A design methodology for synthesizing low order robust controllers for flexible structures

Abstract

In this research, a design methodology is developed for realizing low order robust controllers for flexible structures modelled as partial differential equations (PDEs). The efficacy of the methodology is illustrated by synthesizing robust controllers for (i) a free-free beam system and (ii) a flexible robot link system. The performance of these controllers are evaluated in simulations and in actual implementation on a flexible robot link set up. Reduced (finite) order models are frequently used in designing controllers for flexible structures due to their simplicity. They often lead to control spillover effects which tend to degrade the performance or even destabilize. The control spillover can be completely removed only by designing a controller based on a full (infinite) order model. Recently full order models have been used for designing controllers by modern robust control design techniques such as H[infinity] and H[2]. However, the resulting controllers from these techniques typically have excessively high orders since the optimization involved calls for a systematic cancellation of the stable poles and zeros of the plant. The design methodology proposed here is an outgrowth of the standard quantitative feedback theory (QFT) and utilizes the closed form irrational transfer function obtained from an infinite-dimensional model described by hyperbolic PDEs. Although standard QFT has many attractive features such as its capacity to deal with parametric plant uncertainty and cost of feedback, the loop-shaping procedure is not necessarily straightforward. Hence when the standard QFT procedure is applied to these infinite order plants, the loop-shaping procedure becomes even more difficult. The proposed methodology alleviates this by converting the loop-shaping procedure for an infinite order plant into that of a finite order plant by introducing a finite order quasi-nominal plant. In spite of the challenging loop-shaping task, the method provides enough transparency for one to customize the controllers by trading off some design specifications to achieve more practical or realizable controllers. In particular, low order robust controllers with limited cost of feedback can be obtained without the phenomenon of control spillover.