P. J. Gawthrop, H. Demircioglu, and I. Siller-Alcala. Multivariable Continuous-time Generalised Predictive control: A state-space approach to linear and nonlinear systems. Proc. IEE Pt. D: Control Theory and Applications, 145(3):241--250, May 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... Predictive Control This section summaries the main equations of a Continuous time Generalised Predictive Control (CGPC) used here as a OLFO controller, as they apply to the intermittent version (ICGPC) a complete derivation and discussion (in the non intermittent case) is given elsewhere (Gawthrop et al. 1998). Following (Gawthrop et al. 1998) this paper considers nonlinear systems of the form: x = F (x; u) 4) y = H(x) 5) where the function F and H are smooth (to be precise differentiable N y times with respect to each argument) and the outputy, input u and state x dimensions are n y , n u and ....

.... summaries the main equations of a Continuous time Generalised Predictive Control (CGPC) used here as a OLFO controller, as they apply to the intermittent version (ICGPC) a complete derivation and discussion (in the non intermittent case) is given elsewhere (Gawthrop et al. 1998) Following (Gawthrop et al. 1998), this paper considers nonlinear systems of the form: x = F (x; u) 4) y = H(x) 5) where the function F and H are smooth (to be precise differentiable N y times with respect to each argument) and the outputy, input u and state x dimensions are n y , n u and n x respectively. The algorithm ....

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Gawthrop, P. J., H. Demircioglu and I. Siller-Alcala (1998). Multivariable continuous-time generalised predictive control: A state-space approach to linear and nonlinear systems. Proc. IEE Pt. D: Control Theory and Applications.

....this approach compared to a non linear CGPC. Section 5 concludes this paper by discussing the advantages of this approach and pointing to future work. 2 Continuous time Generalised Predictive Control There are different ways to implement a Model Based Predictive Controller (MBPC) following [5] a multi variable model tracking state space Continuoustime Generalised Predictive Controller (CGPC) is considered here. This paper deals with nonlinear dynamic systems with the state space representation: x = f(x; u) y = g(x) 1) where the function f and g are appropriately differentiable for ....

....tracking state space Continuoustime Generalised Predictive Controller (CGPC) is considered here. This paper deals with nonlinear dynamic systems with the state space representation: x = f(x; u) y = g(x) 1) where the function f and g are appropriately differentiable for the GPC algorithm (see [5] for details) and the output y, input u and state x dimensions are n y , n u and n x respectively. CGPC is designed from local linearisations of the state space. This yields a linearised dynamic systems where the state is assumed to be not measurable. For this reason a linear state observer [13, ....

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P. J. Gawthrop, H. Demircioglu, and I. Siller-Alcala. Multivariable Continuous-time Generalised Predictive control: A state-space approach to linear and nonlinear systems. Proc. IEE Pt. D: Control Theory and Applications, 145(3):241--250, May 1998.

....and the references therein) Most work in Generalised Predictive Control is based on a discrete time approach. As has been pointed in the literature (Gawthrop, 1982; Gawthrop, 1987) there are some problems in purely discrete time methods. The continuous time GPC was developed by Gawthrop and Demircioglu (1991; 1992) using a transfer function approach. Although Ordys and Clarke (1993) suggests that there is no significant different between the transfer function approach and the state space approach, Morari (1994) points that the state space approach has both conceptual and numerical advantages. Moreover as ....

Demircioglu, H. and P. J. Gawthrop (1992). Multivariable continuous-time generalised predictive control. Automatica 28(4), 697--713.

....An alternative (prediction free) version of GPC is shown to provide one possible extension of exact linearisation to cope with nonlinear systems with unstable dynamics. 1 Introduction The Multivariable Continuous time Generalised Predictive Controller (CGPC) has been recast in a state space form [1, 2] and shown to include Generalised Minimum Variance (GMV) and an new algorithm, Predictive GMV (PGMV) as special cases; it is noted that, unlike the transfer function approach, the state space approach extends readily to the nonlinear case. There has been a recent resurgence of interest in ....

....A two link manipulator with delayed measurement is used as an illustrative example. The Bond Graph technique[5, 6, 7] together with symbolic algebra, is used to generate the controller. 2 Continuous time GMV and GPC This section summarises the main features of GMV and GPC as discussed elsewhere [1, 2]. The system equation considered here is x = F (x; u) 1) y = H(x) 2) A special case of Equation 1 is one where the control enters in a linear fashion : x = f(x) g(x)u (3) y = h(x) 4) where f(x) g(x)u = F (x; u) and h(x) H(x) A column vector YNy (t) of output derivatives is defined ....

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P.J. Gawthrop, H. Demircioglu, and I. Siller-Alcala. Multivariable continuous-time generalised predictive control: A state-space approach to linear and nonlinear systems. CSC Research Report CSC98001, Centre for Systems and Control, University of Glasgow, URL http://www.mech.gla.ac.uk/Control/reports.html, 1998.

....An alternative (prediction free) version of GPC is shown to provide one possible extension of exact linearisation to cope with nonlinear systems with unstable dynamics. 1 Introduction The Multivariable Continuous time Generalised Predictive Controller (CGPC) has been recast in a state space form [1, 2] and shown to include Generalised Minimum Variance (GMV) and an new algorithm, Predictive GMV (PGMV) as special cases; it is noted that, unlike the transfer function approach, the state space approach extends readily to the nonlinear case. There has been a recent resurgence of interest in ....

....A two link manipulator with delayed measurement is used as an illustrative example. The Bond Graph technique[5, 6, 7] together with symbolic algebra, is used to generate the controller. 2 Continuous time GMV and GPC This section summarises the main features of GMV and GPC as discussed elsewhere [1, 2]. The system equation considered here is x = F (x; u) 1) y = H(x) 2) A special case of Equation 1 is one where the control enters in a linear fashion : x = f(x) g(x)u (3) y = h(x) 4) where f(x) g(x)u = F (x; u) and h(x) H(x) A column vector YNy (t) of output derivatives is defined ....

[Article contains additional citation context not shown here]

P. J. Gawthrop, H. Demircioglu, and I. Siller-Alcala. Multivariable continuous-time generalised predictive control: A state-space approach to linear and nonlinear systems. Proc. IEE Pt. D: Control Theory and Applications, To appear 1998.

....work by examining networks of continuous time observers each with its own local state. Although most of the classical work on Self tuning Control [11] 12] 13] 14] based on the linear ARMA model and a discrete time representation, a continuous time formulation has been developed [15] 16] 17] [18] which has been rationalised using the concept of an emulator. The purpose of this paper is to combine the LMN concept with the emulator concept to give a system representation which, whilst being founded on the physical system of Equation 1 and thus retaining physical insight, is of convenient ....

....output yr : 0 = f(x r ; u r ) y r = g(x r ; u r ) 19) The terms x r and u r ensure that when y = yr , u = ur . In the context of adaptive control, it is inconvenient to handle the offset terms directly. This point is taken up in Section 3 3 LOCAL EMULATOR NETWORK Emulators [15, 16, 17, 18] provide the basis for various flavours of self tuning control of linear (possibly linear in the parameter) systems; local emulator networks thus provide the basis for self tuning control of nonlinear systems. The natural setting for emulators is a inputoutput Laplace transform system ....

H. Demircioglu and P. J. Gawthrop, Multivariable Continuous-time Generalised Predictive Control, Automatica, 28, 1992.

....controller design ffl the use of control samples (or control moves) as a control signal parameterisation leads to high dimensional optimisation problems. One such continuous time formulation (Demircioglu and Gawthrop, 1991; Demircioglu and Gawthrop, 1992) has been recast in a non linear setting (Gawthrop et al. 1998). Whilst overcoming the problems with discrete time controllers, these methods have a number of remaining problems which include: ffl the optimisation procedure is implicitly assumed to be instantaneous; ffl (open loop) predictions are approximated by Taylor series which become increasingly ....

....assumed available directly or via an observer. In the special case of linear systems: x = Ax Bu (2) y = Cx Following the usual procedure (Demircioglu and Gawthrop, 1991; Demircioglu and Gawthrop, 1992; 1 The extension to MIMO systems is straightforward but beyond the scope of this paper Gawthrop et al. 1998), define an (open loop) input u defined from time t as u(t ) u (t; and, given the state x(t) at time t, the system equations can be numerically integrated to give the corresponding (open loop) predicted output y(t ) y (t; In the special case that the system is the linear ....

[Article contains additional citation context not shown here]

Gawthrop, P. J., H. Demircioglu and I. Siller-Alcala (1998). Multivariable continuous-time generalised predictive control: A state-space approach to linear and nonlinear systems. Proc. IEE Pt. D: Control Theory and Applications.

....a direct physical interpretation ffl the sample rate is chosen before controller design ffl the use of control samples (or control moves) as a control signal parameterisation leads to high dimensional optimisation problems. One such continuous time formulation (Demircioglu and Gawthrop, 1991; Demircioglu and Gawthrop, 1992) has been recast in a non linear setting (Gawthrop et al. 1998) Whilst overcoming the problems with discrete time controllers, these methods have a number of remaining problems which include: ffl the optimisation procedure is implicitly assumed to be instantaneous; ffl (open loop) predictions ....

....y = H(x) where the output y, input u and state x dimensions are n y , n u and n x respectively. Note that the state are assumed available directly or via an observer. In the special case of linear systems: x = Ax Bu (2) y = Cx Following the usual procedure (Demircioglu and Gawthrop, 1991; Demircioglu and Gawthrop, 1992; 1 The extension to MIMO systems is straightforward but beyond the scope of this paper Gawthrop et al. 1998) define an (open loop) input u defined from time t as u(t ) u (t; and, given the state x(t) at time t, the system equations can be numerically integrated to give the ....

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Demircioglu, H. and P. J. Gawthrop (1992). Multivariable continuous-time generalised predictive control. automaticity 28(4), 697--713.

....we believe that CGPC will also find industrial application. One dichotomy in the development of GPC is into the discrete time approach of, for example Clarke, Mohtadi and Tuffs (1987a, 1987b, 1989) and the continuous time approach of Demircioglu (1989) Gawthrop and Demircioglu (1989, 1991) Demircioglu and Gawthrop (1991, 1992) and Demircioglu and Clarke (1992) We use a continuous time setting here for the reasons given by Gawthrop (1986b, 1986a, 1987) In particular, we believe that a continuous time approach exposes the fundamentals of the underlying control problem which are obscured by sampling: this is ....

....One such unrealisable dynamic system is the multiple derivative operator given, in Laplace Transform terms, by s N . Such emulators form the basis of (continuous time) generalised minimum variance control (GMV) Gawthrop(1987, 1986b, 1986a) and generalised predictive control (GPC) Gawthrop and Demircioglu(1991, 1992) and the corresponding self tuning controllers. Example 2.1 This example system, of the form of Equation 1, is used throughout this paper to illustrate the development of the theory. A = 0 1 Gamma1 1 ; B = Gammafi 1 ; C = Gamma 1 0 Delta (3) The corresponding transfer ....

[Article contains additional citation context not shown here]

Demircioglu, H. and P. J. Gawthrop (1992). Multivariable continuous-time generalised predictive control. Automatica 28 (4), 697--713.

....can easily be incorporated. As discussed by Costello and Gawthrop [4] the unknown inputs then become states of the observer. 3. 4 Controller Design Recent research by Gawthrop and Siller Alcala[13] has shown that the continuoustime generalised predictive control of Demicioglu and Gawthrop [5, 6] can be extended to cover certain non linear systems. As in the geometric approach of Isidori [17] the algorithm requires the symbolic calculation of (possibly highorder) Lie derivatives. These are hard to generate by hand, but a tool has been added to MTT which automatically generates the ....

H. Demircioglu and P. J. Gawthrop. Multivariable continuous-time generalised predictive control. Automatica, 28(4):697--713, 1992.

....as optimisation within a set of axes which, although fixed in time for the purposes of optimisation, moves forward with time for the purposes of determining the control action. This general approach has been called Open loop Feedback Optimal (OLFO) Control [2] In the continuous time context [3] a similar approach is taken. It is different in that the optimal control signal, instead of being specified as a series of control values, is specified as a continuous polynomial function of time and in that the moving axes move continuously. It is the same in that, in the receding horizon ....

.... Report CSC 98015 2 Intermittent Generalised Predictive Control This section summarises the main equations of Continuous time Generalised Predictive Control as they apply to the new intermittent version; a complete derivation and discussion (in the non intermittent case) is given elsewhere [3]. Following [3] this paper considers nonlinear systems of the form: x = F (x; u) 1) y = H(x) 2) where the function F and H are smooth (to be precise differentiable N y times with respect to each argument) and the outputy, input u and state x dimensions are n y , n u and n x respectively. ....

[Article contains additional citation context not shown here]

P. J. Gawthrop, H. Demircioglu, and I. Siller-Alcala. Multivariable continuous-time generalised predictive control: A state-space approach to linear and nonlinear systems. Proc. IEE Pt. D: Control Theory and Applications, To appear 1998.

....not take advantage of the multitude of available nonlinear physical system models. To overcome this problem, a continuous time formulation of a MPC, a Generalised Predictive Controller (GPC) Demircioglu and Gawthrop, 1991; Demircioglu and Gawthrop, 1992) has been recast in a non linear setting (Gawthrop et al. 1998). However, these methods have a number of remaining problems which include: ffl the optimisation procedure is implicitly assumed to be instantaneous; ffl (open loop) predictions are approximated by Taylor series which become increasingly inaccurate with time and assume that the system output is ....

....input u and state x dimensions are n y , n u and n x respectively. Note that the state are assumed available directly or via an observer. In the special case of linear systems: x = Ax Bu (2) y = Cx Following the usual procedure (Demircioglu and Gawthrop, 1991; Demircioglu and Gawthrop, 1992; Gawthrop et al. 1998), define an (open loop) Model y Plant y t Realignement Dol t Optimiser y e Constraints t O L C t O L C u Dol u k u k u Figure 2: OLIFO control block diagram The control of the system is dissociated from the optimisation. The system is controlled using the ....

[Article contains additional citation context not shown here]

Gawthrop, P. J., H. Demircioglu and I. Siller-Alcala (1998). Multivariable continuous-time generalised predictive control: A state-space approach to linear and nonlinear systems. Proc. IEE Pt. D: Control Theory and Applications.

....to (finite dimensional) discrete time models. Thus, discrete time MPC can not take advantage of the multitude of available nonlinear physical system models. To overcome this problem, a continuous time formulation of a MPC, a Generalised Predictive Controller (GPC) Demircioglu and Gawthrop, 1991; Demircioglu and Gawthrop, 1992), has been recast in a non linear setting (Gawthrop et al. 1998) However, these methods have a number of remaining problems which include: ffl the optimisation procedure is implicitly assumed to be instantaneous; ffl (open loop) predictions are approximated by Taylor series which become ....

....y = H(x) where the output y, input u and state x dimensions are n y , n u and n x respectively. Note that the state are assumed available directly or via an observer. In the special case of linear systems: x = Ax Bu (2) y = Cx Following the usual procedure (Demircioglu and Gawthrop, 1991; Demircioglu and Gawthrop, 1992; Gawthrop et al. 1998) define an (open loop) Model y Plant y t Realignement Dol t Optimiser y e Constraints t O L C t O L C u Dol u k u k u Figure 2: OLIFO control block diagram The control of the system is dissociated from the optimisation. The system is ....

[Article contains additional citation context not shown here]

Demircioglu, H. and P. J. Gawthrop (1992). Multivariable continuous-time generalised predictive control. automaticity 28(4), 697--713.

....of this approach compared to a non linear CGPC. Section 5 concludes this paper by discussing the advantages of this approach and pointing to future works. 2 Continuous time Generalised Predictive Control There are different ways to implement a Model Based Predictive Controller (MBPC) following (Gawthrop et al. 1998) a multi variable model tracking state space Continuous time Generalised Predictive Controller (CGPC) is considered here. This paper deals with nonlinear dynamic systems with the state space representation: x = f(x; u) y = g(x) 1) where the function f and g are smooth and the output y, input ....

.... lin 0 1 C A ; C = C lin 0 ; x = 0 B x 1 1 C A (23) Note that the addition of the extra state associated with the inclusion of V lin into A can be interpreted as explicitly including a disturbance into the system model and hence giving controller integral actions as a consequence (Gawthrop et al. 1998). The second stage of the successive linearisations set up consists simply in evaluating A and B. This is the on line component of this approach where we simply use the actual vectors x and u that are continuously available. The CGPC design is also readapted on line from this new linear state ....

[Article contains additional citation context not shown here]

Gawthrop, P. J., H. Demircioglu and I. Siller-Alcala (1998). Multivariable continuous-time generalised predictive control: A state-space approach to linear and nonlinear systems. Proc. IEE Pt. D: Control Theory and Applications.

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