Adaptive and fuzzy neural network sliding-mode controllers for motor-quick-return servomechanism
Introduction
Since the variable structure system using sliding-mode control can offer many properties, such as fast dynamic response, insensitivity to parametric variations and external disturbance rejection, the sliding-mode control has been studied by many researches for the control AC motor drive and robot manipulators [1], [2], [3], [4], [5]. However, the applications of the sliding-mode control have two main problems, i.e., the assumption of known uncertainty bounds and the chattering phenomenon in the control effort. Thus, Su and Leung [6] proposed a sliding-mode controller with the bound estimation to accomplish trajectory control of robot manipulator; Yu and Lloyd [7] reduced the chattering phenomenon and increased the robustness of the variable-structure controlled robot manipulator using adaptive control technique; Lin et al. [8] proposed a sliding-mode position control using a novel switching surface and an adaptive sliding-mode position control in which an adaptation law is designed to estimate the uncertainty bounds for PM synchronous motor drive system.
In recent years, much research have been done to apply the fuzzy neural network (FNN) systems, which combine the capability of fuzzy reasoning in handling uncertain information [9], [10] and the capability of artificial neural networks (ANN) in learning from processes [11], [12]. The FNN can be applied in the closed-loop control of nonlinear systems without using complex mathematical model of the system due to the massive parallelism of the real-time data processing ability of the ANN. Moreover, the fuzzy reasoning mechanism enables the FNN to deal with uncertainties of the control systems in an effective way. Furthermore, the FNN can be utilized in sliding-mode control to estimate the bound of uncertainties real-time [13].
The quick-return mechanism has been extensively used in industrial applications for reciprocating cutting tool, such as crank shapers, drag link, offset slider crank and power-driven saw [14], [15]. Its main characteristics are a slow-cutting stroke and a quick-return stroke concerned with a constant angular velocity of its driven crank. Therefore, the ratio of the time required for forward stork to the time for the return stork is greater than unity. Sandor and Erdman [16] gave an example of its use in connection with a flow metering pump. Dwivedi [17] employed the modified whitworth quick-return mechanism to construct a high velocity impacting press. However, the research concerned with the dynamic analysis and the control system design of the motor-quick-return servomechanism is not found in the previous studies.
To develop high-performance position controllers with robust control characteristics for the motor-quick-return servomechanism, an adaptive sliding-mode controller and an FNN sliding-mode controller are investigated in this study. First, Hamilton’s principle and Lagrange multiplier method are applied to formulate the equation of motion. Next, the adaptive sliding-mode controller is introduced. In the proposed adaptive sliding-mode controller, an adaptive law is used to adjust the bound of uncertainties real-time. Then, an FNN sliding-mode controller, in which the FNN is utilized to estimate the uncertainties real-time, is developed. Moreover, the stability analyses based on Lyapunov’s theorem for the adaptive and FNN sliding-mode controllers are described in detail. Finally, simulated and experimental results due to periodic step and sinusoidal commands show that the dynamic behaviors of the proposed controllers are robust with regard to uncertainties.
Section snippets
Field-oriented control PM synchronous motor-mechanism coupling system
The simplified control system block diagram of a field-oriented control PM synchronous servo motor drive is shown in Fig. 1(a) [18], [19], in whichwhere τe is the electric torque; Kt is the torque constant; is the torque current command; Pt is the number of pole pairs; Lmd is the d-axis mutual inductance; Ifd is the equivalent d-axis magnetizing current; s is the Laplace operator; τm is the load torque; Bm is the torsional damping
Adaptive sliding-mode controller
Using the computed torque technique, Eq. (16) can be rewritten as follows:whereThen, the proposed adaptive sliding-mode controller is shown in Fig. 3(a), where , x, vc, and v are the command slider position, slider position, command angle of link 2, and angle of link 2, respectively. Since x is the desired control objective and v is the state of the
Fuzzy neural network sliding-mode controller
The best feature of a sliding-mode controller is insensitive to parameter variations and external disturbance once the control system entering the sliding mode. However, the parameter variations of the system are difficult to measure, and the exact value of the external disturbance is also difficult to know in advance for practical applications. Therefore, an FNN is adopted in this study to facilities the estimation of the uncertainties. In order to derive the FNN sliding-mode controller, Eq.
Numerical and experimental results
By use of Runge–Kutta fourth order numerical integration method, Eq. (14) is solved for the motor-mechanism coupling system. The parameters of the motor system are given as follows:For the convenience of the controller design, the position and speed signals in the control loop are set at and , respectively. Moreover, the parameters of the quick-return mechanism are:
Conclusions
This study successfully demonstrates the application of adaptive and FNN sliding-mode controllers to control the slider position of the motor-quick-return servomechanism. First, the mathematical model of the motor-quick-return servomechanism was introduced. Then, the theoretical bases and the stability analyses of the proposed adaptive and FNN sliding-mode controllers were described in detail. Moreover, simulation and experimentation were carried out using periodic step and sinusoidal reference
Acknowledgements
The authors would like to acknowledge the financial support of the National Science Council of Taiwan, ROC through grant number NSC 89-2213-E-033-048.
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