Friction Compensation And Adaptive Control For The Linear Single Inverted Pendulum

Friction, which is a complex nonlinear physical phenomenon, appears in allmechanical servo system．The effects of friction are mainly demonstrated as the stick-slip motion, at a low velocity, relatively big static errors or limit cycle oscillation andeven lead the control system to be unstable．The most researches on invertedpendulum system only considered the viscous friction, whereas the friction in theactual system is more complex than this, so small amplitude oscillations resulted,when the controllers designed based on this model as implemented in experimentalsystem．To offset the impact of friction and get rid of the oscillation, frictioncompensation strategy for the linear inverted pendulum is proposed in this paper, withthe following major elements:Firstly, Lagrange method is employed to model the linear inverted pendulum, thenLQR controller is designed in the case that without considering the frictioncompensation, to make the pendulum stable．Genetic algorithms is utilized as anoptimization method to identify the parameters of exponential friction model as well asLuGre friction model．Compared with the linear identification method, this schemecan effectively avoid the problem of local minimum．Secondly, model-based fixed compensation and adaptive compensation methodsare utilized to compensate the friction of the inverted pendulum system． For thefixed compensation, the non-linear friction models with the parameters identified bythe genetic algorithms are utilized to verify the friction between the cart and the trackis the source of the small amplitude oscillations．In order to compensate the friction,new controllers are designed based on different friction models, respectively．Frictionidentification along with compensation scheme based on radial basis function neuralnetwork (RBF network) with δ learning-rule plus momentum is proposed in theadaptive friction compensation section．Simulation results are given to prove thevalidity and feasibility of the proposed fixed compensator and adaptive compensator, by establishing SIMULINK control block diagrams．...