D. Vaes, Optimal static decoupling for multivariable control design, 2005

Abstract

The dissertation deals with the design of multivariable feedback controllers based on decoupling. Such a design consists of two steps: (1) the calculation of input and output decoupling transformations such that the transformed system is optimally decoupled and (2) the design of independent SISO controllers for the diagonal elements of the transformed system.

This research is motivated by the unsatisfactory results of the existing MIMO control design approaches: (1) a decentralized controller,i.e. a combination of independent SISO controllers, often yields insufficient performance, (2) the advanced MIMO techniques, e.g. μ-synthesis, are hard to tune and implement in practice, and (3) the existing decoupling procedures yield suboptimal decoupling results and consequently a limited performance.

A new method to design and optimize the decoupling transformations is developed. The optimized procedure is a maximization of the performance achievable with a decentralized controller designed for the transformed system. The resulting optimal decoupling yiels the following advantages: (1) no MIMO model is required (the decoupling step is based on the measured FRF matrix), (2) the decoupling calculation is fully integrated with the subsequent robust decentralized control design yielding improved performance, (3) the control design is as straightforward as a decentralized control design and (4) the obtained control performance is comparable or in most case even better than achieved with μ-synthesis, and is significantly better than the performance obtained with other decoupling procedures.

In order to make the control design more straightforward, guidelines are developed which predict the achievable performance of a linear controller based on easily measureable characteristics of the test setup. This allows to state a priori what is and what is not achievable with a linear controller.

This new decoupling procedure is thoroughly compared with all existing procedures, both on simulation and experimental examples. The experimental validation is performed on three automotive vibartion test rigs. The MIMO control problem in these applications consists of applying predefined loadings by controlling the hydraulic actuators of the test rig. The experiments confirm the favorable properties of the developed optimal decoupling approach and the accuracy of the developed guidelines to predict achievable performance.

Order Code

Code: 05D7