Parametric Stability Analysis And Designed Controller Application For Interconnected Systems With Quantization

With the popularity of network and digital controller, the problem of quantization has ignited increasing attentions. Owing to the advantage of high efficiency and reliability etc, the decentralized control has been the main control strategy for large-scale systems. In many practical systems, it is often the case that there exist uncertain parameters and variations of these parameters result in a moving or even disappeared equilibrium, which leads to the systems unstable. In evaluating the dynamic properties of interconnected systems with quantization, it is convenient to use the concept of parametric stability, which simultaneously captures the existence and the stability of a moving equilibrium. The design and application of decentralized controller are studied for interconnected systems with quantization in this thesis. Moreover, the parametric stability has been analyzed. The main contents of this thesis are shown as follows:(1) The problem of dynamic output feedback H∞controllers and quantizers is considered for uncertain interconnected networked systems. The quantizers will probably lead to instability of the systems. For this purpose, under the assumption that a decentralized dynamic output feedback controller has been designed by using the homotopy method, a quantized control strategy is proposed which is dependent not only on the controller states but also on the system measurement outputs and control inputs so that the quantized closed-loop system is asymptotically stable and with the same H∞disturbance attenuation level as on no quantizers circumstance. Both the designed controllers and the quantizers’ parameters are constructed in a decentralized manner, depending on local information. An example is proposed to illustrate the effectiveness of the proposed method.(2) The analysis of parametric stability and the design of decentralized state feedback controller are studied for interconnected systems with quantization which consist of N subsystems. The output of each controller need to be quantized by logarithm quantizer before it is passed to the subsystem, and the quantized density would affect the stability of the systems. Firstly, the decentralized state feedback controller is proposed to make the closed-loop system parametric stable. Then, the lower bound of the quantized density could be evaluated by local information, so that the closed-loop system is still parametric stable when the parameters change in a certain region. Finally, the controller is optimized. The simulation results show that by using the designed quantized controllers, the interconnected large-scaled systems are parametric stabilized.(3) The problem of parametric stability and decentralized controllers with quantization is studied for interconnected inverted pendulum systems. Firstly, Lagrange method is used to construct the model of the interconnected systems composed of two coupled inverted pendulum by a sliding spring. Then, based on the solution of LMI, the decentralized state feedback controller is designed to make the closed-loop system parametric stable. The logarithm quantizer is used to quantizing the control input of each subsystem and the range of quantized density is regulated by local information, so that the closed-loop system is still parametric stable under structural perturbations caused by the jumps of the coupled spring. Finally, the simulation results show that the designed controllers can parametric stabilize the interconnected inverted pendulum systems effectively.