Controller Design Based On Random Algorithm

In traditional methods, some dynamic performance indicators, used for analyzing the system, such as overshoot, adjusting time and peak time, can reflect the dynamic performance well, but they are only suitable for the low-order system. When designing the controller based on these performance indicators, it is necessary to reduce the characteristic equation order and change the characteristic equation into the representation form with dominant of closed-loop poles, which will lead the final result deviate. On the other hand, uncertainty widely exists in actual control systems. Taking uncertain factors into the controller design is the traditional robust control, whose basic idea is that the controller should make the system still stable when 'the worst case' occurs. The robust controller designed based on 'the worst case' has two shortcomings. One is that 'the worst case' seldom occurs in actual control systems, even never. So, consideration of 'the worst case' will restrict the choice rang of controller parameters greatly. The other is that robust control has a higher calculation complexity and a larger application limitation, by which lots of problems can not be solved.For problems mentioned above, random algorithm is used for a further solution. Since most of the traditional dynamic performance indicators are used to analyze performance of the system with determined parameters. Application of random algorithm in the system with determined parameters and with uncertain parameters is mainly studied in this paper. Random algorithm is used in the controller design for the system with determined parameters. At first, based on traditional dynamic performance indicators, sets of controller parameters meeting the performance requirements are obtained, which are taken into the system for simulation validation. Next, random algorithm is used for the optimal controller design. Sampling points are produced continuously and randomly during the parameter changing interval, and values of constraint function and objective function are calculated. By comparing values ofthe objective function one by one, controller parameter sets with smaller objective function values are retained, and the optimal approximate solution is obtained. Finally, controller parameters are taken into the system simulation validation.The system with uncertain parameters used in this paper is a second-order vehicle active suspension, which has four independent uncertain parameters, and application of the random algorithm is studied from the following two aspects. On one hand, the random algorithm is used to design the state feedback controller. Considering two distribution cases of uncertain parameters, random numbers are used to simulate random values of the independent uncertain parameters. In accordance with certain performance indicators, controller parameters under the two distribution cases of uncertain parameters are obtained, which are compared to those obtained from LQG method by simulation, showing that the controller obtained by the random algorithm has better control effect. On the other hand, the random algorithm is used to design the probability regulator. Random numbers are also used to simulate random values of the independent uncertain parameters. According to the required accuracy and risk factor, a set of regulator parameters are found by iteration, making the system matrix always meet the required matrix inequality when uncertain parameters are multiple values. Finally, simulation comparison is made to the controller parameters obtained with LQ method, showing that the regulator obtained by random algorithm has better control effect.Random algorithm can change the resolving processes of some problems from complicated to simple, but its application has shortage in two the hands. On one hand, for independent uncertain parameters in the actual system, it's difficult to describe their distribution with one or several functions. At present, random algorithm is used under the assumption of a certain distribution of independent uncertain parameters. On the other hand, if to obtain the accurate solution, all cases of uncertain parameters should be selected. However, when the system contains several independent uncertain parameters, and a high accuracy is required, it needs a long running time, which may seriously beyond the reasonable range. With the development of computer technology and the improvement of mathematical theory, random algorithm can be used more and more widely.