Time Delay Output Feedback Control Of Dynamic System And Its Application

Dynamic system control has to be driven by a control algorithm which reads the structural response and makes a decision about the value to be assigned to the adjustable parameters of the actuator. Such a control chain is characterized by time delays which exit in an actively controlled system of structural vibration inevitably. Another important issue for the vibration control of dynamic system is the measurement of the state variables. Realizing state feedback needs to measure all the state variables, which is difficult in general. Therefore, output feedback control of structural vibration plays an important role in practical application. Considering the two aspects mentioned above, this paper deals with the time delay control of dynamic system by output feedback, i.e., utilizing the measurable output to realize an active vibration control of the entire system. The differential equation of motion of the system is first transformed to a state-space model with time delay control input. Then, a transformation with a linear term and an integral term is employed to transform the original time delay system into a form without time delays. Accordingly, the principle of output feedback is used to design an optimal control law for the system in terms of a reasonable performance index. As an example, the dynamical responses of a three-story model under earthquake loadings are investigated by numerical calculation, where the value of the time delay is integer times the sampling period and the integration time step is chosen to be identical to the sampling period. The numerical results show that instability in structural responses may occur if the system with time delay is controlled using the control strategy designed in the case of no time delay; The value of time delay, which is different, might lead to different effectiveness of the control for dynamic systems; All the results concluded from the simulation show that the time delay control algorithm of structural vibration by output feedback is valid and practically applicable. Since a lot of energy requirement provided by external facility limits the implementation of active control in practice, semi-active control which is yet stale and low-power required damping systems is also studied here. The output feedback controller is designed for dynamic vibration system in terms of"on-off"control strategy. The semi-active time delay output feedback control law designed based on the active control strategy proposed here is verified numerically by application to civil structure and a quarter car suspension, respectively. Simulation results for semi-active control, in compared with those for active control, indicate that both the active and semi-active control have good results. What is more, semi-active control has itself special property, so semi-active time delay control algorithm for the system implemented with MR damper is effective and meaningful.