A PID Control Method Based on Internal Model Control to Suppress Vibration of the Transmission Chain of Wind Power Generation System

Abstract

Vibrations occur in the wind turbine drivetrain due to the drivetrain’s elasticity and gear clearance. Typically, the PID control method is used to suppress elastic vibration, while the method with the disturbance suppression function is used to suppress nonlinear gear clearance vibration. The purpose of this paper is to propose an equivalent PID control method based on the internal model control (IMC) for suppressing vibration caused by the wind turbine drivetrain’s elasticity and gear clearance. The equivalent PID controller can suppresses elastic vibration; the IMC controller can suppresses gear clearance vibration. First, the vibration principle of the two-mass wind turbine drivetrain with clearance is discussed. After analyzing the nonlinear characteristics of the gear clearance, the nonlinear clearance system is decomposed into a linear unit and a nonlinear bounded disturbance unit. To suppress nonlinear bounded disturbances, a disturbance suppression method based on IMC is proposed; simultaneously, an equivalent PID controller based on IMC is designed to resolve the vibration issue caused by the wind turbine drivetrain’s elasticity. The simulation experimental results show that the clearance vibration is suppressed by the original IMC method. The PID controller obtained by the IMC equivalent transformation can suppress the elastic vibration.

Robust sampled‐data PID controller design for regulation control of nonlinear systems with output delay

“…𝛾 2 > 0 and applying Schur complement, 37 this concludes that V + 2𝛼V ≤ 0 can be guaranteed by the condition (11), which completes the proof. ▪ Remark 4.…”

“…Furthermore, the performance comparison between the designed sampled-data PID controller and the classical PID controllers is proposed, such as continuous-time PID controller and IMC (internal mode control)-PID 10,11…”

“…It is worth noting that the functional V 1 , … , V 4 are extended to analyze the descriptor system (12) based on Selivanov and Fridman, 28 which are proved to be positive. According to the Lyapunov functional (13), Theorem 1 employees the descriptor method to reduce the product terms and the coupling of the system matrices B, B 𝜖 , B d and the decision variables Q, r, z in the LMI (11), which makes it possible to design the robust sampled-data PID controller in the next subsection.…”

“…then set P 3 = 𝜅P 2 > 0, where the scalar 𝜅 > 0. Hence, the LMI ( 21) is derived by denoting P 3 = 𝜅P 2 and Kp , Ki , Kd1 , Kd2 for the LMI (11). Note that the matrix P 2 has a special property that the sum of the first row and the sum of the second row of P −1 2 are both zero, and the sum of the third row of P −1 2 is P −1 33 .…”

“…1 Due to its simplicity and robustness, PID control has been widely and commonly used in engineering and practice. The research on PID control has been applied in various control aspects, such as delay robustness of linear time-invariant (LTI) systems, 2,3 active disturbance rejection control (ADRC), [4][5][6] PID control parameters tuning, [7][8][9] internal mode control (IMC)-PID 10,11 and desired dynamic equational (DDE)-PID, 12,13 to name a few. Recently, more researchers focus on PID control of nonlinear systems.…”