Robust PD controller design

In control systems, when the standard design methods are used to minimize H-infinity norm of the system, the controllers which were obtained should have least same degree with the system. In this condition, even if there is not any problem for low-order systems at first sight, the system degree are going to increase due to the weighted functions which can be added to systems? input and output for creating performance outputs according to the requests. So the controllers which were obtained with usage of the standard design methods have low feasibility in practical applications, especially in the embedded systems and the aerospace industries. Because of the these reasons, the low-order or fixed-order H-infinity controller design problem has become the most important field in the control engineering and the studies have increased related with this subject. However, fixed-order controller design problem is defined in a nonconvex cluster and there is not any polynomial solving algorithm for general solution in nonconvex clusters, so different solution methods used in recent studies. While the fixed order H-infinity controller is being designed, one of the most important points to be considered is system uncertainties for industrial control systems. Otherwise the controllers can not represent the systems and the production loss will be occured. The main purpose of this thesis is to develop fixed-order robust H-infinity controller design method to minimize H-infinity norm of the system. While the controller is being desired, polynomial approach method is used which is created on basis of positive polynomial matrices? features instead of the using standard design approaches. The certain non-convex structure which is known from base of the problem is reduced to a convex shape with Positive Real Lemma. LMI is used to solve and represent the convex problem. Conservatism of the design method is depend selected central polynomial completely. In this study, firstly a full-order H-infinity controller is designed by considering the uncertainty of the system for trolley on the jib subsystem which belongs to a three degree of freedom crane system. Secondly, the fixed order robust H-infinity controllers (especially PD controller) which have different controller degrees are designed with proposed method for same system. Finally, the controllers are applied to systems in simulation network and the system outputs are obtained.