MULTIPURPOSE DESIGN OF MULTIVARIABLE NONLINEAR SLOWLY VARYING SYSTEM

This paper deals with the multivariable nonlinear time-varying discrete-time system with nonsquare plant to achieve the following multipurpose control objectives simultaneously: (i) closed-loop stability; (ii) input-output decoupling; (iii) desired time responses; (iv) tracking; in an operation region according to adequate exogenous scheduling trajectory varying between the known upper and lower bounds of a set of scheduling parameters. By employing the linear frozen-time design, a table of scheduled multipurpose controllers is built for the linearized plant around the operating points. A new, explicit and simple algorithm of such multipurpose design is presented. Based on an equivalent active system, the multipurpose performances of the nonlinear time-varying system are analyzed. It is shown that if the equivalent active linearized plant trajectory is slowly varying and the deviation between the true scheduling trajectory and the equivalent active scheduling parameter trajectory is sufficiently small in the operation region, then the multipurpose control objectives will be achieved. An example of the orbit control of a satellite will illustrate the claimed results.