Performance indices for multivariable PI-control with incomplete feedback

1987

AIChE Journal

A new self-tuning controller (STC) has been developed for a general class of nonlinear multiinput, multioutput process models. These models can include arbitrary, known nonlinear functions of the old inputs and outputs as well as the products of these functions and any powers of the most recent inputs. A very general control algorithm has been proposed that allows different numbers of inputs and outputs, different time delays for each input-output pair, and a performance index that can include different penalties on the outputs and on the incremental changes in the outputs. Simulation results are presented for two-point composition control of a pilot-scale distillation column. The results demonstrate that the new nonlinear STC performs significantly better than conventional STC's based on linear models.Correspondence concerning this paper should be a d d r d lo bumani et al., 1981;Lachmann, 1982;Dochain and Bastin, 1984;Svoronos et al., 1981). However, the applicability of these techniques is limited to processes with specific nonlinearities such as polynomials in the manipulated input or bilinear products of output and input. This paper presents a new self-tuning controller for multipleinput, multiple-output (MIMO) processes based on a very general class of nonlinear process models. The analysis is an extension of the modified nonlinear STC for single-input, singleoutput (SISO) systems that was previously developed by the authors (Agarwal and Seborg, 1985) to MIMO systems. The new MIMO STC algorithm provides several advantages over an alternative presented in an earlier paper (Agarwal and Seborg, 1986): it is applicable to a broader class of systems, it requires estimation of fewer parameters, and it allows different penalties on the elements of the output in the performance index. Problem StatementThe problem is to derive a new self-tuning controller that minimizes a quadratic cost function objective based on a very general class of nonlinear models that can include arbitrary, known nonlinear functions of the old inputs and outputs as well as the products of these functions and any powers of the most recent inputs. It is assumed that the nonlinear MIMO process can be described adequately by a discrete-time model, which is linear in system parameters and allows for different numbers of inputs and outputs and different time delays between different input-output pairs. Such a model can be represented in the following general form:

Section: P'(z-i)mentioning

confidence: 99%

A multivariable nonlinear self‐tuning controller

Agarwal

1987

AIChE Journal

“…However, it is more convenient to use the input-output data to estimate directly the parameters required in the control law of equation (12). For this implicit estimation problem, rearrange equation (7) where the inequality results if k, < k m a x -1 for any r, due to one or more parameters in A(2-I) being known to be zero according to the assumption stated in Section 2.…”

Section: On-line Parameter Estimationmentioning

confidence: 99%

“…If the model parameters in equation ( I ) are unknown, they can be estimated on-line from input-output data. However, it is more convenient to use the input-output data to estimate directly the parameters required in the control law of equation (12). For this implicit estimation problem, rearrange equation (7) as (1).…”

Section: On-line Parameter Estimationmentioning

confidence: 99%

A self‐tuning controller for mimo non‐linear systems

Agarwal

Adaptive Control & Signal

1987

A new self-tuning control (STC) strategy for non-linear, multi-inputlmulti-output control problems is proposed. This strategy is applicable to a broad class of non-linear systems, which can include any nonlinear functions of the old inputs and outputs as well as the products of these functions and any powers of the most recent inputs. Simulation results for a two-link robot manipulator demonstrate that the new non-linear STC strategy provides significant improvement over conventional STCs based on linear models.

Optimal proportional plus integral control for regulator and tracking problems

Wong

Optim Control Appl Methods

1985

SUMMARYTwo new design methods are proposed for optimal PI control which give fast recovery from load disturbances without producing large overshoots associated with set-point changes. Unlike existing methods, such as set-point filtering or any other scheme that essentially detunes the controller for set-point changes, the proposed methods do not increase the rise time significantly in order to reduce overshoot. The first method resets the integral term in the control law when the new set point is reached. The second method is a modified model-following approach that does not increase the overall dimension of the system. Two numerical examples demonstrate that the proposed methods are superior to alternatives such as set-point filtering and conventional model following.KLY WORDS Optimal proportional-integral control Model following Reset wind-up . INTRODUCTIONI t is usually desirable to include integral action in optimal control systems in order to eliminate offset due to unmeasured load disturbances or modelling error. Three basic approaches for incorporating integral control action have been reported in the literature. In the first method, a term involving the time derivative of the control vector is included in the performance index. '-' The resulting control law contains integrals of all of the state variables. However, this approach is valid only for systems where the number of control variables is at least equal to the number of state variables. Otherwise, it is not possible to eliminate offset in all of the state variables.4 A second way of incorporating integral action is to augment the state vector with integrals of selected state variables.4p5 The main advantage of this approach is that it allows the designer to choose the set of output variables for which integral control action is desired. The third approach for including integral control action is to use a disturbance model. This scheme has the advantage of allowing the designer to tailor the control system design to the specific type o f disturbances that are anticipated. However, the added complexity of requiring state estimation and a disturbance model is a significant disadvatage. Other approaches, such as the one suggested by Waller and Gustafson,' which includes the time derivative of both the output and the control vector in the performance index, are also reported in the literature.Although integral control action is essential for eliminating offsets, it creates a problem in designing the controller. In particular, the choice of the weighting matrices in a quadratic performance index usually involves a compromise between load and setpoint responses. The present paper proposed a remedy for this problem based on modifying the integral term in the PI control law.