Analysis and control of the cable-supporting system including actuator dynamics

https://doi.org/10.1016/j.conengprac.2011.02.001Get rights and content

Abstract

This paper is concerned with modeling, analysis, and control of the cable-supporting system including actuator dynamics for the next generation large spherical radio telescope. According to its 50-m scaled model, to begin with, the dynamic formulations of the electromechanical coupling system including servomechanism dynamics and parabolic curve of the long-span cable sag effects are established; at the same time the relationship among cable force, cable end displacement and cable length variation is obtained by utilizing parabolic equation, and the dynamic modeling for control can be justified by the numerical example. In addition, taking account of the characteristics of nonlinearity, slow time-variant and multivariable coupling, a fuzzy control plus proportional-integral control method is utilized to control the wind-induced vibration of the cable-supporting system. Finally, simulation results from the 50-m scaled model control system, regarding the wind-induced vibration control of the cable-supporting structure in stationary position and the tracking control of the cable-supporting system, show the satisfactory performance of the proposed control scheme as compared with a discrete-time automatic disturbances rejection controller in the presence of internal model uncertainties in both the cable-supporting mechanism and servomechanism dynamics and external disturbances.

Research highlights

► Dynamic formulation of the whole cable-supporting system is established. ► Wind-induced vibration control of the cable-supporting system is carried out. ► Tracking control of the cable-supporting system is studied. ► Modeling and control of the whole system can be justified by the example.

Introduction

So far the largest antenna is the Arecibo spherical radio telescope with the diameter of 305 m, which was built in the 1970s and located in Puerto Rico, USA. As for Arecibo-type telescope, there exist three problems: high cost, narrow frequency band (entire control system), and spherical error. Due to the foregoing problems, one plan proposed by Chinese astronomers and engineers is to build a set of large spherical reflectors in the extensively existing karst landform in southwest China. The next generation large radio telescopes (LT) with the collecting area of up to one square kilometers are to be completed in the decade 2010–2020 through international scientific cooperation and partnerships, and many different technological solutions have been brought forward and studied by institutes (Duan and Du, 2007, Nan, 2006); and the papers propose a multidisciplinary design project and made nonlinear analysis about it with many reasonable results (Duan, 1999, Qiu, 1998, Su and Duan, 2000). The design project presents a number of outstanding innovations: (1) the unique karst landform in Guizhou province, southwest China; (2) the main active reflector enabling to shift the illuminated part of the spherical dish to a parabolic shape, together with the commonly point feeds on the movable plate, the frequency bandwidth be enlarged dramatically, and spherical error due to spherical reflector (Qiu, 1998); and (3) the light-weight feed cabin driven by six long-span cables. The feed cable-supporting system is a cable-supporting parallel robot (CPR) where the cabin serves as the end-effector. To achieve the desired position precision of the feeds a fine- tuning system (Stewart platform) is added to the end-effector (Su & Duan, 2000). Although this project can make it easier to implement the LT engineering, it raises a much higher requirement for the control engineering. This is due to the use of the long-span flexible driving cables with large lag effects to pull the cabin structure weighing 20–30 t.

Cable-supporting parallel robots are relatively simple in form, with multiple cables attached to a mobile platform or end-effector, and have several advantages over conventional rigid-link mechanisms: (1) remote location of motors and controls; (2) structural simplicity; (3) potentially large workspaces; (4) high load capacity; and (5) reliability. For the preceding reasons, cable manipulators have received attention and have been recently studied since 1980s (Borgstrom et al., 2009, Motoji et al., 2004, Oh and Agrawal, 2005).

As you know, dynamics is a huge field of study devoted to investigating the forces required to cause motion. In order to accelerate the CPR from rest, glide at a constant end-effector velocity, and finally decelerate to a stop, a complex set of torque functions must be applied by the joint actuators (Craig, 2005). One method of controlling the CPR to follow a desired path involves calculating these actuator torque functions by using the dynamic equations of the CPR. Six cables of LT are several hundred meters in length, and the driving force of the slack cable on the end-effector (cabin) must be considered to guarantee a more accurate mechanical model. In addition, as demonstrated in the paper (Anupoju, Su, & Oya, 2005), servomechanism dynamics constitute an important component of the complete robotic dynamics. Therefore, the dynamics of the servomotors and its gears must be modeled for control design. However, the literature on the control of the CPR system including the actuator dynamics is sparse.

In view of a control aspect, recently, there has been an increasing interest in the CPR, and different control schemes, derived from nonlinear control theory, classical control techniques have been proposed with various theoretical and practical contributions being made (Fang et al., 2004, Heyden and Woernle, 2006, Yamamoto et al., 1999). It is well known that up until now, a conventional proportional-integral-derivative (PID) controller is most widely used in industry due to its simple control structure, ease of design, and inexpensive cost (Khodabakhshian and Edrisi, 2008, Yu et al., 2007). However, the PID controller cannot yield a good control performance if a controlled object is highly nonlinear and uncertain. On the other hand, in order to design a new controller for an enhanced control performance, the advantages of the PID controller can be kept. Fuzzy controllers using fuzzy if-then rules are able to effectively incorporate nonlinear properties and unmodeled effects into its basic design (Sanchez & Flores, 2006). Since Mamdani did the first fuzzy control application, fuzzy control is being increasingly applied to many systems with nonlinearity and uncertainty (Chang, 2010). Especially, the most successful fuzzy logic controllers applied into industrial plants are designed by control engineers. Recently, fuzzy logic and conventional-technique are combined to design fuzzy logic controller (Akkizidis et al., 2003, Li et al., 1999), and the control technology based on fuzzy logic is being increasingly applied to systems with nonlinearity and uncertainty. A genetic-fuzzy control strategy for parallel Hybrid Electric Vehicles is designed, which is tuned by a genetic algorithm (Poursamad & Montazeri, 2008). Siripongwutikorn, Banerjee, and David (2005) proposed an augmented Fuzzy control algorithm for a quantitative packet loss rate guarantee to aggregate traffic in packet switched networks. Hwang and Kim (2006) employed an adaptive fuzzy logic method to provide the solution to the control of an electrically driven robot. In this investigation, a fuzzy plus proportional-integral controller combining PI control with fuzzy logic control is developed for more effective and robust performance in the presence of random wind and other disturbances.

On the basis of the 5-m scaled model of LT, considering the orientation change and the drawback of weak twisting stiffness of the CPR system, authors have performed optimization design and twisting stiffness analysis, and qualitative and quantitative analysis of effect of the stable cables on electronic performance of the structure by adding stable cables; on the other hand, the inverse kinematics and dynamic analysis and the active control of the CPR regardless of servomechanism dynamics was investigated (Duan et al., 2009, Zi et al., 2008). Moreover, authors have also addressed the Jacobian analysis and forward solution and accuracy adjustment analysis and optimization of an active cable-mesh main reflector of the long-span CPR system according to the static equilibrium equations (Du et al., 2010, Duan and Du, 2007). In this paper, aiming at the 50-m scaled model of LT, we focus on our work to the dynamic equations and analysis of the electromechanical coupling CPR system including actuator dynamics and parabolic curve of the long-span cable sag effects were established, and the wind-induced vibration control of the cable-supporting structure in stationary position and the tracking control of the CPR. The remainder of this paper is as follows. First, the dynamic formulation of the whole system is established, and the dynamic modeling for control can be justified by the example in Section 2. Then, the structure of the controller is described in Section 3. Simulation results are presented in Section 4. Finally, concluding remarks are provided in Section 5.

Section snippets

Whole system dynamic model

The whole dynamic model is presented in three parts: (1) the feed cabin model (end-effector system); (2) the curved cable model (driving cable); and (3) the actuator dynamics (servomechanism).

Controller design

A robot control scheme stems from two frameworks. One is to design a control on the workspace and the other is on the linkspace. The linkspace control is a conventional control, and is a kind of tracking control to follow the desired link length computed from the position command of the mobile plate by inverse kinematics. Normally, most controllers in applications are based on the linkspace coordinates, which they consider only an approximated manipulator model (Kim, Kang, & Lee, 2000). The

Simulation results and analysis

In this section, some computer simulation results, regarding the wind-induced vibration control of the cable-cabin structure in stationary position and the trajectory-tracking control of the CPR, are presented. So as to verify the robustness of FPPIC strategy, the performance of FPPIC versus automatic disturbances rejection controller (ADRC) will be compared.

Because the CPR is suspended in the space, the random wind disturbance has significant effect on the tracking precision. Therefore, in

Concluding remarks

In this research, dynamic equations and analysis of the electromechanical coupling CPR system including actuator dynamics and parabolic equation of the cable sag effects were established on the basis of cable mechanical equation and equivalent circuit of the servomechanism. In addition, a fuzzy plus proportional-integral controller combining PI control with fuzzy logic control was designed for the wind-induced vibration control of the cable-supporting structure in stationary position and the

Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant 50905179, and the Postdoctoral Science Foundation of China under Grants 20090451254 and 201003605. The authors would like to express their sincere appreciation to Prof. B. Duan, Associate Prof. H. Bao, and Prof. Y. Qiu at Xidian University, for their help in the study. The authors also deeply appreciate the comments and valuable suggestions of anonymous referees and editors to improve the quality of the

References (32)

  • Z.Q. Zuo et al.

    Fault tolerant control for singular systems with actuator saturation and nonlinear perturbation

    Automatica

    (2010)
  • C.M. Anupoju et al.

    Adaptive motion tracking control of uncertain nonholonomic mechanical systems including actuator dynamics

    IEE Proceedings—Control Theory and Applications

    (2005)
  • P.H. Borgstrom et al.

    Design and implementation of NIMS3D, a 3-D cabled robot for actuated sensing applications

    IEEE Transactions on Robotics

    (2009)
  • J.J. Craig

    Introduction to robotics-mechanics & control

    (2005)
  • B.Y. Duan

    A new design project of the line feed structure for large spherical radio telescope and its nonlinear dynamic analysis

    Mechatronics

    (1999)
  • B.Y. Duan et al.

    On analysis and optimization of an active cable-mesh main reflector for a giant Arecibo-type antenna structural system

    IEEE Transactions on Antennas and Propagation

    (2007)
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