Properties of the Self-tuning Minimax Predictive Control (MPC)

Abstract

This paper examines the stability, performance, and robustness of a self-tuning two degree of freedom receding horizon control law based on the mixed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> minimization. The paper briefly reviews the derivation which is carried out as follows. First, the integrand in the frequency domain representation of the generalized predictive control (GPC) performance criterion is decomposed into disturbance and reference spectra. Then the controller is derived whose H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> part minimizes the peaks of the disturbance spectrum and the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> part minimizes the integral of the reference spectrum on the unit circle. The resulting two degrees of freedom control strategy referred to as the minimax predictive control (MPC) is shown to have stabilizing and robustness properties superior to the GPC for identical horizons. The MPC synthesis, based on spectral factorization and Diophantine equations, is much simpler than the standard state space H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> optimal controller. Then, the two degree of freedom MPC design is combined with a long range predictive estimator to form the self-tuning minimax predictive control. The self-tuning algorithm is very similar to the indirect self-tuner based on the standard GPC control law with extended least squares estimator. The two degree of freedom self-tuning MPC is shown to have stability and robustness properties superior to those of self-tuning GPC.