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Robust control algorithm using time delay estimation for speed mode of twisted string actuator

https://doi.org/10.1016/j.mechmachtheory.2019.103733Get rights and content

Highlights

  • Feedback control for speed mode twisted string actuator (SM-TSA).

  • PID control and robust time delay control (TDC) were applied for SM-TSA.

  • Both control methods can provide precise positional control in SM-TSA.

  • TDC shows more accurate and robust performances against the changes of payload and external disturbance.

Abstract

Twisted string actuators (TSAs) have been used where conversion of the rotational motion of a motor into a translatory motion by twisting two strings to control the length of the actuator is needed, e.g., in robot applications. Speed mode TSA (SM-TSA) improves the translatory motion achieved in previous TSAs by adding a shaft between two strings. However, the nonlinear response of the translatory displacements remains a problem. Modeling has been one approach, but payload changes or disturbances make it difficult to solve the nonlinear response of SM-TSA through modeling. Here, proportional–integral–derivative (PID) control and time delay control (TDC) in SM-TSA are evaluated as feedback mechanisms during translatory displacements. By following the desired trajectory through PID control and TDC under conditions of payload changes and spring disturbances in SM-TSA and evaluating tracking results, we show that both control methods can provide somewhat precise positional control in SM-TSA even if there are payload changes or spring disturbances. However, TDC shows smaller tracking errors and yields more robust performance against payload changes and disturbances compared to PID control.

Introduction

Tendon actuation using a mechanically translatory reciprocating motion of wires has been widely used for applications including steering flexible endoscopes, driving minimally invasive surgical robots, actuating the movement of artificial arms and fingers, and wearable robots [1], [2], [3], [4]. In general, the translatory reciprocating motion of wires in tendon actuation is realized by electric motors and winches [5]. However, because the motor and the winch must be aligned, and the wire for the tendon actuation should be connected in a perpendicular direction to the winch, tendon actuation can have design limitations.

Recently, a twisted string actuator (TSA) was proposed, where the translatory reciprocating motion is realized based on the principle that length decreases or increases when two strings that are linearly aligned are twisted or untwisted [6,7]. Speed-mode TSA (SM-TSA) is a type of TSA that produces a large translatory displacement of the twisted string through rotation of a motor by adding a shaft between two twisted strings. The conversion ratio of the twisted-string translatory displacement and the rotation of the motor in SM-TSA can be adjusted by changing the diameter and length of the shaft [8,9].

However, one limitation of TSAs is that the rotation of the motor is not linearly proportional to the resulting translational displacement of the twisted strings. To overcome this limitation, several studies have compensated for the nonlinear displacement of TSAs by accurate modeling 7,10,11, and various models of TSAs and SM-TSAs have been proposed [10,11]. We also proposed an enhanced SM-TSA modeling method by improving previously proposed modeling methods and analyzing the twisting tendency of the twisted strings in SM-TSAs [12]. Meanwhile, there were many kinds of research on the controls based on system modeling [13,14]. However, because there is a big difference between the modeling and the actual SM-TSA when payload changes or disturbance exists, it is very difficult to apply the modeling-based controls to SM-TSA system.

Therefore, under conditions where disturbances such as payload changes exist, feedback control is necessary to follow a desired trajectory in SM-TSAs. M. Hosseini proposed a finger actuated by a TSA where the force was measured by force sensor and the finger was controlled by the measured force [15]. S. H. Jeong developed a robotic hand using TSAs where a new optical force sensor was proposed, and the robotic hand was controlled by an optical force sensor [16]. In these studies, they adopted force feedback controls for the finger and the robotic hand using TSAs. In this paper, however, we will study a feedback control to follow the desired trajectory in an SM-TSA using a displacement sensor.

Generally, proportional–integral–derivative (PID) control methods are widely used because they have a simple structure, yet their control is precise. However, in SM-TSAs, nonlinear responses can be increased by payload changes or external disturbances, and PID control might exhibit poor tracking accuracy. Therefore, we adopted a time delay control (TDC), which is known to be robust control algorithm. Generally, TDC has a simple algorithm structure, does not require a real-time computation for nonlinearities and uncertainties of the control targeted system, and does not need a parameter estimation, unlike an adaptive control. And, TDC can indirectly estimate and compensate for nonlinearities such as payload changes or external disturbances through a time delay estimation, and thus can maintain robust control performances [17], [18], [19]. There were no reports on the application of robust controllers to TSA or SM-TSA. Therefore, in this paper, we firstly applied TDC, one of the robust controllers, to SM-TSA with large nonlinearities and uncertainties.

This paper is organized as follows: the experimental setup of SM-TSA and control algorithms (PID control and TDC) are described in Section 2; the experimental results of using PID control and TDC for the desired trajectory of a sinusoidal waveform in SM-TSA with payload changes or external disturbances is presented in Section 3; the results are discussed in Section 4; and our conclusions are proposed in Section 5.

Section snippets

Force mode and speed mode of twisted string actuator

Generally, TSA uses one or two strings, where one end is fixed at an actuation unit and the other end is connected to a motor that rotates the strings. When the motor rotates, the strings are twisted and the distance between the actuation unit and the motor decreases.

Hence, the rotation of the motor generates the displacement of TSA and controls the TSA's stiffness [4,6]. TSAs can have two actuation modes: force mode and speed mode.

First, a force mode TSA (FM-TSA) does not use a shaft along the

Results

In this section, we applied the two control algorithms (PID control and TDC) to SM-TSA with the payload changes and the external disturbances and evaluated whether the SM-TSA system could follow a desired trajectory using the control algorithms. In this study, we selected the following sinusoidal wave continuous function as a desired trajectory:xd(t)=10(sinπ20(tπ2)+1)where the unit of time (t) is seconds and the unit of displacement (xd) is millimeter.

The gains of the controllers used in the

Discussion

In this study, we introduced feedback control to avoid the degradation of the actuation performance caused by the nonlinearity of the SM-TSA system, where PID control and TDC with a time delay estimation were applied to the SM-TSA system. We implemented payload changes and external disturbances in the SM-TSA system and compared the trajectory tracking of the two control methods for the desired trajectory of a sinusoidal waveform. As a result, we found that tracking errors with TDC are much

Conclusion

In this paper, we applied the PID control and TDC methods to a SM-TSA system in which nonlinearities such as friction, payload changes, and external disturbance changes were introduced. Tracking accuracy tests for the desired trajectory of the sinusoidal waveform were performed with these two SM-TSA systems. The results indicate that compared to the SM-TSA system with PID control, the SM-TSA system with TDC has superior tracking accuracy and more robust control performance against payload

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.

Acknowledgment

This research was supported by the DGIST R&D Program of the Ministry of Science and ICT (19-RT-01) and the Korea Health Technology Development R&D Project through the Korea Health Industry Development Institute (KHIDI), funded by the Ministry of Health & Welfare, Republic of Korea (grant number: HI19C0642).

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