Predictive control based on discrete convolution models

Abstract

In several recent studies a discrete convolution representation of a dynamic system has been used to develop new digital control algorithms based on the prediction of future outputs. This paper presents a fundamental analysis of the concepts involved In designing both predictor and control elements for such algorithms. For single-input, single-output systems, the predicted controller Is equivalent to a discrete feedback controller which operates on the current output and past input signals. Simulation and experimental results for several single-input, single-output systems provide a comparison of a predictive control technique with standard RID control. The predictive controller Is shown to be quite effective even for systems with inverse response characteristics.

Real-time comparison of a number of predictive controllers

“…1, the prediction outputs depend on the control signals u(t + k|t), which are calculated by minimizing a quadratic cost function of the errors between a reference trajectory and the predicted process output, over P. Usually only the first control signal, u(t|t), is sent to the plant and the procedure is repeated at the next sampling instant. The reason for implementing the first control signal is to keep the predictions closer to the measured values of the controlled variable [16], to account for unmeasurable disturbances and to react to set-point changes. At this stage, the theory will be presented on several MPC controllers.…”

Fuzzy Model Identification for Control

“…Their formulations were heuristic and algorithmic and took advantage of the increasing potential of digital computers at that time. For open-loop stable processes, dynamic matrix control (DMC) quickly become popular particularly in chemical process industries, due to the simplicity of the algorithm and to the use of easily obtainable impulse or step response models [177,69]. To handle a wider class of unstable and non-minimum phase systems the generalized predictive control (GPC) scheme was introduced [77].…”

Characteristic equations and robust stability of a simplified predictive control algorithm

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In predictive control, control calculations are done such that the difference between the desired and the predicted response of the process is minimized. Marchetti et al (1983) recommended small values of optimization and control horizons. Earlier papers have shown that the control performance obtained using the DMC algorithm can also be obtained by using a simplified algorithm where the error is minimized at one point and one future control move is calculated.

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“…Marchetti et al (1983) recommended small values of optimization and control horizons. Another approach is to see if minimizing errors over a prediction horizon of four to five time constants in length and calculating a number of control moves is really necessary.…”