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| Discrete-time optimal control method for linear time-delay systems |
| Revised:July 30, 2002 |
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| DOI：10.7511/jslx20042033 |
| KeyWord:time-delay,discrete optimal control,building structure,earthquake response |
| Pan Ying~ |
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| Abstract: |
| A discrete-time optimal control method for linear systems with time-delay is proposed, in which a numerical algorithm for control implementation is presented. The controller is designed in terms of two cases that the time delay is respectively integer and non-integer times of the sampling period. The motion equation of system with time delay is transformed into standard discrete form that contains no time delay. Then, the optimal controller is designed by using the classical optimal control theory. The discrete quadratic function is used as objective function in design of the controller to guarantee good control efficiency on sampling points. In every step of computation of the deduced controller, it contains not only current step of state feedback but also linear combination of some former steps of control. Since the optimal controller is obtained directly from the time-delay differential equation, the control method proposed is prone to guarantee stability of the controlled structures. Instability in responses might occur if the system with time delay is controlled by the optimal controller designed with no consideration of time delay. Furthermore, the control method presented is available for the case of large time delay. Simulation results demonstrate that the continuous time performance index is superior to that of discrete-time and the control method presented ensures the stability of the controlled structures as well as the desired reduction in the maximum responses. The performance of the proposed control method under different sampling periods is investigated numerically to illustrate the feasibility for application to seismically excited linear systems. |
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