Improved generalized proportional integral observer based control for systems with multi-uncertainties

It is difficult to control systems with multi-uncertainties directly based on traditional active disturbance rejection control (ADRC) framework, due to the mismatched condition, non integral-chain form. Besides, the traditional Hurwitz bounded stability of the extended state observer (ESO) may not guarantee acceptable observation accuracy. To this end, this paper presents an improved generalized proportional integral observer (IGPIO) to estimate the multi-uncertainties and the derivatives, and an IGPIO based control (IGPIOBC) strategy is proposed to eliminate the multi-uncertainties actively and accurately. The proof of bounded stability for the IGPIO and the closed loop system are derived by the singular perturbation approach and Lyapunov theory. Meanwhile, the corresponding relationship between the gain parameters and the bandwidth of the IGPIO is deduced. The simulations of the numerical example, RLC circuit and DC motor system verify the effectiveness of the proposed method.