control vector may be made according to the following :
1. From the updated adaptive-predictive model (updated by the output of adaptive feedback mechanism 6), the predicted incre-mental process output vector di~k+r+l) at the sampling instant k+r+l, will depend upon the incremental control vector u(k), and is given by the equation :
h f d;~k+r=l) = ~ Ai(k) ~(k+r+l-rl-i) + ~ Bi(k) u(k+l-i) i=l i=l + ~ Ci(k) w(k+r+l-r2-i) (equ. 12) i=l The incremental control vector u(k) is computed by making the predicted incremental process output vector dl(k+r+l) equal to the desired incremental output dl(k+r+l) and is given by :
r u(k) = Bl1(k) dl(k+r+l) - Bl ~ Bi( ) _( Bl (k) ~ Al(k) y(k+r+l-r~ Bl (k) ~ Ci(k) w(k+r+l+r2 (equ. 13) 2. From u(k), the control vector will be computed by :
up~k) = u(k) + up(k-r) (equ. 14) h) If desired,the control vector up(k) can be limited checked be-fore being applied to the process.
In its implementation the adaptive-predictive control system ~o can use incremental input, output and disturbance vectors as described in the above operations; but another way of imple-menting the system is to compute the incremental input, output :, ' ,~ . ,.
5~
and disturbance vectors with respect to some constant vectors chosen conveniently and, conse~uently, in the specific equations described above the equation 1, 3, 4, 11 and 14 need to be respectivelly modified as follows :
y(k) = ~p~k) ~ Ypc (equ. 15) u(k-i-r) = up(k-i-r) - UpC (equ. 16) w(k-i-r2) = wp(k-i-r2) wpc (equ. 17) dl(k+r+1) = dp(k~r+l) - y (equ. 1~) Up(k) = u(k) + UpC (equ. 19) Likewise, when it is considered convenient to give specific values to some of the adapt-ive-pre~ictive model parame-ters (for instance, because of a certain knowledge of the proc-ess), these ~alues can be given to the respective parameters and the corresponding~ coefficients will be set to zero. Also it is possible to stop the updating operations of the adaptive-predictive model parameters as long as it is considered con-venient.
When the system performs in its identification mode it only needs to carry out the operations a to e, and this iden-tification action can be performed in reattime or off-line, and even in between the sampling intervals.
It will be observed that in the operation g to compute u(k), the matrix Bl(k) must be inverted. The risk of singularity of the matrix Bl(k) can be practically almost always avoided by adding time delays to the components of the input and output process vector, and controlling the resultant process. An illus-trative experimen~tal example of this procedure is presented in this patent application.
- l -'?!' ~.,, li25414 According to the present invention there is provided a method for generating a control vector during each of a plurality of sampling instants k, said control vector to be applied to an electromechanical apparatus which carries out a process having at least one input variable and at least one output variable, at least one of said input variab~es defining a process input vector, said apparatus varying said process input vector in accordance with the value of said control vector, said method comprising the steps of: storing a model which is capable of predicting the dynamic value of a process output vector, which vector is composed of at least one of said process output variables, at a future sampling instant k+r+l as a function of said control vector; generating a desired dynamic process output vector, independently of said stored model, at each of said sampling instants k, said desired dynamic process output vector being representative of a desired value of said process output vector at said future instant k+r+l; generating, at each of said sampling instants k, that control vector whlch said model predicts will cause said dynamic process output vector to be equal to said desired dynamic process output vector at said future sampling instant k+r+l; and applying said control vector to said apparatus whereby said apparatus varies said process input vector accordingly.
According to the present invention, there i5 also provided a control system for controlling an electromechanlcal apparatus carrying out a process having at least one input variable and at least one output variable, said control system comprising: an electromechanical device for adjusting said at least one input variable as a function of a control vector applied thereto, driver block means responsive to a set point vector v(k) and an instantaneous process output vector ~.~
11;~5~
yp(k) for generating a desired incremental process output vector dl ~k~r+l) during each of a plurality of sampling intervals k, said desired incremental output vector dl (k+r+l) corresponding to the desired incremental change in an output vector of said process between the sampling interval k and the sampling interval k+r+l; control block means responsive to said desired incremental output vector dl (k+r~l) for generating an incre-mental control vector u(k) during each said sampling inter-val k in accordance with an adaptive-predictive model, said adaptive-predictive model serving to predict the process output vector and to determine the incremental control vector u(k) which must be applied to the process during sampling interval k to make the predicted process output vector equal to the desired process output vector during sampling interval k+r+l as determined by said incremental desired output vector dl (k+r+l); said driver block means generating said desired incremental process output vector dl (k+r+l) independently of said adaptive-predictive model; identification block means responsive to said incremental control vector u(kJ and an incremental process output vector y(k) for generating an estimated incremental process output vector d(k) during each said sampling interval k in accordance with said adaptive-predictive model, said estimated incremental process output vector d(k) being representative of the incremental process output which the adaptive-predictive model, as updapted during a sampling interval prior to sampling interval k, predicts should occur during interval k as a result of the generation of the incremental control vector u(k-r-l) during sampling interval k-r-l; means for generating an estimated error vector e(k) during each of said sampling intervals k, said estimated error vector e(k) being representative of the difference between said estimated incremental process output 2a-112S~
vector d(k) and said incremental output vector _(k); feedback means responsive to said estimated error vector e(k) for modifying the parameters of said adaptive-predictive model during each said sampling interval k, said feedback means to modify the parameters of said adaptive-predictive model in such a manner that said estimated error vector e(k~ is reduced towards zero; and means for applying said incremental control u(k) vector to said electromechanical device.
, . .~,.
~ 2b-11~5~
The present invention uses a digital computer to accomplish the adaptive control of single-input sinyle-output or m~ltivariable time-variant processes with known or unknown parameters and with or without time delays, in such a way that the b,ynamic output vector of the process is predicted and the control vector, to be applied to the process, is computed with the objective that the predicted dynamic output vector becomes equal to the desired dynamic output vector, and this is done at every sampling or control instant by a number of simple and specific operations.
The implementation of the invention will be described in a general way with reference to the accompanying figures, followinf this the results of a particular application od the control system will be shown~.
Fig. 1 shows the general and conceptual structure - of the adaptive-predictive control system.
Fig. 2 shows the distillation column on which the adaptive-predictive control system was implemented to carry out a multivariable control of the top and battom compositions as outputs with reflux and steam flow rates as inputs.
Fig. 3 shows results of one such experiment on the adaptive-predictive control of a distillation column..
At any sampling instant K, two modes of operation of the control system are possible; an identification mode and a control mode. Which mode is employed is determined by either a human or an automatic operator 2. In either case, the modes are as shown in Figure 1 :
1)~ Identification mode: In the identification mode, the control vector u (K) is directly applied from the operator 2 to both the apparatus 10 carrying out the process being control-led and the identi~ication block 3 as known by path 1. The iden-tification block 4 uses an adaptive-predictive model stored in 11~5~1~
the computation block 5 to compute an estimated incremental process output vector d(k). An error vector e(k) which re-presents the difference between the actual and estimated in-cremental process output vectory(k) and d(K), respectively, is used to update the parameters of the previously-mentioned adaptive-predictive model through an adaptive feedback machanism 6. The control vector u(k) is delayed by r+l sampling periods in delay block 11 before being acted upon by computation block 5.
2) Control mode: In this mode, the parameters of the adaptive-predictive model are updated as explained above.
The control vector u(K) to be applied to the apparatus 10 being controlled is computed by the control block 8, using the same updated adaptive-p~edictive model as identification block 4, in such a manner that the desired incremental output vector of the process dl(k+r+l), at the sampling instant k+r+l, will be equal to the predicted incremental process output vector at the same instant k+r+l, where r is the number of sampling time delays observed or conveniently considered in the process.
dl(k~r+l) is computed at the instant k by the driver block 9 in reponse to the operator 2 inputs.
The input of driver block 9 is set by the operator of the control system and represents the desired set point value of the output of the process. Driver block 9 generates the desired output trajectory which is desired dynamic trajectory over which the process output reaches the desired static output. dl(k~r+l) is the value of this trajectory at time k+r+l, i.e., the desired process output at instant k+r+l. This value is computed at instant k by the driver block 9 in response to the operator input ~(k) as set forth in some detail of the description of operation on (f) later in he application. As u~k) does not act on the process output until the lnstant k+r+l, the desired output vector ~.:1259~
of the process dl (k+r+l) at instant k must be known in order tocompute u(k). r is the number of sampling delays considered in the process.
~ o properly control the process being carried out by apparatus 10, the adaptive-predictive control system will always use incremental values of the output, input and meas-urable disturbance vectors of the process. Additionally, the control vector can be limit checked. The specifia operations that the control system will carry out, with the help of a digital computer, at every sampling instant k during the control mode are described as follows :
a) Measurement`(by sensor 12) and, if it is considered con-venient, filtering of the output variables of the process carried out to obtain the process output vector yp(k)l the dimension of which is considered to be n.
b) Computation of the incremental process output vector y(k) by:
X(k) = ~p(k) - yp(k-y) (equ.l) Where ~is an integer that can be conveniently chosen and represents the increment of the incremental process output vector ~(k).
c) Computation (in identification block 4) of the estimated incremental process output vector d(k) by the adaptive-pre-dictive model, which can be defined by :
h f d(k) = ~ Ai (k-l) y(k-i-rl) + ~ Biu~k 1-- i--+ ~ Ci(k-l~ w(k-i-r2) tequ. 2) i=l Where the vector u(k-i-r) and w(k-i-r2)are obtaine~ by :
u (k-i-r) = up ~k-i-r) - up(k-i-r-~) (equ. 3) w(k-i-r2) = wp(k-i-r2) - wp(k-i-r2-r) (equ.`h 11254~4 Where up(k-i-r) and wp(k-i-r2) are control and the measurable disturbance vector, respectively, of dimensions nl and m, at the sampling instants k-i-r and k-i-r2, respectively. In equation 2 the integers h, f and g can be conveniently chosen, and like-wise the integers rl and r2 can also be conveniently chosen taking into account the available or forecasted measurements of the output and disturbance vectors, respectively. The matrices Ai(k-l), Bi(k-l) and Ci(k-l~ of the adaptive-predictive model dimensions and their values correspond to a past value before being updated at the instant k. If the dimension of the control vector is bigger than the dimension of the output vector then, in most of the cases, supplementary conditions should be added to obtain a unique control solution, or simply some of the control vector components can be included in the disturbance vector; as a particular case it will be considered that nl=n.
d) Computation of the incremental estimation error vector by :
e(k) = ~(k) _ d(k) (equ.5) e) Computation (in adaptive feedback mechanism 6) of the updated values at instant k of the parameters aijq(k), bijq(k), and cijq(k), that are the elements in the jth row and qth column of the matrices Ai(k), Bi(k) and Ci(k), respectively, by means of the following algorithms :
aijq(k) = ~aijq4j(k) ej(k) yq(k-i-rl) + aijq(k-l) (equ.6) bijq(k) = ~bijq~ (k) ej(k) uq(k-i-r) + bijq~k~l) (equ.7 - - cijq(k) = ~cijq ~ (k) ej(k) wq(k-i~r2) + cijq(k~l) (equ.8) Where ej(k), yq(k-i-rl), uq(k-i-r) and wq(k-i-r2) are the corresponding components of the vectors e(k), ~(k-i-r), u(k-i-r) and w(k-i-r), reQpectively ~aijq' ~bijqand ~cijq are coefficients that ca~ be conveniently tuned, and aj(k) (j=l,n) are variable 112S4~4 gains that can be easely chosen among the wide range of possi-bilities that the well known gradient parameter identification techniques permit. A particular choice of these variable gains can be the following : h n aj(k) = 1/~1+ ~ ~ ~aijq Yp~k~i-rl)2 i=l q=1 f n g m + ~ ~ ~bijq Uq(k-i-r)2 + ~ ~ ~cijq wq~k-i-r2) i=j q=l i=j q=l ~ n) (equ. g) f) Computation (in driver block gk of the desired incremental output vector dl(k+r+l), which can be carried out as follows:
1. Computation of the desired process output vector dp(k+r+l) of dimension (nxl) which can be done in various ways, such as using a model reference with desired dynamics or using any other design that will take into account the desired dynamics and also the previously measured or forecasted process out-puts. For example, this last type of design can be defined by the following equation :
t s dp(k+r+l) = ~ F; yp(k+r+l-rl-i) +'~ Hj v(k+l-i) (equ. 10) i=l ,~=1 Where yp ~k+~+l-rl-i) and v(k+l-i) are the process output vector and the driver block input vector at the sampling instant k+r+l-rl-i and k+l-i, respectively. v~k+1-1) is a vector of dimension n, that is generated directly by the -- operator; and the matrices Fi(i = 1, t) and Hj(j = 1, s) as well as the integers t and s, can be chosen freely, to take - into account the desired dynamics. An illustration of this choice is given in the Experimental Example, below.
2. From the value of the desired output vector of the process dp~k+r+l), the desired incremental output vector dl~k+r+l) can be easely computed in various manners; a particular one, ~: ' ll~S~i~
usually convenient when y~r, is given by the following equation:
dl(k+r+l) = dp(k+r+l) - ~p(k+r+l-~) teqU. 11) IE found necessary the value of dl(k+r+l) can be limit checked.
g) Computation (in control block 8) of the control vector may be made according to the following :
1. From the updated adaptive-predictive model (updated by the output of adaptive feedback mechanism 6), the predicted incre-mental process output vector di~k+r+l) at the sampling instant k+r+l, will depend upon the incremental control vector u(k), and is given by the equation :
h f d;~k+r=l) = ~ Ai(k) ~(k+r+l-rl-i) + ~ Bi(k) u(k+l-i) i=l i=l + ~ Ci(k) w(k+r+l-r2-i) (equ. 12) i=l The incremental control vector u(k) is computed by making the predicted incremental process output vector dl(k+r+l) equal to the desired incremental output dl(k+r+l) and is given by :
r u(k) = Bl1(k) dl(k+r+l) - Bl ~ Bi( ) _( Bl (k) ~ Al(k) y(k+r+l-r~ Bl (k) ~ Ci(k) w(k+r+l+r2 (equ. 13) 2. From u(k), the control vector will be computed by :
up~k) = u(k) + up(k-r) (equ. 14) h) If desired,the control vector up(k) can be limited checked be-fore being applied to the process.
In its implementation the adaptive-predictive control system ~o can use incremental input, output and disturbance vectors as described in the above operations; but another way of imple-menting the system is to compute the incremental input, output :, ' ,~ . ,.
5~
and disturbance vectors with respect to some constant vectors chosen conveniently and, conse~uently, in the specific equations described above the equation 1, 3, 4, 11 and 14 need to be respectivelly modified as follows :
y(k) = ~p~k) ~ Ypc (equ. 15) u(k-i-r) = up(k-i-r) - UpC (equ. 16) w(k-i-r2) = wp(k-i-r2) wpc (equ. 17) dl(k+r+1) = dp(k~r+l) - y (equ. 1~) Up(k) = u(k) + UpC (equ. 19) Likewise, when it is considered convenient to give specific values to some of the adapt-ive-pre~ictive model parame-ters (for instance, because of a certain knowledge of the proc-ess), these ~alues can be given to the respective parameters and the corresponding~ coefficients will be set to zero. Also it is possible to stop the updating operations of the adaptive-predictive model parameters as long as it is considered con-venient.
When the system performs in its identification mode it only needs to carry out the operations a to e, and this iden-tification action can be performed in reattime or off-line, and even in between the sampling intervals.
It will be observed that in the operation g to compute u(k), the matrix Bl(k) must be inverted. The risk of singularity of the matrix Bl(k) can be practically almost always avoided by adding time delays to the components of the input and output process vector, and controlling the resultant process. An illus-trative experimen~tal example of this procedure is presented in this patent application.
3~ Another way of implementing the control system is to put the adaptive-predictive model in form that the vector d(k) will not be the estimation of the vector y(k), but the estimation B g i~Z~4 of any other output or input vector in a previous sampling ins-tant; the error of this estimation will be used to update the adaptive-predictive model.
In some cases, an equivalent way of applying the control system presented here, is to decompose it to a set of single-output multi-input systems, each one of which will im-pose a condition to ve verified by the components of the con-trol vector at every sampling instant, and from the set of the n corresponding linear equations the control vector can be computed ar every sampling instant.
Finally, the static gains of the process can be modified by multiplying the componets of its output, input, and disturbance vectors or incremental vectors by scalars gain;
also the dynamics of the process can be modified in an analogous way; in this control system will control the process through the control of the modified process-.
EXPE~IMENTAL EXAMPLE: Multivariable control of a binary distil-. _ lation column.
The adaptive-predictive control system, previously described, has been implemented for the multivariable control of top and bottom compositions(in weight % of methanol) of a binary distillation column, at the Chemical Engineering Depart-ment, University of Alberta, Edmonton, Alberta (~anada).
As shown in Figure 2, the feed flow 11 enters into the distillation column 10 at the fourth ashtray, the top pro-duct condensates in 12 by cooling water, and falls to the con-tainer 13. The objective of the exper1ment that we are going to present is to control the composition of the bottom product 15, that goes away from the bottom of the column.
We have use as control variables, the reflux flow rate 16 and the steam flow rate 17, that heats the reboiler 18 in the bottom of the column. To accomplish the experlment we 5~
have used a digital computer 19, that takes the ~easurements of top and bottom compositions made by a composition recorder 20 and a gas chromatograph system 21, respectively, and that controls the setpoint of the flow recorder controllers 22 and 23. In addition the column had the following equipment: two liquid level indicator controller 24, two flow records 25, a pressure indicator controller 26, two temperature recorder controller 27 and a flow recorder controller 28.
The control variables were the reflux and the steam flow rates, and the sampling period was of 256 sec. Due to this large sampling period, there is no time delay between top com-position and reflux and steam flow rates. There exists a mea-surement time delay of one sampling period between bottom com-position and steam flow rate, because of the analysis time needed to measure the bottom composition, and the time delay between bottom composition and reflux rate was observed to be two sampling intervals. No significant disturbance was acting upon the process.
To avoid the problem of the singularity of B1~k), previously discussed, a sampling time delay was added to the top composition measurement; consequently, the corresponding component of the process output vector related to the top com-position at the sampling instant k, is the measurement of the top composition at instant k-l; likewise this component at instant k+l, is already known at instant k.
In accordance with the previously described circum-stances, at every sampling instant k, the sequence of operations performed by the adaptive-predictive control system during its control action were:
1) Measurement of top and bottom compositions to obtain the pro-cess output vector yp~k), the components of which are the top composition measured at k-l, ypl(k)~ and the bottom composition ~1254i~
measured at k, yp2~k).
2. The number of sampling ~ime delay considered for the process r is, in this case, equal to 1, and the integary was chosen equal to 2; consequently the increments output vector is computed by: ~
~(k) = yp(k) - yp(k-2) (equ. 20) 3. In the adaptive-predictive model the integer h, f and rl were chosen equal to 3, 4 and 0, respectively, and no disturb-ance vector was considered; consequently; the estimated incre-mental output vector d(k) was computed by :
dl~k) 3 Yl(k-i) 4 ul(k~ ) = ~ Ai(k-lj i-l (equ.21) d2(k) Y2(k-1) l u2(k-i-1) ~
Where dland Yl are the compo lents related to the top compo-sition; and d2 and Y2 are the components related to the bottom composition. ul and u2 are the incremental reflux and steam flow r-ates respectively. The incremental control vector u(k-i-l) is obtained by :
u(k-i-l) = up(k-i-l) - up(k-i-3) (equ. 22) Where up(k-i-l) is the control vector applied at instant k-i-l, The matrices Ai~k-i-l) ~i = 1, 3) and Bi~k-l) ~i = 1, 4) were chosen being :
.
alll~k-l) O a211~k-1) 0 Al(k-l) = ; A2~k-1) = ; A3(k-1) =
0 0 a222'k-1) l =1~ 1 L a322~k-~,.,' ~b~ k-l) bll2(k-1)1 211(k-1) b212(k-1 Bl(k-l) = ; B2(k-1) =
_ bl22(k-l) 221(k-1) b222(k-1 -O O- -O O-B3(k-1) = ; B4~k-1) =
321(k 1~ b322(k-l) . 421(k 1) 0
In some cases, an equivalent way of applying the control system presented here, is to decompose it to a set of single-output multi-input systems, each one of which will im-pose a condition to ve verified by the components of the con-trol vector at every sampling instant, and from the set of the n corresponding linear equations the control vector can be computed ar every sampling instant.
Finally, the static gains of the process can be modified by multiplying the componets of its output, input, and disturbance vectors or incremental vectors by scalars gain;
also the dynamics of the process can be modified in an analogous way; in this control system will control the process through the control of the modified process-.
EXPE~IMENTAL EXAMPLE: Multivariable control of a binary distil-. _ lation column.
The adaptive-predictive control system, previously described, has been implemented for the multivariable control of top and bottom compositions(in weight % of methanol) of a binary distillation column, at the Chemical Engineering Depart-ment, University of Alberta, Edmonton, Alberta (~anada).
As shown in Figure 2, the feed flow 11 enters into the distillation column 10 at the fourth ashtray, the top pro-duct condensates in 12 by cooling water, and falls to the con-tainer 13. The objective of the exper1ment that we are going to present is to control the composition of the bottom product 15, that goes away from the bottom of the column.
We have use as control variables, the reflux flow rate 16 and the steam flow rate 17, that heats the reboiler 18 in the bottom of the column. To accomplish the experlment we 5~
have used a digital computer 19, that takes the ~easurements of top and bottom compositions made by a composition recorder 20 and a gas chromatograph system 21, respectively, and that controls the setpoint of the flow recorder controllers 22 and 23. In addition the column had the following equipment: two liquid level indicator controller 24, two flow records 25, a pressure indicator controller 26, two temperature recorder controller 27 and a flow recorder controller 28.
The control variables were the reflux and the steam flow rates, and the sampling period was of 256 sec. Due to this large sampling period, there is no time delay between top com-position and reflux and steam flow rates. There exists a mea-surement time delay of one sampling period between bottom com-position and steam flow rate, because of the analysis time needed to measure the bottom composition, and the time delay between bottom composition and reflux rate was observed to be two sampling intervals. No significant disturbance was acting upon the process.
To avoid the problem of the singularity of B1~k), previously discussed, a sampling time delay was added to the top composition measurement; consequently, the corresponding component of the process output vector related to the top com-position at the sampling instant k, is the measurement of the top composition at instant k-l; likewise this component at instant k+l, is already known at instant k.
In accordance with the previously described circum-stances, at every sampling instant k, the sequence of operations performed by the adaptive-predictive control system during its control action were:
1) Measurement of top and bottom compositions to obtain the pro-cess output vector yp~k), the components of which are the top composition measured at k-l, ypl(k)~ and the bottom composition ~1254i~
measured at k, yp2~k).
2. The number of sampling ~ime delay considered for the process r is, in this case, equal to 1, and the integary was chosen equal to 2; consequently the increments output vector is computed by: ~
~(k) = yp(k) - yp(k-2) (equ. 20) 3. In the adaptive-predictive model the integer h, f and rl were chosen equal to 3, 4 and 0, respectively, and no disturb-ance vector was considered; consequently; the estimated incre-mental output vector d(k) was computed by :
dl~k) 3 Yl(k-i) 4 ul(k~ ) = ~ Ai(k-lj i-l (equ.21) d2(k) Y2(k-1) l u2(k-i-1) ~
Where dland Yl are the compo lents related to the top compo-sition; and d2 and Y2 are the components related to the bottom composition. ul and u2 are the incremental reflux and steam flow r-ates respectively. The incremental control vector u(k-i-l) is obtained by :
u(k-i-l) = up(k-i-l) - up(k-i-3) (equ. 22) Where up(k-i-l) is the control vector applied at instant k-i-l, The matrices Ai~k-i-l) ~i = 1, 3) and Bi~k-l) ~i = 1, 4) were chosen being :
.
alll~k-l) O a211~k-1) 0 Al(k-l) = ; A2~k-1) = ; A3(k-1) =
0 0 a222'k-1) l =1~ 1 L a322~k-~,.,' ~b~ k-l) bll2(k-1)1 211(k-1) b212(k-1 Bl(k-l) = ; B2(k-1) =
_ bl22(k-l) 221(k-1) b222(k-1 -O O- -O O-B3(k-1) = ; B4~k-1) =
321(k 1~ b322(k-l) . 421(k 1) 0
4. Computation of the estimation error vector as indicated in equation 5.
5. Computation of the updated values at instant k of the para-meters of the matrices Ai(k) (i = 1, 3) and Bi(k) (i = 1,4), accor-ding to the equations 6, 7 and 9, taking into account that no disturbances were considered and that the value of the coeffi-cients ~ corresponding to the non-zero parameters in the top and botton rows were set to 1 and 0.1, respectively, and the ~' s corresponding to remaining zero parameters in both the rows were set equal 0.
6. The components of the desired process output vector dp~k+2) at instant k+2, dpl(k+2)and dp2(k+2).,related to top and bottom compositions, respectively, are computed by the following scalar : .equations, that are a particular case of the equation 10:
dpl(k+2) =i~l fliYl(k+2-i) +i~l hli Vl( ) (equ. 23) - i=l 2i 2 i) +i~l h2i v2~k+l-i~ (equ. 24) Where vl(k+l-i) and v2(k+1-i) are the compone~ts related to the top and bottom compositions, respectively, of the driver block input vector v(k+l-i) at instant k+l-i. The parameters of equations 23 and 24 were chosen equal to those of a second order model, without and with a sampling time delay respectively, a natural frequency of 0.0056 rad/sec, a damping ratio and static ;, :' '' llZ5~14 gain equal to 1. Given that the value of the previously men-tioned static gain is the unity, the components vl(k+l-i) and v2~k+1-i) have the physical meaning of being the setpoint values for top and bottom compositions, respectively, at instan~ k+l-i.
In equation 23 the value yl(k+l) was previously computed by :
yl(k+l) = Ypl(k+l) ~ Ypl(k-l) (equ. 25) Note that ypl(k+l~ is the value of the top compositions measured at instant k.
From dp(k+2) the desired incremental process output vector d1(k+2) is computed by :
dl(k+2) = dp~k+2) _ yp(k) tequ. 26) The components of dl(k+2), dll(k+2~ and dl2(k+2), related to the top and bottom compositions, were limited to the absolute values of 0.3 and 0.6~, respectively.
dpl(k+2) =i~l fliYl(k+2-i) +i~l hli Vl( ) (equ. 23) - i=l 2i 2 i) +i~l h2i v2~k+l-i~ (equ. 24) Where vl(k+l-i) and v2(k+1-i) are the compone~ts related to the top and bottom compositions, respectively, of the driver block input vector v(k+l-i) at instant k+l-i. The parameters of equations 23 and 24 were chosen equal to those of a second order model, without and with a sampling time delay respectively, a natural frequency of 0.0056 rad/sec, a damping ratio and static ;, :' '' llZ5~14 gain equal to 1. Given that the value of the previously men-tioned static gain is the unity, the components vl(k+l-i) and v2~k+1-i) have the physical meaning of being the setpoint values for top and bottom compositions, respectively, at instan~ k+l-i.
In equation 23 the value yl(k+l) was previously computed by :
yl(k+l) = Ypl(k+l) ~ Ypl(k-l) (equ. 25) Note that ypl(k+l~ is the value of the top compositions measured at instant k.
From dp(k+2) the desired incremental process output vector d1(k+2) is computed by :
dl(k+2) = dp~k+2) _ yp(k) tequ. 26) The components of dl(k+2), dll(k+2~ and dl2(k+2), related to the top and bottom compositions, were limited to the absolute values of 0.3 and 0.6~, respectively.
7. Computation of the control vector by:
u(~) = Bll(k) dl(k+2) - B11 (k) ~ Bi(k) u(k+l-i) _1 3 i=2 - B1 (k) ~ Ai(k) y~k+2-i) ~equ. 27) up(k) = u(k) t up(k-2) (equ. 28)
u(~) = Bll(k) dl(k+2) - B11 (k) ~ Bi(k) u(k+l-i) _1 3 i=2 - B1 (k) ~ Ai(k) y~k+2-i) ~equ. 27) up(k) = u(k) t up(k-2) (equ. 28)
8. The absolute and the incremental value of up(k) was limit checked before being applied to the process.
Fig. 3 shows, from the begining of the control action, the results of a 6 hrs. 24 min. experiment in which the distillation column was controlled by the adaptive-predictive control system.
In figure 3, the diagrams A, B, C and D represent, in the Y-axis, the top composition (%), the bottom composition (%~, the reflux flow rate (g/s) and the steam flow rate (g/S), respecti-vely, and in the X-axis the time in sampling instants.
~B - 14 -. . . ~
il~5414 The initial values of the parameters of the adaptive-predictive model were rationally chosen, and the control system performed in its identification mode for two sampling instants before starting the control action. When the control action starts, the control system drives the process top and bottom compositions from 96.5 and 1% to 96 and 3% respectively.
Later on, at the instant 29, while the bottom composition is held at 3%, the top composition is driven to 97%j and at the instant 55, the bottom composition is driven from 3 to 5~ and the top composition is held at 97~.
Note that the multivariable control problem of a binary distillation column that the adaptive-predictive control system has solved commendably, has been for a long time for a long time an often cited example of difficulties in interacting multivariable chemical processes.
.~
,
Fig. 3 shows, from the begining of the control action, the results of a 6 hrs. 24 min. experiment in which the distillation column was controlled by the adaptive-predictive control system.
In figure 3, the diagrams A, B, C and D represent, in the Y-axis, the top composition (%), the bottom composition (%~, the reflux flow rate (g/s) and the steam flow rate (g/S), respecti-vely, and in the X-axis the time in sampling instants.
~B - 14 -. . . ~
il~5414 The initial values of the parameters of the adaptive-predictive model were rationally chosen, and the control system performed in its identification mode for two sampling instants before starting the control action. When the control action starts, the control system drives the process top and bottom compositions from 96.5 and 1% to 96 and 3% respectively.
Later on, at the instant 29, while the bottom composition is held at 3%, the top composition is driven to 97%j and at the instant 55, the bottom composition is driven from 3 to 5~ and the top composition is held at 97~.
Note that the multivariable control problem of a binary distillation column that the adaptive-predictive control system has solved commendably, has been for a long time for a long time an often cited example of difficulties in interacting multivariable chemical processes.
.~
,
Claims (12)
1. A method for generating a control vector during each of a plurality of sampling instants k, said control vec-tor to be applied to an electromechanical apparatus which carries out a process having at least one input variable and at least one output variable, at least one of said input variables defining a process input vector, said apparatus varying said process input vector in accordance with the value of said control vector, said method comprising the steps of:
A) storing a model which is capable of predicting the dynamic value of a process output vector, which vector is composed of at least one of said process output variables, at a future sampling instant k+r+1 as a function of said control vector;
B) generating a desired dynamic process output vector, independently of said stored model, at each of said samplinginstants k, said desired dynamic process output vector being representative of a desired value of said pro-cess output vector at said future instant k+r+1;
C) generating, at each of said sampling instants k, that control vector which said model predicts will cause said dynamic process output vector to be equal to said desired dynamic process output vector at said future sampling instant k+r+1; and D) applying said control vector to said apparatus whereby said apparatus varies said process input vector accordingly.
A) storing a model which is capable of predicting the dynamic value of a process output vector, which vector is composed of at least one of said process output variables, at a future sampling instant k+r+1 as a function of said control vector;
B) generating a desired dynamic process output vector, independently of said stored model, at each of said samplinginstants k, said desired dynamic process output vector being representative of a desired value of said pro-cess output vector at said future instant k+r+1;
C) generating, at each of said sampling instants k, that control vector which said model predicts will cause said dynamic process output vector to be equal to said desired dynamic process output vector at said future sampling instant k+r+1; and D) applying said control vector to said apparatus whereby said apparatus varies said process input vector accordingly.
2. The method of claim 1, wherein said desired dynamic process output vector is generated taking into account the desired dynamics for said process and as a function of both a desired steady state process output vector and said dynamic process output vector.
3. The method of claim 2, wherein said step of generating said desired dynamic process output vector includes the step of generating an incremental desired dynamic output vector representative of the incremental difference between the desired dynamic process output vector and said dynamic process output vector.
4. The method of claim 1, wherein said control vector is an incremental control vector representative of the incremental variation in the input vector of said process which said model predicts will cause said dynamic process output vector to be equal to said desired dynamic output vector at said future sampling instant k+r+1.
5. The method of claim 3, wherein said control vector is an incremental control vector representative of the incremental variation in the input vector of said process which said model predicts will cause said dynamic process output vector to be equal to said desired dynamic output vector at said future sampling instant k+r+1.
6. The method of claim 1, further including the step of periodically updating the parameters of said model in such a manner that the difference between the actual dynamic process output vector at sampling instant k+r+1 and the dynamic process output vector which said model predicted would result at sampling instant k+r+1 is reduced towards zero.
7. The method of claim 6, wherein said step of updating the parameters of said model comprises the steps of:
A) periodically generating an estimated process output vector representative of the dynamic process output vector which said model, as updated during some first predetermined prior sampling instant, estimates should have occurred at sampling instant k as a result of the generation of said control vector at said prior sampling instant k-r-1;
B) periodically generating an estimated error vector representative of the difference between said estimated process output vector at said sampling instant k and said dynamic process output vector at said sampling instant k;
C) periodically modifying the parameters of said model as a function of said estimated error vector.
A) periodically generating an estimated process output vector representative of the dynamic process output vector which said model, as updated during some first predetermined prior sampling instant, estimates should have occurred at sampling instant k as a result of the generation of said control vector at said prior sampling instant k-r-1;
B) periodically generating an estimated error vector representative of the difference between said estimated process output vector at said sampling instant k and said dynamic process output vector at said sampling instant k;
C) periodically modifying the parameters of said model as a function of said estimated error vector.
8. The method of claim 7, further including the step of generating an incremental process output vector representative of the difference between the actual dynamic process output vector at instant k and the actual dynamic process output vector at some second prior sampling instant.
9. The method of claim 8, wherein said estimated process output vector is the value estimated by the model, as updated at said first prior sampling instant, of the incremental dynamic process output vector.
10. The method of claim 9, wherein said step of generating an estimated error vector comprises the step of determining the difference between said incremental process output vector and said estimated process output vector.
11. A control system for controlling an electro-mechanical apparatus carrying out a process having at least one input variable and at least one output variable, said control system comprising:
an electromechanical device for adjusting said at least one input variable as a function of a control vector applied thereto;
driver block means responsive to a set point vec-tor v(k) and an instantaneous process output vector vp(k) for generating a desired incremental process output vector d1 (k+r+1) during each of a plurality of sampling intervals k, said desired incremental output vector d1 (k+r+1) cor-responding to the desired incremental change in an output vector of said process between the sampling interval k and the sampling interval k+r+1;
control block means responsive to said desired in-cremental output vector d1 (k+r+1) for generating an incre-mental control vector u(k) during each said sampling inter-val k in accordance with an adaptive-predictive model, said adaptive-predictive model serving to predict the process output vector and to determine the incremental control vec-tor u(k) which must be applied to the process during sampling interval k to make the predicted process output vector equal to the desired process output vector during sampling interval k+r+1 as determined by said incremental desired output vec-tor d1 (k+r+1);
said driver block means generating said desired incremental process output vector d1 (k+r+1) independently of said adaptive-predictive model;
identification block means responsive to said in-cremental control vector u(k) and an incremental process output vector y(k) for generating an estimated incremental process output vector d(k) during each said sampling inter-val k in accordance with said adaptive-predictive model, said estimated incremental process output vector d(k) being repre-sentative of the incremental process output which the adap-tive-predictive model, as updated during a sampling interval prior to sampling interval k, predicts should occur during interval k as a result of the generation of the incremental control vector u(k-r-1) during sampling interval k-r-1;
means for generating an estimated error vector e(k) during each of said sampling intervals k, said estimated error vector e(k) being representative of the difference between said estimated incremental process output vector d(k) and said incremental output vector y(k):
feedback means responsive to said estimated error vector e(k) for modifying the parameters of said adaptive-predictive model during each said sampling interval k, said feedback means to modify the parameters of said adaptive-predictive model in such manner that said estimated error vector e(k) is reduced towards zero; and means for applying said incremental control u(k) vector to said electromechanical device.
an electromechanical device for adjusting said at least one input variable as a function of a control vector applied thereto;
driver block means responsive to a set point vec-tor v(k) and an instantaneous process output vector vp(k) for generating a desired incremental process output vector d1 (k+r+1) during each of a plurality of sampling intervals k, said desired incremental output vector d1 (k+r+1) cor-responding to the desired incremental change in an output vector of said process between the sampling interval k and the sampling interval k+r+1;
control block means responsive to said desired in-cremental output vector d1 (k+r+1) for generating an incre-mental control vector u(k) during each said sampling inter-val k in accordance with an adaptive-predictive model, said adaptive-predictive model serving to predict the process output vector and to determine the incremental control vec-tor u(k) which must be applied to the process during sampling interval k to make the predicted process output vector equal to the desired process output vector during sampling interval k+r+1 as determined by said incremental desired output vec-tor d1 (k+r+1);
said driver block means generating said desired incremental process output vector d1 (k+r+1) independently of said adaptive-predictive model;
identification block means responsive to said in-cremental control vector u(k) and an incremental process output vector y(k) for generating an estimated incremental process output vector d(k) during each said sampling inter-val k in accordance with said adaptive-predictive model, said estimated incremental process output vector d(k) being repre-sentative of the incremental process output which the adap-tive-predictive model, as updated during a sampling interval prior to sampling interval k, predicts should occur during interval k as a result of the generation of the incremental control vector u(k-r-1) during sampling interval k-r-1;
means for generating an estimated error vector e(k) during each of said sampling intervals k, said estimated error vector e(k) being representative of the difference between said estimated incremental process output vector d(k) and said incremental output vector y(k):
feedback means responsive to said estimated error vector e(k) for modifying the parameters of said adaptive-predictive model during each said sampling interval k, said feedback means to modify the parameters of said adaptive-predictive model in such manner that said estimated error vector e(k) is reduced towards zero; and means for applying said incremental control u(k) vector to said electromechanical device.
12. The control system of claim 11, further including means for applying said control vector to said apparatus in a manner which will cause said apparatus to vary said process input vector in accordance therewith.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA286,253A CA1125414A (en) | 1977-09-07 | 1977-09-07 | Adaptive predictive control system |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA286,253A CA1125414A (en) | 1977-09-07 | 1977-09-07 | Adaptive predictive control system |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA1125414A true CA1125414A (en) | 1982-06-08 |
Family
ID=4109474
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA286,253A Expired CA1125414A (en) | 1977-09-07 | 1977-09-07 | Adaptive predictive control system |
Country Status (1)
| Country | Link |
|---|---|
| CA (1) | CA1125414A (en) |
-
1977
- 1977-09-07 CA CA286,253A patent/CA1125414A/en not_active Expired
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