Comparison of a Double and Triple Nonlinear Hyperbolic Proportional-Integral-Derivative (PID) compensator for a servo pneumatic actuator

Steady-state attributes are significant criteria for designing a single rod double actuating pneumatic servo system controller. Scholars have proposed various compensators for research enhancement in industrial applications. One of the main problems observed for the industry application is that the compensators that are applied are linear type, thus is a mismatch to the pneumatic system that is highly nonlinear. Owing to this reason, a Double Nonlinear Hyperbolic and two types of Triple Nonlinear Hyperbolic Proportional-Integrator-Derivative (PID) compensator are designed to overcome the system's nonlinearity. Both the Double and Triple Nonlinear Hyperbolic PID shows a better steady-state error compared to the basic PID compensator based on the simulation and experimental analysis. The transient response performance of each nonlinear compensator is also not compromised in achieving a better steady-state. The Double Nonlinear Hyperbolic PID compensator presents the best actual position in the experimental analysis. However, the Triple Nonlinear Hyperbolic PID presents the best results for the Integral Absolute Error (IAE) analysis. In addition, each of the controllers will be analyzed for stability adapting the Popov plot. The Triple Nonlinear hyperbolic PID controller could be further improved by optimizing the parameter by adapting advanced optimization tools such as Particle Swarm Optimization (PSO) and Genetic Algorithm (GA).