Fast Adaptive Robust Differentiator Based Robust-Adaptive Control of Grid-Tied Inverters with a New L Filter Design Method

Abstract

In this research, a new nonlinear and adaptive state feedback controller with a fast-adaptive robust differentiator is presented for grid-tied inverters. All parameters and external disturbances are taken as uncertain in the design of the proposed controller without the disadvantages of singularity and over-parameterization. A robust differentiator based on the second order sliding mode is also developed with a fast-adaptive structure to be able to consider the time derivative of the virtual control input. Unlike the conventional backstepping, the proposed differentiator overcomes the problem of explosion of complexity. In the closed-loop control system, the three phase source currents and direct current (DC) bus voltage are assumed to be available for feedback. Using the Lyapunov stability theory, it is proven that the overall control system has the global asymptotic stability. In addition, a new simple L filter design method based on the total harmonic distortion approach is also proposed. Simulations and experimental results show that the proposed controller assurances drive the tracking errors to zero with better performance, and it is robust against all uncertainties. Moreover, the proposed L filter design method matches the total harmonic distortion (THD) aim in the design with the experimental result.

Synchronous Generator Rectification System Based on Double Closed-Loop Control of Backstepping and Sliding Mode Variable Structure

“…where k 1 is the proportional gain, k 2 is the integral gain. Bringing Equation (16) into Equation ( 15), the following is given:…”

“…Therefore, the construction of the reasonable virtual control variable is the most important step in the design of the backstepping control method. In [16], a new nonlinear and adaptive state feedback controller with a fast-adaptive robust differentiator was presented, which avoids the complexity of the existing backstepping method but its velocity of tracking input error is slow. In [17], a robust integral backstepping controller is designed to reduce overshoot/undershoot and steady-state error, but its response time is long and the design process is complex.…”