Optimal Control Approach for Robust Control Design of Uncertain Dynamic System with Delay

• Main Authors: Yu-Chen Lin, 林昱成
• Other Authors: Chun-Liang Lin
• Format: Others
• Language: en_US
• Online Access: http://ndltd.ncl.edu.tw/handle/72790957765777611067

博士 === 國立中興大學 === 電機工程學系所 === 97 === In realistic control system design, time delay exists inevitably. Neglecting time delay may cause degradation of control performance or even induce instability to the dynamic system. This dissertation presents an optimal control approach for a robust control design problem of the linear time-delay systems by taking parameter uncertainties and time delays into account. Based on a variety of robust control theories, many significant research results have been presented and shown through analysis and controller design for uncertain time-delay systems during the past decades. Although those robust control law have been utilized to improve the performance and stability robustness of uncertain time-delay systems effectively; however, the design of robust controllers is always so complex that the value of the hybrid performance function is difficult to calculate explicitly. Therefore, to solve this robust control problem, it is first shown that the robust control problem can be equivalently transformed into an optimal control problem so that the amount of plant uncertainties is indirectly reflected in the performance index. By some algebraic manipulations and appropriate uncertainty descriptions, the uncertain dynamical system can achieve not only stability, but also the guaranteed level of performance. A suitable linear state feedback control law is characterized via Lyapunov stability theory to ensure asymptotic stability and performance robustness of the closed-loop system. The dynamic programming idea in principle of optimality in this dissertation is to derive the solution to the optimal control design problem in the continuous time-delay systems with matched uncertain case. In addition, since robust control design problem can be exactly equivalently transformed into a class of optimal control problem with bounded plane uncertainties, the proposed approaches can be directly applied to state delay, control input delay, matched uncertainties and unmatched uncertainties systems. For stability analysis, we consider the Lyapunov stability theory for plant uncertainties systems with control input time delays with the application of Razumikhin approach. The stabilizability criteria will be derived by introducing some relaxation correlative weights and turning parameters, which lead to lesser conservative results. On the other hand, instantaneous a class of optimal control approach for the robust control design problem for vibration control of uncertain the light rail vehicle’s (LRV’s) asymmetric dual-stage pantograph-catenary systems with actuator time delays in control is investigated. Because of the uncertain time-varying contact force between the pantograph shoe and catenary and external excitations in the pantograph systems, it is essential to design a control law that will guarantee the performance robustness of the pantograph systems under uncertainties and external excitations. Simulation results indicate that our proposed optimal control approach is feasible and is an attractive strategy for dealing with the actuator delay in vibration active pantograph suspension systems and is effective in suppressing maximum structural responses. The benefits of our proposed scheme are demonstrated in the simulation of an active pantograph suspension system with model uncertainty, external disturbances and actuator delays, and the approach can efficiently replaced with the conventional complex and difficult robust control design problem. In this dissertation, we present the following results: (i) optimal control design process for the generalized dynamic systems associated with the state delay and uncertainties; (ii) application of the active pantograph suspension systems associated with the actuator delay and matched uncertainties; (iii) stability analysis of the above dynamic systems. Extensive simulations of the above topics are well performed to demonstrate the efficacy of our proposed approach. Finally, numerically illustrative examples of the LRV’s pantograph suspension model are given to verify the performance improvement achievable with the proposed optimal control approach when the plane uncertainties and control input delay is considered simultaneously.