Study On Performance Optimizations And Design Constraints Of Control Systems

The design constraints of feedback control systems and optimizations of networkedcontrol systems are focal and hot topics of great interest recently in science and engineering.The relationship between the performance limitations and system intrinsic characteristic,such as, nonminimum phase zeros, unstable poles and reference signal, is vitalreference to the controller design. The perfect performance limitations for tracking problemshave been uncovered. But when the steady tracking error is zero, how about therelationship between the the minimum control energy and the characteristics of controlsystems? The networked control system structure will prevail in the future. With theimpact of network circumstance, many issues emerged inevitably, such as network induceddelay, limited bandwidth, data packet dropouts, error caused by the quantization,disturbance signals etc. Under the networked environment condition, how to considerthe performance limitations caused by communications? This thesis, based on previousworks of the others, systematically and deeply investigates the minimum control energyfor the systems with zero steady tracking error. And furthermore, the initial results aboutthe performance limitations for networked control systems are got.The continuous feedback control system is considered. The problem under considerationis the minimum input energy for tracking control. The reference signal is unity stepsignal. Using a time-domain integral of the square of the input as a performance index,we derived the relations between the limitations and plant characteristics that depend onthe unstable poles, nonminimum phase zeros, the stable part of the plant and the referencesignal direction vector. Two degree of freedom controller is effective to eliminatethe influence of unstable poles for the performance index.Minimum tracking energy for multi-variable discrete feedback systems were studied.The fundamental limitations imposed by the plant structure are given. The referencesignal is unity step sequences. Using the input usage as a measure of tracking energy.We derived relations that represent fundamental limitations on the achievable infimumof the tracking energy for general MIMO discrete systems. The relations depend on the unstable poles and the stable part of the plant and the reference signal direction vector.Two-degree-of-freedom controller case is considered, too.A class of impulsive switched control systems are considered. Where the objectiveis to minimize a cost functional defined on the output and input. The optimal controllerscan be obtained through the solutions of a series of Riccati matrix equations. The performancefor optimal control and cheap optimal control are respectively given. Sufficientconditions for passivity of impulsive switched control systems are obtained, and the optimalinput controllers of system are addressed, too. The conclusions showed the impulsesare critical elements to the performance indices. Which are useful references to the controllersdesign.The optimal tracking problems for networked feedback systems were investigated.The reference signal is step signal. Two degree of freedom controller is adopted. Based onthe Youla parametrization of controller, suppose there is an impulsive disturbance fromthe sensor to the controller, the best performance for tracking limitation under energyconstraints is given. Continuously, we considered the tracking limitation in the case thatthe disturbance is Gaussian white noise. The performance limitation is tightly dependenton the nonminimum phase zeros, and the plant gain in the frequency range etc.The minimum energy regulation problem for partly networked control systemswas investigated. We adopted the coprime factorization of transfer function, Youlaparametrization of controller and Bezout identity. The explicit expression for the minimumregulation energy is related to the magnitude of plant, unstable poles and the directionsof unstable poles.Synchronization in leader-follower networks with varying time-delay interconnectionswas investigated. In such a network, the leader had its own dynamics and wasfollowed by all the other nodes. Specifically, a variable structure control strategy was developedfor the synchronization of the leader-follower networks based on the Lyapunovstability theory. An illustrative example was given to demonstrate the effectiveness of theproposed method.Finally, a summary has been done for all discussions in the dissertation. Theresearch works further study are presented for the networked control systems.