Subspace predictive control: stability and performance enhancement

Saba Sedghizadeh

doi:10.32920/ryerson.14662608

Abstract

In the absence of prior knowledge of a system, control design relies heavily on the system identifi- cation procedure. In real applications, there is an increasing demand to combine the usually time consuming system identification and modeling step with the control design procedure. Motivated by this demand, data-driven control approaches attempt to use the input-output data to design the controller directly. Subspace Predictive Control (SPC) is one popular example of these algorithms that combines Model Predictive Control (MPC) and Subspace Identification Methods (SIM). SPC instability and performance deterioration in closed-loop implementations are majorly caused by either poor tuning of SPC horizons or changes in the dynamics of the system. Stability and performance analysis of the SPC are the focus of this dissertation. We first provide the necessary and sufficient condition for SPC closed-loop stability. The results introduce SPC stability graphs that can provide the feasible prediction horizon range. Consequently, these stability constraints are included in SPC cost function optimization to provide a new method for determining the SPC horizons. The novel SPC horizon selection enhances the closed-loop performance effectively. Note that time-delay estimation and order selection in system modeling have been a challenging step in applications and industry. Here, we propose a new approach denoted by RE-based TDE that simultaneously and fficiently estimates the time-delay for the SIM framework. In addition, we use the recently developed MSEE approach for estimating the system order. Moreover, we propose an arti- ficial intelligence approach denoted by Particle Swarm Optimization Based Fuzzy Gain-Scheduled SPC (PSO-based FGS-SPC). The method overcomes the issue of on-line adaptation of SPC gains for systems with variable dynamics in the presence of the noisy data. The approach eliminates existing tuning problem of controller gain ranges in FGS and updates the SPC gains with no need to apply any external persistently excitation signals. As a result, PSO-based FGS-SPC provides a time efficient control strategy with fast and robust tracking performance compared to conventional and state of the art methods.

Highlights

1.1 Dissertation ObjectivesTwo fundamental steps in developing control systems are: (i) obtaining model of the system, and (ii) designing a controller for the system
While this dissertation only concentrates on the Subspace approach of system identification which are used for Subspace Predictive Control (SPC), here we provide a brief review on Classical approaches of system identification that are historically before Subspace approach
Focus of this dissertation was on analysis and improvement of the Subspace Predictive Control (SPC)

Summary

Introduction

1.1 Dissertation ObjectivesTwo fundamental steps in developing control systems are: (i) obtaining model of the system, and (ii) designing a controller for the system. Where A, B, C and D are system matrices, K is the Kalman predictor gain, and ζ(k) is innovation sequence This state-space model is more suitable for MIMO systems, and it is transferable to the general form of the model in (2.2) by using following equations, Gp(q−1; θ) = C(θ)[qI − A(θ)]−1B(θ) Gd(q−1; θ) = I + C(θ)[qI − A(θ)]−1K(θ) (2.16) (2.17). In MIMO systems, the constrained SPC problem is considered as a Quadratic Programming (QP) problem and solved by a QP function solver to reference input(k) predicted output This method is called Constriction PSO, which is formulated as follows, vi(t + 1) = χ[vi(t) + r1φ1(pbi(t) − pi(t)) + r2φ2(pg(t) − pi(t))] pi(t + 1) = pi(t) + vi(t + 1) (2.177) (2.178). Parameter χ guaranties a decreasing velocity for each particle by increasing the number of iterations [120, 126]

Methods

Results

Conclusion