Modeling and Analyses of the N-link PenduBot
As the foundation of the multi-link PenduBot control, the mathematical model should be established first. Based on the method of kinematics and dynamics, the N-link PenduBot mathematical models are established in this paper, including the nonlinear model, the linear model and the generalized model which considers the motor characteristic. The natural characteristic of the system is analyzed. By using the condition number of the controllability matrix, the control difficulty for the higher order systems is compared. From the comparison result, the control law of the different links PenduBot is obtained. Increasing with the count of PenduBot links, the control difficulty is growing dramatically. Only a strong control measure can make it stable. So, further study on multi-link PenduBot can be carried on.
Design of control system with limited feedback gain based on CPSO algorithm
To solve the problem that the feedback gain is too high during high-order control system design, we propose the design idea of limited feedback gain. Using the chaos particle swarm algorithm (CPSO), we realized the process of limited feedback gain control system design. Taking the three-link PenduBot controller as an example, the design process is illustrated in detail. Simulation and physical control results indicate that the design method is effective, the gain we get is relatively low, and could be easily implemented. The design idea provides a new and effective method for high-order control system design.
Dynamic models of a rotary double inverted pendulum system
This paper describes the dynamic models of a double rotary inverted pendulum, which has been developed for the laboratory experiments. Two different-length rigid pendulums are connected to a horizontally rotating disc which is attached directly to a DC motor. The derivation of the dynamical equations and the linearized model are described. Finally, the time responses of open-loop system are shown and compared with the experimental data to verify the model validity.