ORAL

SESSION: MathematicsWedAM-R3	2nd Intl. Symp. on Sustainable Mathematics Applications
Wed Oct, 25 2017	Room: Peninsula 1
Session Chairs: Peter Rowlands; Dean Vucinic; Session Monitor: TBA

12:00: [MathematicsWedAM03]
Performance Enhancement for Active Disturbance Rejection Control
Zhuoyun Nie¹ ; Yijing Ma² ; Qingguo Wang³ ; Ruijuan Liu⁴ ; ¹, Xiamen, China; ²School of Information Science and Engineering, National Huaqiao University, Xiamen 361021, China, Xiamen, China; ³Institute for Intelligent Systems, the University of Johannesburg, 2146, South Africa, Johannesburg, South Africa (zuid Afrika); ⁴School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, P. R. China., Xiamen, China;
Paper Id: 92 [Abstract]

Active disturbance rejection control (ADRC) is a new kind of control technology which improves the inherent tradeoff between fast response and overshoot in the classic PID control. The basic idea of ADRC control technology is regarding the model uncertainties, external disturbances and even nonlinearity as a total disturbance, which is estimated and actively compensated by an extended state observer (ESO). After that, pole placement is easily achieved by state feedback for the desired closed-loop system. ADRC has some remarkable advantages, with small overshoot, fast respond, high precision, strong robustness, and simple tuning rules. Many ADRC applications have been reported in the literatures, such as load frequency control, magnetic rodless pneumatic cylinder, and diesel engines. Originally, ADRC is a control technique proposed by Prof. Han in the form of nonlinear feedback, including a tracking differentiator for the desired response reference and nonlinear state error feedback for the control input and a nonlinear ESO for the state and disturbance estimations. However, complex control structure and nonlinear parameter tuning make it hard to implement with digital computer and limit its practical application. To simplify the tuning process, Gao proposed the linear active disturbance rejection control (LADRC) where linear ESO and state feedback are used. Furthermore, bandwidth parameterization method is proposed to reduce the number of parameters for ADRC to two bandwidth parameters, which are closely related to the tracking and disturbance rejection performance of the controlled system. Tan shown that linear ADRC structure can be changed to a two-degree-of-freedom internal model control (IMC) structure. The analysis of LADRC can be done via the IMC framework by tuning two time constants of the setpoint filter and the disturbance rejection filter in IMC. Although many remarkable applications and improvements are made to ADRC, the existing ADRC design and parameter tuning methods still have limitations. Firstly, we know that ADRC is independence of accurate mathematic model, but it demands the accurate relative degree for the extended state observer design. When the relative degree of the plant is changing, it is necessary to redesign ESO and controller parameters. Second, there is a strict requirement on the minimum-phase (MP) plant or non-minimum phase (NMP) plant because the designs for these two cases are fundamentally different. If uncertainties cause right-half plane (RHP) zero involved, the system would become unstable. This paper first introduces an integral action in the control structure of ADRC to improve the tracking error. For the uncertainties that would cover RHP zeros, full-dimension ESO is used in ADRC, which will also allow relative-degree changing. The control system can be simply tuned by bandwidth-parametric method with better performance. Finally, the validity of the proposed method and its advantages are demonstrated through the simulations of comparative examples.

SESSION: MathematicsWedAM-R3	2nd Intl. Symp. on Sustainable Mathematics Applications
Wed Oct, 25 2017	Room: Peninsula 1
Session Chairs: Peter Rowlands; Dean Vucinic; Session Monitor: TBA

12:30: [MathematicsWedAM04]
Model Reference Compensation of Rate-dependent Hysteresis Nonlinearity for Piezoelectric Actuator
Zhuoyun Nie¹ ; Qingguo Wang² ; Yijing Ma³ ; Ruijuan Liu⁴ ; Dongsheng Guo⁵ ; Hui Shao⁵ ; ¹, Xiamen, China; ²Institute for Intelligent Systems, the University of Johannesburg, 2146, South Africa, Johannesburg, South Africa (zuid Afrika); ³School of Information Science and Engineering, National Huaqiao University, Xiamen 361021, China, Xiamen, China; ⁴School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, P. R. China., Xiamen, China; ⁵, , ;
Paper Id: 93 [Abstract]

Smart materials, such as piezoelectric actuator, magnetostrictive actuator and memory alloy, play an important role of micro-positioning systems. Piezoelectric actuator is widely used in micro-positioning system, and exhibits the merits of high precision, large driving force and rapid response. However, the inherent hysteresis nonlinearity, often leads to tracking error and oscillations, which prevent its industry application. Piezoelectric actuator can be driven by direct current voltage. The existing control schemes can be divided into two categories: model-based and model-free. The first one compensates the nonlinearity by an inversed hysteresis model, which plays the role of a feed forward compensator. This method is dependent on the exact hysteresis model, and very sensitive to model error and uncertainty. Therefore, the model-free method has been paid great attentions for better performance. Xu proposed a slide mode control strategy for piezoelectric actuator without hysteresis model required. Zhang introduces disturbance observer (DOB) control for piezoelectric actuators using robust design. Combined with mode-based feed forward compensation and feedback control, an asymmetric hysteresis model is used for the composite control. Extended state observer (ESO) is originated from active disturbance rejection control (ADRC). The key idea of ESO is to regard model uncertain and external disturbance as an equivalent disturbance and make the real-time observation and compensation. Unlike the traditional disturbance observer, ESO exhibits strong ability in disturbance rejection by an extended state. It has been paid more and more attention in control theory and engineering. Recently, a new model reference control scheme has been proposed in some literatures. Different from the existing adaptive reference control, disturbance rejection technology was employed for the model reference compensation. The goal of the paper is to apply this method to a real piezoelectric actuator. The remainder of this paper is organized as follows. Section 2 introduce the mechanism of piezoelectric actuator. Section 3 presents the transformation of equivalent feedback model (EFM) and the proposed control scheme. Section 4 shows the experiment results to verify the effectiveness of the control method. Section 5 draws the conclusions.