Adaptive control scheme for plants with time-varying structure using on-line parameter estimation

Nonlinear adaptive control aims at the stabilization of nonlinear plants using on-line adaptation of the controller to compensate for the changes that the plant may suffer in time and/or for lack of a precise model describing the plant. Among the nonlinear plants, the feedback linearizable class is broad and contains many systems of practical interest. This work is concerned with the mathematical development of an adaptive control scheme applicable to strict feedback plants with a time-varying structure which belongs to a class of feedback linearizable plants. This type of plants show a dependence of the plant dynamics on an exogenous variable that can be considered as an additional input to the system. Previous work on this type of systems used some amount of information about the plant in order to generate a stabilizing control law, i.e., some knowledge of the plant dependence on the exogenous variable was included in the controller in order to obtain the stabilization of the plant. In the present work, no knowledge of the plant dependence is assumed with the exception of the bounds of the exogenous variable, and the variations of the plant dynamics due to changes on that variable are estimated on-line. A Direct Adaptive Control (DAC) theorem is presented along with its proof, and some remarks about the characteristics of this scheme. Since the purpose of this work includes the comparison of the performance of the DAC scheme with other relevant nonlinear control schemes, a brief review of three schemes selected for comparison is presented. In order to test the performance of the DAC scheme, a simulation of its operation is performed using the slender delta wing rock phenomenon as practical example. Wing rock is a nonlinear phenomenon in which an aircraft suffers oscillations of its roll angle, for high angles of attack. The magnitude and frequency of these oscillations are dependent on the angle of attack, aircraft configuration and some other flow conditions. Three other nonlinear control schemes found in recent relevant literature are also simulated. The comparison is made in base to the following measures of performance: Ability to reach stability, range of operation, state and control energy, performance under saturation conditions, and transient response. The results are presented in tabulated and graphical form and some weight is given to each of the variables measured to obtain an overall measure of performance for each scheme on each simulation. Such measure shows that the DAC scheme outperforms the other three schemes for the selected criteria.