A Systematic Approach of Loop Filter Tuning of TD-Based PLLs Using LQR-Based Approach Considering Time Delay

A systematic design approach for loop filter (LF) tuning of transport delay-based phase-locked loops (TD-PLLs) to ensure an optimal control effort is presented in this article. The linear quadratic regulator (LQR) problem is applied to TD-PLL and nonfrequency-dependent TD-PLL (NTD-PLL) without approximating their time-delay functions through their appropriate state-space transformations. The systematic design guidelines of weighting matrixes selection for the LQR problem are discussed to ensure optimal performance of TD-based PLLs. The effectiveness of the suggested LQR method in tuning TD-PLL and NTD-PLL, considering time-delay function, is finally evaluated through extensive experimental results. Results also show the ability of the suggested method to achieve the desired dynamic performance in terms of faster system response without significant overshoot and steady-state error and with improved grid disturbance rejection capability compared with the existing tuning methodologies.