A universal digital motion controller design for servo positioning mechanisms in industrial manufacturing
Introduction
Control technology has long been playing an influential role in various automation systems in industrial manufacturing, see e.g., Ouyang and Acob [1], [2], [3], [4], [5], [6]. Especially, for robotic manipulators in assembly lines and feed servo systems in machine tools, fast and accurate motion control is essential for production efficiency and precision. This requirement eventually boils down to the design of high-performance control system for industrial servo mechanisms which typically involve electric motors. Actually, this subject has been extensively studied and is still a hot topic for the control community. So far, the Proportional, Integral and Derivative (PID) control is the most widely used technique in control systems design, and extensive research efforts on PID control have been reported, see e.g., Heertjes et al. [7], [8], [9], [10], [11], [12], [13]. However, PID has the potential problem of windup, and its performance would exhibit a degradation with the change of target reference or disturbance, even if some anti-windup methods are included. Intelligent methods, such as neural network or fuzzy logic, are also being integrated into controller design for performance improvement, see e.g., Giulio et al. [14], [15], [16]. In recent years, an emerging control technique related to PID, i.e, the fractional order control, is gaining increasing attentions from researchers, see e.g., Monje et al. [17], [18], [19]. The strength of PID-type control and/or intelligent control lies in the independency of plant model, i.e., the design process can be model free. However, for industrial servo mechanisms which typically are built upon electric motors, physical principles and system identification techniques are available to obtain the mathematical model of the system, thus enables the usage of model-based control techniques to achieve better performance. Indeed, the control performance of servo systems, can significantly contribute to the productivity and quality of industrial manufacturing, which inspires a persistent exploration of control systems design methodology.
The past two decades have witnessed the popularity of Active Disturbance Rejection Control (ADRC) scheme (see e.g., Han [20], [21], [22]). ADRC models the system as a chain of integrators with a nominal gain, and uses an extended state observer (ESO) to estimate the states for state-error feedback, together with a total disturbance for compensation. However, due to the challenge in design and tuning of nonlinear ADRC controller, recent research efforts are being directed towards linear ADRC, see e.g., Yoo et al. [23], [24], [25]. In [26], [27], a composite nonlinear control scheme was proposed for servo systems with control input saturation. The controller combines a linear control law with a nonlinear part to achieve a fast and low-overshoot output response for set-point tracking. In the presence of unknown constant disturbance, Peng et al. [28] proposed an integration enhancement to be embedded in the composite controller so as to improve the steady-state accuracy. Later on, the control scheme in [28] was extended to discrete-time systems with unknown disturbance [29]. Unfortunately, the integration-based composite controllers of both [28], [29] still have to face the potential risk of integrator windup. In [30], a linear extended-state observer was employed in the discrete-time servo controller design, and a better robustness in performance was reported.
The design of composite servo controller in [29], [30], especially its nonlinear feedback part, is not an easy task, and some kind of expertise or experience would be useful to produce a desirable solution. In [31], an optimized tuning method for the parameters of the nonlinear gain function in composite nonlinear controller was proposed. The paper [32] reported a MATLAB toolkit for the design and simulation of composite nonlinear controller in continuous-time domain. In [33], a parameterized design of integration-enhanced composite nonlinear controller was presented. However, all the designs were formulated in continuous-time domain, and the resulting controller needs to be discretised before real implementation, which normally requires a high sampling frequency to preserve the performance equivalence. Hence, when it comes to implementation, a discrete-time controller design would be more amenable. Due to the complicated relation between the gain matrices of discrete-time controller and the design parameters (e.g., the pole locations), a control engineer normally would resort to some software tool (e.g., MATLAB) to calculate the controller gain matrices (in numerical values) first at the design stage and then hard code the control algorithm on an embedded system at the implementation stage. If the control performance turns out to be unsatisfactory, the engineer may have to go through the design stage again to derive a new set of controller matrices and then modify the software program for implementation. Such an iterative process is time-consuming and inefficient, especially when the parameters of plant model are not known exactly. If the discrete-time controller can be designed in a parameterized way, to be specific, if the controller gain matrices are formulated as some explicit expressions of the model parameters and some fundamental tuning parameters (e.g., closed-loop damping and natural frequency), and these expressions, instead of particular numerical values, are included in the software program for controller implementation, it will be possible to tune the controller on line for better performance. Moreover, if an identification algorithm for model parameters is also available, then a self-tuning control system can be easily constructed by combining the control law with the identification block. Indeed, this is the motivation of our work.
In this paper, a discrete-time parameterized motion controller is designed for typical position servo systems in industrial manufacturing. The motion controller features a synergy of linear control and smooth nonlinear feedback for improved targeting and settling, and resorts to an extended-state observer for disturbance rejection, instead of using integration action directly. The controller has a modular structure, and its gain matrices will be presented in closed-form expressions based on some fundamental parameters, which offers a flexibility for algorithm implementation and performance tuning. The design will then be verified on a permanent magnet synchronous motor (PMSM) via MATLAB simulation and implementation using a TMS320F28335 digital signal controller (DSC) board, and comparisons with a conventional linear controller and a nonlinear ADRC controller will be made.
The outline of the paper is as follows. Section 2 presents the design of parameterized motion controller in discrete-time domain. Section 3 analyzes the control performance and stability of closed-loop system. In Section 4, the proposed design is applied to a permanent magnet synchronous motor for position regulation. Simulation and experimental results are provided. Finally, some concluding remarks are given in Section 5.
Section snippets
Parameterized motion controller design
This section deals with the design of digital motion controller for industrial servo positioning mechanisms driven by electric motors. In such systems, the position-speed dynamics, which corresponds to the mechanical motion subsystem, can be typically characterized as [34]:where θr (rad) and ωr (rad/s) are the mechanical angle and speed of motor, J is the motor inertia, kb is the frictional coefficient, TL is the load torque, kt is the torque constant, and is is
Analysis of closed-loop stability
Define the state error and the estimation error
Then the control law in (10) can be rewritten as,with .
Next, choose a symmetric positive definite matrix to satisfy the following condition:and solve the following Lyapunov equationfor a positive definite matrix Q.
Define a four-dimensional set with the level of c ≥ 0 as follows:
Verification and comparison
The controller was verified on a PMSM servo test bench. PMSMs have found extensive applications in industrial servo mechanisms where high performance and efficiency are desired. The dynamic model of PMSM in the dq frame is given bywhere θr, ωr, TL, J, kt and kb are the same as those appearing in model (1). Ud and Uq are the voltage components in dqcoordinate, id and iq are the electric currents, Ld
Concluding remarks
A parameterized digital motion controller has been designed for positioning servo mechanism in industrial automation. The design was based on the composite nonlinear control framework with an extended-state observer for disturbance rejection. The controller was verified on a DSC-controlled PMSM. Comparisons with a conventional linear controller and a nonlinear ADRC controller have been presented. The results confirm that the proposed controller design can achieve desirable performance with
Declaration of Competing Interest
We wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support 14 this work that could have influenced its outcome.
We confirm that the manuscript has been read and approved by all named authors and that there are no other persons who satisfied the criteria for authorship but are not listed. We further confirm that the order of authors listed in the manuscript has been approved by all of us.
We confirm that we
Acknowledgment
The authors wish to thank the anonymous reviewers for their constructive comments and suggestions which helped to improve the final presentation of the paper. This work was partly supported by the National Natural Science Foundation of P. R. China under grant 51977040.
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