Achieving Precise Linear and Circular Trajectory Tracking through Fuzzy PID Controller Design

A fuzzy PID controller is an intelligent control method that combines traditional PID control with fuzzy logic, demonstrating exceptional performance in nonlinear and complex systems. For linear and circular trajectory tracking problems, the fuzzy PID controller dynamically adjusts PID parameters to adapt to system variations, thereby achieving more precise control outcomes.

Fuzzy PID Controller Design Approach Fuzzification Process: Input error and error rate of change are converted into fuzzy quantities through fuzzy rules, representing linguistic variables in the control process (such as "large error" or "small error"). In code implementation, this typically involves defining membership functions using triangular or trapezoidal shapes and mapping crisp inputs to fuzzy sets through degree-of-membership calculations. Fuzzy Rule Base: A set of "IF-THEN" rules is established to adjust PID parameters (proportional, integral, and derivative gains) based on different error and error change rate conditions. For example, if the error is large and changing rapidly, the proportional gain can be increased to improve response speed. Programmatically, this is implemented using a rule evaluation matrix that processes input combinations through min-max operations. Defuzzification: The output from fuzzy inference is converted into precise control quantities used to adjust the actual system output. Common implementation methods include centroid calculation or weighted average approaches to derive crisp control values from aggregated fuzzy sets.

Linear and Circular Trajectory Tracking Optimization Linear Trajectory: The system requires maintaining stable velocity and direction. The fuzzy PID controller reduces steady-state error by adjusting the integral term while utilizing the derivative term to suppress overshoot. Algorithm implementation involves continuous monitoring of positional deviation and velocity errors to trigger appropriate rule-based parameter adjustments. Circular Trajectory: Due to continuous curved motion requirements, the fuzzy PID controller must dynamically adapt to directional changes. Through fuzzy inference-based parameter tuning, it ensures smooth transitions and minimal tracking errors. Code implementation typically incorporates tangent angle calculations and curvature compensation in the control loop to handle circular path dynamics.

The advantage of fuzzy PID controllers lies in their adaptive capabilities, making them particularly suitable for dynamic systems requiring high-precision tracking. Through proper design of fuzzy rules, the tracking performance for both linear and circular trajectories can be effectively enhanced. The controller's robustness is demonstrated through its ability to handle system nonlinearities without requiring precise mathematical models of the controlled plant.