Enhanced Bounded Integral Control of Input-to-State Stable Nonlinear Systems

The bounded integral controller (BIC) was recently proposed to replace the traditional integral controller (IC) for the regulation of any input-to-state stable (ISS) nonlinear system and guarantee closed-loop system stability with a bounded control output. In this paper, an enhanced version of the BIC is presented to provide a better approximation of the traditional IC in the entire bounded range of the control output and relax the assumption on the selection of the initial conditions of the original BIC. Using Lyapunov methods, it is analytically proven that the enhanced BIC maintains the zero-gain property and guarantees closed-loop stability of any nonlinear ISS plant with a given bound at the control output, without suffering from integrator windup issues. The plant dynamics and structure can be unkown as long as the plant is ISS. Hence, the proposed enhanced version of the BIC can replace the traditional IC in many applications where closed-loop stability cannot be proven, without changing the controller operation. A practical example is simulated to verify the performance of the proposed enhanced BIC compared to the original version and the traditional IC.