| Time delay inevitably exists in active control systems. Sometimes it is inherent in control systems such as sensor signals gathering and conveying, controller calculating and process for actuator to build up the required control force; sometimes it is a voluntary introduction into the system such as the using of data filter. Time delay may result in non-synchronization of control force, making the actuator input energy into the controlled system when energy is not needed. This may cause the degradation of control efficiency or even the instability of the control system. Moreover, even original dynamic system is linear, the system may behave with many complex nonlinear dynamic behaviors when active control is applied and time delay is taken into account. Therefore, the research on time delay is of important theoretical significance and practical value. Today time delay is also one of the hot frontiers in mathematics, control mechanics and structural engineering etc.Generally speaking, study on time delay falls into two categories: elimination technology and utilization technology. Elimination technology takes time delay as a"bad"factor and, in control design, tries to eliminate its negative effect on system performance. General practices in elimination technology include the Taylor series expansion, phase shift technique and advance state estimation etc. While time-delay utilization technology not only ignores the inherent delay in the system but introduces a voluntary delay and takes it as a design parameter for control feedback and, by adjusting the magnitude of time delay, to get satisfying control performance and effectiveness. This technology includes time-delay resonator, time-delay filter, time-delay utilization for controlling chaotic motion and for improving system stability etc. Although up to now researches have been done much on the elimination and utilization of time delay, most work is theoretically based and little on the experiment. Furthermore, the work is more about single time-delay problems and little about multiple time-delays. This dissertation presents theoretical and experimental studies on multiple time delays in active control of flexible structures. The research was funded by the National Natural Science Foundation of China (Grant No.'s 10772112, 10472065), the Key Project of Ministry of Education of China (Grant No. 107043), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20070248032), and the Key Scientific Project of Shanghai Municipal Education Commission (Grant No. 09ZZ17). Some achievements are obtained both in theory and application and a few highlights are as follows:(1)This dissertation studies the Discrete Processing Method for multiple time-delay problems, with the finite degree-of-freedom system (building structure) and the distributing parameter system (flexible beam and plate) being regarded as structure models. In design of the discrete time-delay controller, by a particular augmentation of state variables, the system state equation with multiple time delays is discretized and transformed into a standard discrete form without any explicit time delay, then the controller with time delays is designed using the discrete optimal control method and the discrete variable structure control method. The detailed design process of this controller, the iterative algorithm for all parameters and the stability criteria for the delay system are all provided. The designed time-delay controller contains not only the state feedback of current step but also the linear combination of some previous steps of control. Since the time-delay controller is designed directly from the time-delay differential equation and no approximation and hypothesis involved, it tends to guarantee the stability of control systems, and is suitable for both small time delay and large time delay. Simulation results have shown that this controller is feasible and effective in the vibration suppression of flexible structures. In addition, the location of piezoelectric (PZT) actuator on the flexible plate is optimized by using the controllable Gramian matrix and the particle swarm optimizer (PSO) algorithm.(2)This dissertation also probes the Continuous Processing Method for multiple time delays, with a manipulator system being the structural model; the first-order approximation equation being the dynamics model; the optimal tracking control method being the controller and a piezoelectric patch being the actuator adhered on the flexible arm. In design of continuous multiple-time-delay controller, by a particular integral transformation for state variables, the system state equation with multiple time delays is first transformed into a standard form without any explicit time delay and system dimensions stay unchanged, and then the active controller can be designed based on the standard state equation. The design process of continuous multiple-time-delay controller and the iterative algorithm of integral term in the integral transformation are both detailed in the paper. The following three cases are considered in the numerical simulations: (i) Only the joint torque is applied for system control and it has time delay; (ii) Both the joint torque and PZT actuator are applied for system control and only the PZT actuator has time delay; (iii) Both the joint torque and PZT actuator are applied for system control and they have different time delays. Simulation results indicate that the designed time-delay controller can make the manipulator system arrive at an expected position in a specified time and the vibration of flexible arm can also be suppressed.(3)Based on a DSP control board, the experimental study is conducted for active control of the flexible beam, plate and manipulator, in which single time delay and multiple time delays are both considered. Experimental scheme is programmed and secondary development of the DSP program is also implemented. All practical problems encountered in the experiment such as signal differential, circuit and friction compensation are effectively solved. Both the discrete and continuous time-delay processing methods prove effective in the experiment.(4)This dissertation explores the delay identification problem in the time-delay dynamic system as well. When doing this, delay identification is converted to an optimization problem, where the sum of absolute values of the difference between the predicted response and actual response of the controlled system in a period of time makes the objective function and the particle swarm optimizer makes the optimization algorithm. The identifications of single time delay and multiple time delays are both discussed. Simulation results indicate that the identification method presented is effective in determining the real delay in control systems.Time-delay problem is a challenging research topic, where many aspects need further study and more efforts. At conclusion, a summary of work done in this dissertation is given out and some problems of interest are also brought forward for future research.
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