Variable Structure Control Of A Class Of Non-Linear System

In this paper, the stability control of double inverted pendulum system which located on a cart is studied,whose application background is the stability control model of rockets and missiles before their launching.Variable structure control theory(VSC) with sliding mode which has strong robust to external disturbance and perturbation parameters is adopted,and three kinds of variable structure control with sliding mode and their switching functions are designed,then the simulation results indicate that the control aims have been achieved.The research results have important theory significance and project application values in the controller design of flight vehicles such as rockets and missiles.After the introduction of basic conceptions and basic questions of variable structure control system,the dynamics and mathematic model of the double inverted pendulum system is established using Lagrange equation with the view of energy,and its invariability to external disturbance and perturbation parameters is analysied.After its linear model is obtained,we have designed three kinds of variable structure control with sliding mode based on pole placement,optimal quadric form and whole sliding mode,in order to guarantee the stability control near the unstable point.The symbolic function in the variable structure control is replaced by the saturation function to reduce the chattering which is brought by the variable structure control system.After the corresponding theory analyse,a concrete numerical control model is obtained with the substitution of actual parameters of the double inverted pendulum system.With the help of MATLAB,the three concrete variable structure control with sliding mode are promoted,and theirs'corresponding simulation results approve the feasibility and validity of the designed schemes.