Fractional Order PID Control of a Nonlinear Missile Trajectory in the Pitch Channel

This paper explores the application of fractional order PID (FPID) and gain-scheduled FPID (GSFPID) controllers for regulating the nonlinear trajectory of a missile in the pitch channel. The FPID and GSFPID controllers are designed and their parameters are optimized using Simulink design optimization within the Matlab toolbox. This optimization process aims to determine the optimal parameters for achieving superior tracking performance with a step reference signal.

The GSFPID controller is specifically engineered to address the physical limitations of the actuator in the pitch channel. Its design consists of two distinct stages: a boost stage, where thrust is maximized, and a sustainment stage, where thrust is minimized. This two-stage approach effectively mitigates actuator limitations, enhancing overall control effectiveness.

To accurately represent the nonlinear missile model with FPID and GSFPID controllers, the equations of motion are derived and implemented within the Matlab-Simulink environment. The performance of both controllers in controlling the nonlinear missile trajectory is then evaluated and compared. The study further investigates the impact of wind effects and dynamic uncertainties on system performance, providing a comprehensive analysis of the controllers' robustness.

Finally, to assess the stability of the closed-loop nonlinear system, a linearization procedure is performed at a critical operating point (t = 5.8 seconds) using the Simulink linear analysis tool. This stability analysis provides valuable insights into the system's behavior and guarantees its stability under diverse operating conditions.

In conclusion, this research contributes to the advancement of nonlinear control systems by demonstrating the efficacy of FPID and GSFPID controllers for regulating the trajectory of a nonlinear missile model. The study encompasses controller design, parameter optimization, performance evaluation under various disturbances, and stability analysis of the linearized system, offering a holistic understanding of the system's capabilities.