Modeling and Control of a Two-Axis Stabilized Gimbal Based on Kane Method

A two-axis stabilizing gimbal is a device that ensures a sensor is working properly on a moving platform. When classical mechanics (Newton-Euler and Lagrange) is employed to model a two-axis stable gimbal, its limitations can complicate the modeling process. To address this issue, a method for establishing a dynamic model for a two-axis stabilizing platform based on the Kane method is proposed in this paper. The Kane method offers the advantage of a simple model structure and computational efficiency. Initially, utilizing a generalized coordinate system, expressions of the generalized velocities, deflection velocities and angular velocities are derived. Subsequently, the generalized active forces and inertial forces acting on the two-axis stabilized gimbal are analyzed. Finally, by combining force and velocity with the Kane equation, the dynamic model of the two-axis stable platform is obtained, demonstrating the validity of the Kane method for establishing the two-axis stable platform model. To ensure the pointing accuracy stability of the two-axis stabilizing platform, a Novel Particle Swarm Optimization Proportion Integration Differentiation (NPSO-PID) controller is designed using the PSO algorithm. It is then simulated in MATLAB/Simulink and compared with a classical PID controller. Simulation results demonstrate that NPSO-PID exhibits superior object tracking performance compared to classical PID controllers and better optimization of control parameters compared to traditional PSO-PID controllers.