Reduced-order controllers for nonlinear and discrete-time systems

This dissertation deals with the design and implementation of reduced order controllers for nonlinear and discrete-time systems.; A modified nonlinear quadratic Gaussian control method that guarantees the stability characteristic of 60{dollar}spcirc{dollar} minimum phase margin and infinite gain margin for complete state information case is proposed. This control method is easier to implement and more robust than Beaman's nonlinear quadratic Gaussian control method. An LQG controller reduction method is applied to the nonlinear quadratic Gaussian controller to obtain a linear reduced order optimal controller for the nonlinear system. The illustrative example demonstrates a successful reduction of a 23rd order controller to a 10th order controller.; A nonlinear H{dollar}sb{lcub}infty{rcub}{dollar} control method is presented. This method combines statistical linearization and H{dollar}sb{lcub}infty{rcub}{dollar} norm-bounding control to provide an H{dollar}sb{lcub}infty{rcub}{dollar} control approach for nonlinear stochastic systems with a Gaussian noise. The H{dollar}sb{lcub}infty{rcub}{dollar} norm of the closed-loop system is guaranteed to be smaller than a prescribed scalar {dollar}gamma{dollar}. Unlike other nonlinear H{dollar}sb{lcub}infty{rcub}{dollar} control methods based on small perturbation linearized model, this control method can accommodate any range of noise magnitudes. The extension of H{dollar}sb{lcub}infty{rcub}{dollar} controller order reduction to observer-based nonlinear H{dollar}sb{lcub}infty{rcub}{dollar} control enables the design of low order controllers for these systems. The effectiveness of this controller reduction method is demonstrated in the simulation results. The nonlinear H{dollar}sb{lcub}infty{rcub}{dollar} controller is reduced from 23rd to 4th order.; A controller reduction technique for discrete-time H{dollar}sb{lcub}infty{rcub}{dollar} control is also presented. Based on discrete-time H{dollar}sb{lcub}infty{rcub}{dollar} control with two uncoupled Riccati equations, the relationship between the discrete-time H{dollar}sb{lcub}infty{rcub}{dollar} characteristic values and the Hankel singular values is studied. The results turned out to be of the same form as those of their continuous-time counterparts. A discrete-time coprime factorization method is developed by introducing a weighting matrix. This method makes it possible, for discrete-time systems, to obtain state-space realizations of a pair of weighted coprime factors without the explicit computation of spectral factors. H{dollar}sb{lcub}infty{rcub}{dollar} balanced truncation is then applied to the normalized factorization to obtain a reduced order system. A stability test is given to guarantee that the reduced order controller stabilizes the full order plant based on this factorization. The form of the final test criterion is proved to be the same as that of the continuous-time case. An illustrative example is included to demonstrate the ease of the implementation of the proposed controller reduction method.