The use of model following methods to generate suboptimal feedback control†

Abstract

Implementation of linear optimal control laws oftentimes requires that all system state variables be physically available for measurement and feedback. The well known impracticality of this requirement motivates the work described in this paper which is addressed to the use of model following methods in the synthesis of sub-optimal feedback controllers which do not require sensing all of the system state variables. The approach presented here consists of first computing a complete set of optimal feedback gains and thus generating optimum system response which is then used as a model toward which a suboptimal design can strive. A suboptimal control is postulated with zero feedback gains as desired, the remaining gains being as yet arbitrary. The average integrated difference between the model closed loop response and the suboptimal closed loop response is then minimized by selection of these remaining feedback gains. For a given feedback configuration, the method thus determines the suboptimal closed loop control yielding a response which is as close as possible in a given well-defined sense to the model response. Defining equations are derived and parameter optimisation methods are utilized to compute the free feedback gains. The method is particularly well suited to digital computation requiring only the use of standard parameter optimization algorithms as well as an algorithm to solve a set of bilinear matrix equations. An example involving regulation of the longitudinal modes of a VTOL flight vehicle is presented to illustrate the model following capabilities of the synthesis procedure.