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This paper explores the significance and feasibility of addressing a notion that the system error of a nonlinear feedback control can be decorated by an inverse tangent function in order to attain a sound energy-efficient performance. The related mathematical model and relevant evaluation of this concept are further illustrated by demonstrating a case study about the control performance of water tank level. The rationale of robust control and theoretical algorithm of Lyapunov stability theorem are outlined to evaluate the effectiveness of nonlinear feedback with inverse tangent function in terms of improving robustness of PID (Proportional–Integral–Derivative) controller and energy-saving capability. By demonstrating five simulations of different scenarios, it ultimately proves that the modified robust PID controller by inverse tangent function meets the requirement of energy-saving capacity. Comparing with the routine PID control, the mean control input of controlling water tank level can be reduced up to 39.2% by using modified nonlinear feedback controller. This nonlinear feedback PID controller is energy efficient and concise for its convenient use, which is feasible to expand its utility to other applications.

Inverse Tangent Functional Nonlinear Feedback Control and Its Application to Water Tank Level Control