Design of limited state feedback controllers for linear multivariable systems
Thesis DisciplineElectrical Engineering
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
The control of linear multivariable systems (LMS) where only some of the state variables are directly measurable is considered. The control configurations adopted employ feedback from the measurable state variables, i.e., the system outputs, via multivariable dynamic compensators. The design problem of determining the compensator parameters is approached via the following methods: (1) The minimization of quadratic performance indices in the state and control variables, i.e., the optimal control method. (2) The positioning of the closed-loop system poles, i.e., the pole placement (or modal control) method. (3) The realization of appropriate state feedback laws through the use of observers. The optimal output feedback control of essentially noise-free LMS is first examined. A gradient-type solution algorithm is developed that appears to be more efficient computationally than previous techniques; a modified algorithm for handling open-loop unstable LMS is also described. The treatment is then generalized to include cases where the LMS contains appreciable amounts of process and measurement noise; both stationary and non-stationary stochastic problems are considered. Pole placement via output feedback is next examined as a possible alternative to the optimal control approach. To this end, unrestricted-rank pole placement techniques are developed which enable the closed-loop poles to be positioned either arbitrarily close to specified locations, or within prescribed regions of the complex plane. Unlike previous work, the new techniques enable exact pole placement to be achieved with dynamic compensators having the lowest possible order. Consideration is then given to the more general problems of achieving exact (or approximate) pole placement while minimizing (a) quadratic performance indices in the state and control variables, (b) pole sensitivities to small or large system parameter variations, and (c) steady-state following errors due to measurable and unmeasurable disturbances. Finally, the construction of minimal-order observers is formulated as a static optimization problem for which a gradient-type solution technique is proposed. The suitability of using such observers to realize state feedback laws for achieving optimal control, pole placement or decoupling is also examined.