A Practical Approach to Robust Sliding Mode Control

In this thesis, important aspects of sliding mode control are investigated. Althoughsliding mode control has many restrictions and drawbacks, this type of controller is attractivebecause it has many powerful characteristics. In order to show the performanceand robustness of the controllers proposed in the thesis, two simulation systems and anexperimental one are studied.In this work, a new approach to design sliding mode and observer is proposed. The systematicway to design and tune sliding mode output feedback controller is proposed. Thedesign problem is solved in two steps, the first involves astate feedback and the second,an output feedback problem. First, using null space dynamics, the sliding hyperplanefor the unmatched uncertainty is designed. Then, by tuning the sliding hyperplane, a robustcontroller is constructed for the whole uncertainty; this problem takes the form of astatic output feedback problem. Based on this, a dynamic output feedback controller forthe system, augmented with the sliding hyperplane, is designed. The synthesis involvesthe solution of an LMI and a BMI problem; the BMI problem is solved iteratively. Thedesigu is based on rninimizing H2 , Hoo nonn. This structure is extended to the LPVsystem to build the LPV sliding mode controller; the controller is simulated to ADIP.The design is achieved by first designing the fixed sliding hyperplane; then, the LPVcompensator is fed the hyperplane with necessary information about the state.A new approach to design controller based robust observer is proposed. The controllerconsists of state feedback gain fed from the observer with necessary information aboutthe states. The parameters of the state feedback gain and observer are designed robustlyagainst parameter uncertainty that can be formulated in polytopic form. This techniquedoes not depend on the separation principle, which is usually used to design the observer.A new method for the synthesis and analysis of BMI is proposed for the design; the BMIproblem is solved by converting it to LMI by fixing one of the decision variables andsolving the others. In addition, based on the robust observer, a free chattering slidingmode controller based variant sliding hyperplane is proposed. The design procedure isalso formulated for the problem in BMI formula that is solved iteratively as explainedpreviously. The efficiency of the methods is demonstrated by comparing them with statefeedback controller based observer, constructed using the separation principle method.All the proposed controllers are applied successfully to the rectilinear mechanical system.The methods for tuning the controller parameters are discussed and the rules to tunethese controllers are given. A new tuning parameter, a ,is proposcd. The influence of thisparameter on the performance and robustness of the ACC problem is shown. It also hasan important role in tuning the controller for real system. For the robust observer, the60 is an important tuning parameter to find the feasible region with good performancefor non-convex matrix inequality.