| Underactuated mechanical system is a kind of system with fewer independent control inputs than degrees of freedom. Because of the reduction of drivers, it particularly is suitable for fields which are sensitive to weight and energy , such as aerospace, robotics. However, the reduction of drivers increases the difficulty of controling system. As a typical underactuated system, studing on the Acrobot is helpful to solve the problem in unedractuated system.In this paper, the aim is to move the Acrobot from its stable downward position to its unstable inverted position. When Acrobot is attached to upright equilibrium, it has a smaller rate. At the same time, the swing up time is reduced as short as possible.In actual system, the torque and angle is restricted. It is more practical studying on this system.The physical system is different from the ideal model. Mathematical model of physical Acrobot is established in this paper. The simulation results verify the validity of the model. Practical factors related to the paremeters is added to the kinetic equation, such as friction, pulleys, etc.. These factors will produce different effects on the system. In addition, for parameter identification of the Acrobot, genetic algorithm is used in the paper, that ensures the design of swing up controller. Bang-Bang control law is used to obtain the optimal swing up time, but it can not complete the heigth task, it only provides a time basis. Based on the time, two fast swing up controllers are designed. One is using partial feedback linearized, whose parameters of controller is optimized by genetic algorithm. The other controller is based on genetic algorithm. In the first controller based on partial feedback linearization, an energy pumping strategy was used to solving the swing up control problem. The second link tracks a dynamic reference trajectory, that ensures the problem of swing-up. In this paper, a new reference function is designed such that the second link may reach upright position simultaneously when the first link reaches upright position. Besides, genetic algorithm is used to optimize the parameters of controller such that the time of swing up can be shorten. The latter based on genetic algorithm does not use the idear of energy pumping strategy. It simulates the biological behavior of genetic and evolutionary operation in the nature. With the mechanism of survival of the fittest, the Acrobot can swing up gradually. In the scheme, the swing up time can be reduced as short as possible. What is more, it can make the rate of Acrobot smaller when Acrobot arrive to the tiptop.At last, the experimental platform is improved. The circuit is designed to enhance the motor output. The simulation platform is established based on the RTW in the Simulink7.2. The experimental results verify the control algorithm. |
