Robust Design For Systems With Parameter Uncertainty

This thesis takes a kind of systems with parameter uncertainty lightly damped modes as a center. It is difficult to obtain excellent robust stability for classical control theory due to lightly damped modes with varying resonant frequency. However, H_∞design methodology which will be discussed and analyzed is a good way to deal with this kind of problems.The general method which treats with structured uncertainty,μ-synthesis will be adopted firstly, which combines two procedures about the analysis of difference between the results achieved by D-K iteration and H_∞norm index and interpretation of D fitness convergence. The controller achieved byμ-synthesis and simulations will be also given. In addition, problems caused byμ-synthesis when dealing with parameter uncertainty are discussed and analyzed.Based on the above studied contents, a novel method based onμ-analysis is given according to specialty of this kind of problems. This method will grasp main contradictions of systems with parameter uncertainty, namely robust stability, and give two design requirements which are robust stability and better nominal performance that system must have. Nominal system will be firstly designed by H_∞methodology, and then whether the system with perturbations meets the design requirements or not will be tested byμ-analysis. Simulation results illustrate that this method achieves better disturbance attenuation thanμ-synthesis.H_∞loop shaping design is also a way to deal with systems with parameter uncertainty. Recently a paper employed a method combining H_∞loop shaping andμ-synthesis to try to achieve better effects. Based on characteristics of two methods, this thesis will analyze this combined method, and discuss the problemsμ-synthesis in H_∞loop shaping solves. Here this problem is not a general robust performance problem in most cases. Then this paper will make detailed discussion. Numeral examples and simulation results illustrate that the H_∞loop shaping plusμ-synthesis is unhelpful to increase perturbation bounds and improve performance.