D.G. Fisher

A review of process identification and parameter estimation techniques

Abstract This paper represents a survey of the recent literature in the area of process identification and parameter estimation techniques applicable to lumped-parameter, deterministic, dynamical systems. Methods reviewed include statistical estimation techniques, direct and indirect methods based on optimal control theory, functional expansion, impulse response, frequency response and a number of other specific methods. Each method is presented in a consistent format which includes an outline of the general characteristics, calculational techniques, experimental techniques, reliability estimates and applications. The overall objective is to provide a basis for comparison of the methods and a guide to particular applications which will assist the reader in selecting the best method for his specific problem Comments and additions are solicited: see page 263.

Stable discrete-time adaptive control in the presence of unmodeled dynamics

Results obtained previously on the stability of adaptive predictive control systems are generalized by reducing the requirements for stability to a single condition that is applicable to linear discrete processes with disturbances and unmodeled plant dynamics. The proposed design approach uses a normalized parameter estimation scheme, which permits a formal proof that the modeling errors can be treated as a bounded disturbance, and a parameter adaptation stopping criterion to guarantee global stability. >

Decoupling of linear time-varying systems with time delays in the control variables or state variables

Sufficient conditions for decoupling by state feedback are developed for several classes of time-varying systems which contain time delays. The sufficient conditions are constructive in nature since they can be used to design the decoupler. Two numerical examples are included to illustrate the design procedure.

Performance adaptive control: General structure and a case study

Abstract This paper proposes a supervisory performance tuner for an adaptive controller. The objective of the performance tuner is to automatically adjust tuning parameters of an adaptive controller such that the actual setpoint-tracking and regulatory performance approaches user specifications and is maintained at this level at all times. Experimental evaluation of the prototype performance tuning loop with adaptive generalized predictive and pole placement controllers on a pilot-scale process demonstrates the practicality and utility of this idea.

Frequency response characteristics of MIMO GPC

This paper is concerned with the frequency response properties of MIMO generalized predictive control. A number of frequency response indicators (characteristic loci, principal gains and Gershgorin bands) are used to evaluate stability and the performance of the closed-loop. This is done via three realistic examples which demonstrate the effect of the predictive controller tuning parameters on the measures of robust stability and performance in the frequency domain. A series of heuristic tuning rules is compiled for methodical tuning of this type of controller in multivariable environments

Disturbance localization in linear systems by eigenvector

Abstract A new concept, undisturbability, is formally defined and related to the concepts of uncontrollability and structural controllability. Necessary and sufficient conditions for a system to have undisturbable state or output variables are expressed in terms of the structure of the coefficient matrices in the state-space model and the structure of the eigenvector matrix. These results and an eigenvector/eigenvalue assignment algorithm (Srinathkumar and Rhoten 1975, Shah et al. 1975) provide the basis of a design procedure for synthesizing multivariable controllers which achieve disturbance localization.

Model reduction for discrete-time dynamic systems †

The model reduction techniques of Marshall and Davison for linear continuous-time models are extended for use in reducing the order of linear discrete-time models. Two approaches for the reduction of high-order continuous-time models to low-order discrete-time models are presented and evaluated. The resulting reduced order discrete-time models obtained by the two approaches are shown to be equivalent. A simple numerical example is solved to demonstrate the techniques presented.

Stable robust adaptive controller

This paper presents a globally stable adaptive controller for linear discrete systems in the presence of unmodelled dynamics and bounded disturbances. The proposed formulation uses an augmented plant representation that incorporates P, Q and R weighting polynomials for the system output, input and setpoint respectively into the predictive control law. The algorithm also includes a normalized estimation scheme, based on a least-squares estimator, and a parameter adaptation stopping criterion to guarantee stability.

Disturbance feedback in model predictive control systems

Abstract Model Predictive Control (MPC) schemes such as MOCCA, DMC, MAC, MPHC and IMC have been shown to provide excellent performance. This is particularly true for servo control applications in which it is assumed that the desired trajectory (setpoint) is known a priori. However, to achieve equivalent performance in regulatory control the future effects of residual values y ( k )- ŷ ( k ), which include the effects of disturbances and model process mismatch, must be predicted. In this paper a state space form of the process step response model is used as the basis for implementing state observer forms and a Kalman filter to predict these residual effects. It is shown that the addition of disturbance step response models to the closed loop observer and the Kalman filter predictor improves the prediction of structured residuals. It is also shown that closed loop feedback/prediction can guarantee zero steady state offset in the presence of non-zero mean residual effects.

Model predictive control using an extended ARMarkov model

Abstract The original ARMarkov identification method explicitly determines the first μ Markov parameters from plant input–output data and approximates the slower dynamics of the process by an ARX model structure. In this paper, the method is extended to include a disturbance model and an ARIMAX structure is used to approximate the slower dynamics. This extended ARMarkov model is then used to formulate a predictive controller. As the number of Markov parameters in the model varies from one to P (prediction horizon)+1, the controller changes from generalized predictive control (GPC) to dynamic matrix control (DMC). The advantages of the proposed ARM-MPC are the consistency of the Markov parameters estimated by the ARMarkov method, independent tuning of the controller for servo and regulatory responses and the ability to combine the characteristics of GPC and DMC. The theoretical results are illustrated through simulation examples.