Modern Approaches in Control

In this thesis a model reference adaptive control algorithm for non linear systems has been proposed. Parameter estimation in non linear systems has motivated a lot of work .The proposed algorithm is based on the separation of the system and controller design. This separation is easy in linear systems and there are many researches in it but in nonlinear system separation of the system and controller design is difficult . The proposed algorithm succeeded to solve this problem.In this thesis a control structure has been proposed so that the plant output is capable of tracking certain desired trajectory .Using a suitable objective function and variation arguments ,a set of necessary conditions have been developed to make the parameters of the proposed model and controller can be determined . Based on these necessary conditions, a numerical scheme is presented for computing the unknowns .This approach depends on reducing the error between the plant output and model output that is known as identification error and reducing the error between model output and model reference adaptive control output that is known as tracking error, the identification error modifies the model and the tracking error modifies the controller .The two errors are adjusted to be minimum concurrent. The parameters are updated directly from knowledge of the output error signal . A basic mathematical analysis will be carried out to adjust the error. The salient feature of these algorithm is that there is no need to solve any Lyapunov equation .An important part of every adaptive control scheme is the on –line estimator used to provide an estimate of the plant or controller parameters . The adaptive law are derived by minimizing the cost function . The type of the cost function and method of minimization determines the properties of the resulting adaptive law, as well as the overall performance of the adaptive scheme. The proposed algorithm succeeded to verify that, and succeeded also to design the controller so that, a control law will force the output to asymptotically track a given reference model output .To demonstrate the applicability of the algorithm ; some examples were applied on the algorithm for linear and nonlinear systems.The obtained computer results prove that the algorithm works well in practice.