Low Order Multivariable Adaptive Control

Adaptive control refers to the control of systems that have poorly known parameters but a well modeled structure. The adaptive control of linear, time-invariant systems is well understood. However, for systems with multiple inputs and multiple outputs the adaptive controller is of high order and complex making the approach inapplicable in a number of practical problems. In this thesis a new approach to adaptive control of multivariable plants is proposed. The proposed controller is of lower order and contains fewer on-line adjustable parameters than other adaptive control methods. For designing the multivariable adaptive controller, the order of the plant is not required to be known. The minimum row relative degrees of the plant transfer function matrix are assumed not to exceed two. A stability proof based on positive realness of the underlying system dynamics is given. Since in practice unmodeled dynamics may be present, a robustified adaptive control algorithm is presented. A proof is given that shows that loop signals remain bounded when unmodeled dynamics are excited. The control approach is well suited to the control of distributed systems which have a high modal density and use multiple inputs and outputs. Two applications are discussed, flexible structures and combustion. In the flexible structure application it is shown that tracking can be achieved in the presence of on-line introduced parametric uncertainties. Using an adaptive version of the internal model principle, attenuation of external disturbances of unknown frequency is accomplished as well. In the combustion application it is shown that unstable pressure modes can be stabilized in the presence of parametric uncertainties in the model and changes in the operating point. Thesis Supervisor: Anuradha M. Annaswamy Title: Assistant Professor