Controller Design For Fractional Order Systems With Input Saturation

Nowadays with the deepening of system science,more realistic and accurate mathematical models are needed to analyze and synthesize the system.In the past,integer calculus is used to describe the real world.However,a lot of physical process and systems cannot be described accurately using integer order differential equation,as our world is essentially fractional order.For example,many systems such as viscoelastic systems,dielectric polarization,electromagnetic waves and so on have turned out to have the memory and the hereditary properties.It is better to reveal the essence characteristics and dynamic behaviors using fractional order models.The introduction of fractional calculus will enable people to better understand the real world,and it will play an important role in science and engineering.Every system has constraints in their nature,in special,input saturation is the most common phenomenon in real world.Input saturation exists in various physical systems,such as chemical plants,mechanical systems,and communication networks.For the integer order systems,input saturation has received much attention from researchers and many significant results have been achieved.Due to the particularity and complexity of the fractional order systems,existing results for the integer order systems subject to input saturation cannot be straightforwardly applied to fractional order systems.Fractional order systems subject to input saturation have rarely been addressed in the literature.This thesis deals with the controller design for the fractional order systems subject to input saturation.Chapter 3 investigates stability and estimation of domain of attraction of fractional order systems subject to input saturation in the case that the fractional order is 1<?<2.The stability condition can be used for fractional order systems with nonlinear element that is Lipschitz in state has been derived.On the basis of exploring the special property of saturation using an auxiliary feedback matrix,another stability condition has been achieved.Estimation of domain of attraction can be expressed as optimizations whose conditions are given in the form of Linear Matrix Inequalities.Also the controller design is proposed.Chapter 4 discusses stability and stable region in the case that 0<?<1.Sector bounded condition of the saturation function is exploited for the discussion,combined with the latest LMI criteria of stability for fractional order systems.Based on the proposed stability condition,Linear Matrix Inequalities for stability test and estimation of the stable region is provided.Furthermore,a controller design method that maximizes the estimated stable region is given.Chapter 5 considers the uncertain fractional order systems subject to input saturation,stabilization conditions and robust controller design method are proposed.Numerical examples are given to verify the effectiveness of the results.