Cascade tracking control of servo motor with robust adaptive fuzzy compensation☆
Introduction
Servo motor drive systems have been widely used in high performance mechatronic systems, such as computerized numeric control (CNC) machines, table drive systems, automotive electronics and visual servoing robotic systems [9], [25], [26], [31]. A complete servo system consists of controllers (linear or nonlinear), the energy supply system (voltage source inverter), the actuator (linear/rotary motor), the detection equipments (sensors) and relevant actuator equipments (e.g., mechanical arms, lathe tools, etc.). There are many types of motors available for servo drive system, however, permanent magnet synchronous motors (PMSMs) are widely adopted because of its compact structure, high force density, low thermal losses, and high torque capability [43].
To obtain higher accuracy during the machining process, the servo system often runs at low velocity or even motion reversal. At this time, the nonlinear friction phenomenon seriously affects its tracking performance. Although the nonlinear friction phenomena may exist in every component of servo system, we can uniformly convert it into the friction torque of the motor to compensate for the controller design [9]. Thus, the development of proper control approaches of servo systems have received much attention from engineers and researchers.
Generally speaking, the friction compensation approaches can be grouped into two major categories: friction-model-based and friction-model-free compensation. In friction-model-based compensation, Lian et al. proposed an adaptive control method using LuGre model for induction motor [15]. In [9], some reasonable assumption was made which add the friction to static models. A new experiments based friction model for distinguishing the regime of friction is established in [18]. The cascade P/PI controller was modified to enable the incorporation of the advanced generalized Maxwell-slip (GMS) friction model in [11], this enhances the tracking performance for a linear-drive X-Y feed table. More model-based control approaches can be found in [1], [2]. However, it is a challenging task to identify parameters of friction model, making most of researches to focus on specific applications without rigorously analyzing the stability of the closed-loop system.
Friction-model-free control strategy has received a lot of attention over the past decades. In [5], [6], unknown functions ware approximated by neural networks (NNs) and fuzzy logic systems (FLSs) respectively, the tracking error is guaranteed to be bounded in finite time by adopting the finite-time command filtering control technique [38]. An adaptive fuzzy control algorithm was proposed in [43], where the full-state constraints were constructed [39]. More recently, an algorithm was designed to settle the finite-time control problem by using the fuzzy approximator [16]. Nevertheless, in the design of controllers mentioned above, which use FLSs or NNs to approximate nonlinear functions, one does not take the effect of friction to the system into account. Thus, they may not fit well these existing works for servo systems with inherent friction. Using the reference trajectory, control input and system state, Iwasaki et al. designed an algorithm of group method of data handling (GMDH) to achieve friction compensation [10]. The work reported in [27] proposed a proportion-differentiation (PD) controller with the friction modeling, establising a uniformly ultimately bounded (UUB) stability. However, the friction-model-free strategies with direct compensation lack asymptotic lack stability analysis [10], or at most to concluded the bounded tracking performance [27], [41].
The traditional controllers (e.g., PID, cascade P/PI) are widely adopted in servo control systems. However, along with the increasing performance demands in terms of robust and high-accuracy, these control techniques are limited and hard to achieve desired performances for uncertain systems. To improve the performance of servo drive systems, many controllers have been reported, namely adaptive fuzzy control [23], [36], neural network-based adaptive control [30], [37], disturbance observer-based control [3], backstepping control [6], [42], [43] and so on. The sliding mode control (SMC) technique can deal with bounded disturbance and results in asymptotic stability [40]. However, the discontinuous control inputs have always been a serious problem with SMC. To overcome this, many improved vesions of SMC have been developed [4], [12]. Recently, a continuous control strategy, named robust integral of the sign of the error (RISE), was presented in [33]. Under the assumption that the disturbances are with bounded time derivatives, the uncertainties of systems can be compensated by the RISE feedback. A flurry of RISE-based methods have been developed in industry, such as hydraulic systems [17], [35], the marine surface vessel [7], and DC/AC motor systems [29]. Despite many methods that have been explored, issues related to the servo systems are still retained, including parameter self-tuning, high-accurate compensation of friction, and reconstruction model error. To overcome the varying end-load impact on the tracking performance and achieve asymptotic stability, we propose a novel robust adaptive fuzzy controller (RAFC) in this paper. Our technical contributions can be summarized as follows:
1) Applying an adaptive fuzzy system to estimate unknown nonlinear friction, and using it in cascade controller design to enhance the tracking performance. Different from traditional friction modeling and compensation control in [11], [15], [18], the proposed scheme has stronger adaptation ability to deal with the uncertainties from the friction change.
2) Improving the system adaptation ability with the proposed feedforward compensator through updating the parameters in the fuzzy friction model and the controllers. Compared with the traditional friction compensator using the output signals in [9], [20], [27], the proposed feedforward compensator in this paper can improve position tracking precision and friction disturbance rejection ability.
3) Enlarging the scope of applications of drive AC motor with cascade P/PI controller (such as field-oriented control) in industry, this paper proposed a feedforward compensator to expand the cascade P/PI controller to adapt to the uncertain friction disturbance. Compared with the controllers designed in [27], the proposed controller can not only give full play to the advantages of feedforward control, but also overcome some insufficiencies of the traditional cascade P/PI controller without changing the original structure, which has a potential application for motor control.
The paper is organized as follows. Section 2 introduces the mathematical model of PMSM, control objective and friction model compensation. RAFC is constructed with some important analysis, and the stability analysis based on Lyapunov Theory in Section 3. The numerical simulation study is reported in Section 4. Finally, conclusions are provided in Section 5.
Section snippets
Preliminaries
In this section, we first introduce the mathematical model of PMSM. Then, we analyze the cascade control techniques and state the control objective of servo system with the friction models compensation.
Control strategy
In this section, a RAFC is proposed to achieve high-accuracy position tracking control for servo system. In our work, we do not change the original structure of cascade control, but expanded the original form by adding compensation. The block diagram of the compensation algorithm proposed in this paper is shown in Fig. 2 (Scheme B) and the overall control block diagram with RAFC proposed in this paper is shown in Fig. 4.
Simulation study
In this section, several numerical simulations are carried out to validate the suggested control method. The experimental setup using MATLAB/Simulink environment is shown in Figure 6. We use the P/PI controller, traditional RISE method and friction-model-base controller (FMBC) with several experimental environments with friction to illustrate the superiority of the algorithm proposed in this paper. Finally, the anti load disturbance capability of RAFC is investigated.
Conclusion
In this paper, a robust adaptive fuzzy compensation scheme is proposed for servo motor controller design. The FLS is implemented to approximate the nonlinear friction by adopting a so-called feedforward compensation technique, which results in a faster response. An adaptive updating law is suggested and adjusted by the tracking error and reference trajectory. Using Lyapunov stability theory, we report a property of fuzzy basis function with proof as well as the bounded nature of some variables.
CRediT authorship contribution statement
Y. Liu: Conceptualization, Methodology, Software, Writing - original draft. Z.Z. Wang: Writing - review & editing, Formal analysis. Y.F. Wang: Resources, Writing - review & editing, Supervision. D.H. Wang: Resources, Writing - review & editing, Supervision. J.F. Xu: Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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This work was supported in part by the National Natural Science Foundation of China under Grant 51775103, in part by the State Key Lab of Digital Manufacturing Equipment & Technology under Grant DMETKF2020015.