Optimizing interval type-2 fuzzy logic PID controller with an improved constraint differential evolution algorithm

Compared to electric actuators, hydraulic actuators can deliver greater driving forces within limited spaces due to their high-power density characteristics, making them widely used in high-performance drive applications such as humanoid robots. However, these systems exhibit significant nonlinear dynamic properties, posing challenges for high-precision control of their output forces. To address the control challenges of hydraulic actuators for humanoid robots, this paper first establishes a system model integrating the hydraulic power source with nonlinear hydraulic cylinders. Subsequently, an improved constrained differential evolution with better and nearest option (ICBNDE) algorithm is proposed, featuring an efficient search mechanism and an approximate solution selection strategy. Then, an interval type-2 fuzzy logic PID controller (IT2FL-PID-C) optimized by ICBNDE is constructed for the closed-loop control of the hydraulic actuator system. To validate the proposed algorithm's performance, the convergence and feasibility analyses of ICBNDE are conducted on the CEC2006 constrained benchmark test. Subsequently, the designed controller is compared with a traditional PID controller, and ICBNDE is contrasted with several classical constrained optimization algorithms under identical architectures. Experimental results demonstrate that the ICBNDE based IT2FL-PID-C significantly outperforms traditional PID methods in both control accuracy and system stability. Furthermore, ICBNDE exhibits superior performance compared to other algorithms in controller parameter optimization, validating its effectiveness and superiority in controlling complex nonlinear hydraulic systems.