Model matching two degree of freedom controllers for single input single output and multi input multi output systems

Abstract

Classical techniques of control system design using frequency response plots newlineof Bode, Nichols and Nyquist, or root-locus diagrams of Evans are well newlinedocumented in the literature. These methods which are normally limited to single newlineinput single output (SISO) systems are graphical and of a trial-and-error in nature. newlineModern control law design techniques based on optimal control theory and newlineHand#57345;optimization result in high-order controllers that are at least as complex as the newlinesystem to be controlled. The order of such controllers may be equal to that of the newlineplant or may even exceed it. The complexity of such high order controllers makes newlinepractical implementation very difficult. Optimal controllers often turn out to be newlinefragile, i.e. they are very sensitive to coefficient perturbations. Moreover, such newline optimal controllers often require feedback of all the states that may not always newlinebe amenable to easy measurement. Thus, a need exists for a design method that newlineprovides a simple low order implementable controller, which can adequately newlinecontrol Single-Input Single-Output (SISO) and Multi-Input Multi-Output (MIMO) newlineplants using only output feedback. newlineFor most of the conventional controllers in One Degree Of Freedom (1-DOF) newlineconfiguration, options for tuning are less. Also it is impossible to achieve both the newlinespecifications on the desired system performance as well as disturbance rejection newlinesimultaneously with a 1-DOF controller. To deal simultaneously with the two newlineproblems of, attaining the desired system response as specified by a system newlinetransfer function as well as achieving sufficient feedback to handle plant newlineparameter variations and disturbance acting on the plant, a controller configuration newlinewith at least 2-DOF is necessary. Moreover, the closed loop system with 2-DOF newlinecontroller guarantees stability and at the same time matches the desired newlineperformance and accesses both reference and output signal with the same cost as newlinethat of 1-DOF controller.