Nonlinear Control Based On Virtual Reference Feedback Tuning

Modern control theory usually based on precise mathematical model. However, it is unable to obtain a precise mathematical model, or too difficult to obtain. And in the specific field control, we accumulate a lot of on-line and off-line data. When it is too difficult to establish accurate mathematical model, how to use the input and output data to control has become the urgent problem. Virtual reference feedback tuning method makes the closed loop transfer function to approach to the desired transfer function to realize control targets. So, virtual reference feedback tuning method attracted the attention of many researchers. In this dissertation, we consider nonlinear systems and carry out the following work:(1) We consider a single-input single-output nonlinear system and utilize virtual reference feedback controller tuning method to design two degree of freedom controllers. Its control target is:the closed-loop transfer function between the disturbance input and the output and the closed-loop transfer function between the reference input and the output approaches to the selected transfer functions. Based on the quadratic performance index and the corresponding filter selected we can approximate achieve control targets.(2) We utilize virtual reference feedback tuning method to design one degree of freedom controllers for multi-input multi-output nonlinear systems. Control target of the method is:the closed-loop transfer function between the reference input and the output approaches to the selected reference model. This method is similar to virtual reference feedback controller tuning method of single-input single-output nonlinear system. We analyse the manipulator model with friction, and using virtual reference feedback tuning method to design the controller.(3) For a non-negative imaginary system, we study how to design the controller, which can make the closed-loop system approach to the negative imaginary system. We consider the construction of negative imaginary systems for single-input single-output linear systems, single-input single-output nonlinear systems, multiple-input multiple-output linear systems and multi-input multi-output nonlinear system. Under certain conditions, the interconnected of the discrete time weak strict negative imaginary uncertainties and negative imaginary system is internal stability, so the controller is robust.In the above three problems, the problem of designing controller is transformed into the optimization of performance, then we give the specific algorithm. We also give specific examples of simulation to verify the feasibility of virtual reference feedback tuning algorithm.