Synthesis of Controllers for MIMO Systems with Time Response Specifications

Abstract

This paper proposes the design of fixed low order controllers for Multi Input Multi Output (MIMO) decoupled systems. The simplified decoupling is used as a decoupling system technique due to its advantages compared to other decoupling methods. The main objective of the proposed controllers is to satisfy some desired closed loop step response performances such as the settling time and the overshoot. The controller design is formulated as an optimization problem which is non convex and it takes in account the desired closed loop performances. Therefore, classical methods used to solve the non convex optimization problem can generate a local solution and the resulting control law is not optimal. Thus, the thought is to use a global optimization method in order to obtain an optimal solution which will guarantee the desired time response specifications. In this work the Generalized Geometric Programming (GGP) is exploited as a global optimization method. The key idea of this method consists in transforming an optimization problem, initially, non convex to a convex one by some mathematical transformations. Simulation results and a comparison study between the presented approach and a Proportional Integral (PI) controller are given in order to shed light the efficiency of the proposed controllers.

Real-Time Reconfigurations of Embedded Control Systems

“…The majority of industrial processes, by nature, have multiple outputs and states variables, hence the need to control them. Multi-Input Multi-Output (MIMO) systems are made up of several measurement and control signals which often present complex couplings between them (Ben Hariz M., 2014). This survey describes some of the component-based technologies which seem to be more relevant.…”

Design of controllers for decoupled TITO systems using different decoupling techniques

“…So, we will apply the convexification strategy of the GGP method [10], [11], [15]. We remark that these six terms have positively signed terms, and then the exponential transformation will be applied.…”

“…In previous work [8], we have presented the design of a fixed low-order controller for Single Input Single Output (SISO) systems with some time response performances such as the settling time and the overshoot. The design of this controller for decoupled Multiple Input Multiple Output systems using the simplified decoupling technique was proposed in [10] and [11]. The controller synthesis is formulated as an optimization problem which takes into consideration the desired closedloop performances.…”

Comparison between robust and multi-model controllers

“…The design of controllers for multiple inputs multiple outputs (MIMO) systems was presented in Ben Hariz and colleagues. [24][25][26] In this article, we propose the design and the implementation of a robust fixed low-order controller for uncertain systems. The proposed controller must guarantee some closed-loop specifications.…”