Improving Manual Control of Two-link Pendulum on Gantry Crane with Anti-delay Closed-loop Input Shaping

This paper presents a novel and improved technique in manual control of flexible systems. Flexible systems, when subject to a rapid movement commanded by a human operator, exhibit severe oscillation, causing low positioning accuracy, high fatigue to the human operator, and unsafe accidents. Input shaping filter was proposed to reduce this oscillation by using the destructive interference principle where impulse responses cancel one another resulting in zero residual vibration. Recently, the input shaping filter was placed inside the feedback loop, so-called closed-loop signal shaping, to assist with the manual control of the flexible systems. The vibration was successfully suppressed. However, the input shaping filter also introduced time delays in the feedback loop, which limit the performance of the human operator. This paper offers a breakthrough idea by introducing an anti-delay algorithm called Smith predictor inside the feedback loop. When the plant model is perfect, it can be shown that the Smith predictor can entirely remove the effect of time delay from the feedback loop; therefore, improving the performance of the human operator. Experiments on manual control of a two-link pendulum on a gantry crane show the effectiveness of the proposed algorithm. The human operator was able to move the two-link pendulum with minimum residual vibration. Comparing to the currently world-best technique, the proposed technique could achieve faster maneuvering time, higher accuracy, and with less subjective difficulty. INTRODUCTION Flexible systems vibrate severely when they are commanded to move from point to point rapidly. To understand what are meant by flexible systems, Fig. 1 contains several flexible systems, ranging from elevator with flexible sling, cranes with swinging payload, car wiper with elastic joint, wave having oscillatory dynamics, robot manipulators with flexible link or flexible joint, helicopter having swinging payload, coordinate measuring machine (CMM) with flexible probe, industrial robot with intrinsic elastic property, flexible dynamic between cars in car platoon, spacecraft having flexible appendages, and hard disk read/write head with flexible gimbal. Recent applications of input shaping includes biped walking robot by Yi et al. [1], in which the input shaping was applied to shaping of the reference trajectory of the zero momentum point for a full-size humanoid robot. Khodambashi et al. [2] applied the ZVD input shaper to a 3rdArm supernumerary robotic limb platform, which is a 4 DOF robotic arm that is attached to the human’s shoulder to help the human drummer to perform complicated rhythms. Zou et al. [3] applied the ZV and ZVD input shapers to a circular dielectric elastomer actuator (DEA) to almost completely eliminate transient vibration and overshoot of the DEA under a step input voltage. Input shaping is a technique that substantially reduces residual vibration based on the principle of destructive interference of impulse responses. Consider the cancellation of the two impulse responses in Fig. 2. If the impulse magnitudes