Study on Some Problems in Analysis and Control of Fractional-order Systems
|School||Shanghai Jiaotong University|
|Course||Control Theory and Control Engineering|
|Keywords||Fractional order systems Generalized System Delays Robust Stability Norm bounded uncertainty Polytopic uncertain LMI State feedback Dynamic output feedback|
Fractional Calculus Calculus as a normal promotion, it appears more than 300 years of history. Fractional differential order of the system is determined by a non-integer differential equation systems, compared to integer-order model, fractional order systems more accurately describe the real-world physical systems. Currently, fractional order systems theory research is still in the initial stage. For the average fractional order systems, effective stability analysis and controller design method is still lacking. In this paper, two types of fractional order systems theory, systems, namely Fractional systems and fractional delay systems were studied. According to the authors' knowledge, on Fractional systematic theoretical study is the first time in the country. For generalized fractional order linear time-invariant systems, linear matrix inequality approach, stability of the system is discussed and studied uncertain Fractional Robust stability and robust controller design method; For fractional steady when delay systems, Lyapunov function method using a complex matrix measure method and these two methods to analyze the root system characteristics and stability, and to explore its frequency domain analysis. Specific work of this paper are: (1) study the fractional generalized system regularity and impulse issues. Based on Fractional given system state space description, using Laplace transform state response of the system, discuss the understanding of the existence and uniqueness of the problem and the pulse problem, a generalized system of fractional regularity conditions and no pulse conditions . (2) for Fractional system stability and allowing were studied. Analysis of the generalized system of fractional poles in the complex plane distribution of the system are obtained in the form of pieces of angle stability criterion. Proposed a new generalized system D LMI allowed sufficient condition, and thus derive the necessary and sufficient condition in two forms, namely strict LMI conditions and has a non-strict equality constraints LMI conditions to determine the fractional generalized system permissibility. (3) based on linear matrix inequality approach to study the parameter uncertainty Fractional Robust allow control problem. For bounded and polytopic two kinds of parameter uncertainty, namely uncertainty raised sufficient condition to ensure the robustness of Fractional Admissibility. And under these conditions, the use of variable substitution method was presented by LMI represents state feedback controller, and dynamic output feedback controller design rules, and finally gives some simulation results to demonstrate the correctness and feasibility of the proposed method . (4) studied the fractional delay systems stability problems. Gives the fractional delay system stability and delay-independent definition of stability, using a complex matrix Lyapunov function method and the matrix measure method two methods to derive some delay-independent stability condition, taking into account the delay size, made some delay-dependent stability criterion.