Research On The Application In Inverted Pendulum Based On Optimal Control Theory

Inverted pendulum system is a typical single-in-and-multiple-output and nonlinear unstable system, research on which in theory will involve in many crucial problems existing in system control such as nonlinearity, robustness, and so on. Meanwhile the research on inverted pendulum control bears an important engineering background, the control mode applied to which can be widely applied to the following fields such as military engineering, astronavigation, robot, and industrial process control.In this thesis, mathematical models of both double inverted pendulum and triple inverted pendulum are built, on which an analysis of each motion status of the inverted pendulum is made. The selection principle of weighted matrix is discussed in terms of the fundamental of optimal control theory, hence to sum up three procedures using heuristic method to design optimal controller. Making a qualitative analysis of the effects taking by weighs of the weighted matrix on performance of the inverted pendulum system through simulation on the condition that the system is stable.A optimal controller designed by selecting appropriate weighted matrix to implement simulation control of the double inverted pendulum and triple inverted pendulum systems, and to implement physical control of the double inverted pendulum. The experimental results shows the optimal controller designed by means of heuristic method can implement the control of complex nonlinear system, which, however, features certain defects and the selection of weighted matrix is difficult to considerate all the performance objectives of the system.To offset the shortcomings of the optimal controller designed by heuristic method, in this thesis the system controller is designed by configuration method combined pole assignment and optimal control theory. The designer can choose two main poles of the system to calculate the weighted matrix in terms of it to design poles to configure the optimal controller which favorably implements the simulation and physical control of double inverted pendulum system, the results from which demonstrate the optimal controller configured by the poles calculated can achieve much better and more precise control effectiveness and can offset the shortcomings of heuristic method. And the simulation of the triple inverted pendulum system shows pole-assignment optimal controller can achieve good control performance for more complex nonlinear system too.