Yi Huang

This article puts forward an active disturbance rejection control (ADRC) based tuning rule to the well‐known proportional‐integral‐derivative (PID) control for a class of multi‐input multi‐output non‐affine uncertain systems. It is proved that the PID control with the ADRC‐based tuning rule can guarantee satisfied tracking performance, both for the transient phase and the steady state. Furthermore, it is illustrated that, with the new tuning rule, the PID control is able to timely estimate and compensate for the nonlinear and coupled uncertainties, which explains the reason why PID control does have large‐scale robustness with respect to the uncertainties and can achieve decoupling control with a simple structure. The theoretical results are verified by simulations.

Traditional high-speed precision motion stage (HSPMS) design pursues high-stiffness structure to achieve fast response. However, such structure leads to high-frequency disturbance near dead zone of friction, which causes poor performance in controlling HSPMS. To this end, this paper proposes the active disturbance rejection control (ADRC)-based mechanical design to reduce the bandwidth of friction disturbance and improve the control performance of HSPMS. It is proved that the low-frequency disturbance can be more effectively tackled by the extended state observer (ESO) in the frame of ADRC. In particular, rigid-flexible coupling (RFC) positioning stage is presented for converting the high-frequency friction disturbance into the low-frequency elastic deformation disturbance by flexure hinges. The experimental tests are carried out for both traditional stage and RFC stage. It is clearly shown that compared with traditional design, the control performance of RFC stage is remarkably promoted.

Proportional-integral (PI) control/loop has been widely used in numerous industrial processes. This paper focuses on integrating uncertainty estimator into PI controller for better robustness and transient performance against uncertain nonlinear coupling dynamics and time-varying disturbances. Firstly, the descriptions for the sizes of three kinds of uncertainties in a class of multi-input multi-output nonlinear systems are discussed. Then, the tuning laws of the typical uncertainty estimator, i.e., extended state observer (ESO), are quantitatively presented to ensure the stability of closed-loop systems. More importantly, it is shown that the desired transient performance of tracking error can be ensured by tuning the bandwidth of ESO. In addition, it is proven that much stronger disturbance rejection at low frequency can be achieved by integrating the uncertainty estimator module. The simulation results for calibration-free robotic eye-hand coordination system show the effectiveness of the proposed method.

This paper presents a parameter formula connecting the well-known proportional-integralderivative (PID) control and the active disturbance rejection control (ADRC). On the one hand, this formula gives a quantitative lower bound to the bandwidth of the extended state observer (ESO) used in ADRC, implying that the ESO is not necessarily of high gain. On the other hand, enlightened by the design of ADRC, a new PID tuning rule is provided, which can guarantee both strong robustness and nice tracking performance of the closed-loop systems under the PID control. Moreover, it is proved that the ESO can be rewritten as a suitable linear combination of the three terms in PID, which can give a better estimate for the system uncertainty than the single integral term in the PID controller. Theoretical results are verified also by simulations in the paper.