Robust Stability Analysis And Control Of Uncertain Systems

It is almost impossible to obtain an accurate mathematics model for the practical industrial process. The model under which the controller is designed is usually different from the real plant owing to model reduction; linearizing approximations; unmodeled dynamics; the change of the operating environment errors; unmeasureable disturbances, and so on. Therefore, Based-model the modern control theory is hardly used to analyze and synthesize a practical control system. The differences can be described as the model uncertainties. On the other hand, with pipe transmission processes, net transmission and large-lag links, etc, a large number of industrial processes can be modeled as time-delay systems. The existence of delay is frequently a source of instability and deterioration of system pergormances, so the study of delay systems always attracts considerable attention in the control theory literature. In control applications, most of computer control systems are sampled-data systems, so great efforts should be directed towards these problems for sampled-data systems. The further discussion of the problems not only can perfect the theoretical basis of control systems, but also will promote the practical applications of control theory. Therefore, the robust performance analysis and synthesis problem of uncertain systems, particularly, uncertain systems with time-delay and sampled-data systems, will be mainly studied in this dissertationThis paper consists of two parts: robust stability analysis and robust controller design of uncertain systems with time-delay; robust control of uncertain sampled-data systems applied in the welding quality control.On the robust stability and robust controller design of uncertain systems with time-delay, the main works are as follows:First, a sufficient condition for the stability of linear uncertain systems with a time-varying delay is presented. A vector inequality and the stability theory of Lyapunov are employed to derive the condition, The obtained criterion can include information on the size of delay, and therefore, belongs to delay-dependent criteria.Second, a robust control design method for parameter uncertain systems that have delay in both state and control input is present. Through a certain algebraicRiccati inequality approach, a state feedback controller is obtained, the result is dependent on the size of delay, The uncertain parameters are unknown and time varying, but norm-bounded.Third, the problem of robust stabilization for linear uncertain systems with states and control delays is studies. The uncertain parameters are unknown and time varying, but norm-bounded, the delays are also time-varying. Based on the Lyapunov function, sufficient condition for the robust stabilization via state feedback was presented in terms of linear matrix inequalities, and a memoryless state feedback control law was constructed by using the solutions of the linear matrix inequalities. The result is dependent on the both size of delays and information on the derivative of the delays, therefore the conservativeness of the controller design is reduced.Fourth , the problem of robust stabilization for uncertain time-delay systems with rank-1 is studied. Based on the Lyapunov function, sufficient conditions for the robust stabilization via state feedback were presented in terms of linear matrix inequalities. A state feedback control law was constructed by using the solutions of the linear matrix inequalities. The result can include information on the size of delay, and less conservative than the delay-independent ones.On the robust control of uncertain sampled-data systems applied in the welding quality control, the main works are as follows:First, the single variable mathematics models of pulsed gas tungsten welding flat link welding quality control process are established. The pulse duty ratio, peak current and welding speed are selected as input of system, the width of weld pod backside as output of system, simulation for all of the models and one of the model...