# Robust Input Shapers for Acceleration-Limit Actuators
## 4 Experimental Verification  
As described in this section, the control performances of the proposed ZVD\({}_{\rm AL}\) and EI\({}_{\rm AL}\) shapers were experimentally compared with those of ZVD and EI shapers for robustness to the uncertainties of the system and actuator parameters. The mini bridge crane in Figure 18 has dimensions of 1.3 m (length) \(\times\) 0.75 m (width) \(\times\) 1.5 m (height). Figure 19 shows the hardware and software components of the mini bridge crane used for the experimental verification. Among the hardware components, a programmable logic controller (PLC) was connected to a computer via a wireless local area network to implement the proposed algorithm. The velocity command generated by the PLC is transmitted to the bridge and trolley motor drives. The drive uses an incoming command as the velocity-setting point of the motor. The motor drive used a synchronous AC motor constituting a communication module and a control driver. The system software of the mini bridge crane was programmed using CFC, SCL, and WinCC Flexible 2007 software with the functions of uploading and downloading the experimental data. The magnitude of the payload oscillation was measured using a vision program with a VS720-series vision sensor, which was written using Spectation(r) software. Figure 17: Sensitivity of EI\({}_{\rm AL}\) shaper to \(L\) and \(\kappa_{a}\). Figure 18: Mini bridge crane. To confirm the testbed performance, the actual and shaped demanded commands for the measurement of the absolute encoder signal on the AC motor are shown in Figure 20. To accurately generate the desired input command under the asymmetric acceleration and braking rates of the actuator with the proportional gain of 0.25, an integration gain of 10 ms was set in the motor control driver. For the parameters listed in Table 1, the error velocity is shown within the range of \(\pm\)2 cm/s with small oscillations at the corner of the command. Therefore, the settings of the testbed and experimental input commands can be used to evaluate various input shapers. Figure 21 shows the residual deflections resulting from the actual command shown in Figure 20 while measuring the payload oscillation using the vision sensor. The ZVD\({}_{\mathrm{AL}}\) shaper exhibited almost zero residual deflection, whereas the ZVD shaper produced a periodic residual deflection with an amplitude of 1.2 cm. However, the EI\({}_{\mathrm{AL}}\) shaper generated an oscillation magnitude comparable to that of the EI shaper owing to the allowable residual deflection. The inclusion of actuator dynamics in the shaper design was necessary to achieve better deflection reduction. Figure 22 displays the numerical and experimental sensitivity comparison with uncertain cable length \(L\). The experimental results are presented as the average values of the data obtained from multiple experiments. The ZVD\({}_{\mathrm{AL}}\) and EI\({}_{\mathrm{AL}}\) shapers exhibited better  
Figure 19: Hardware configuration. Figure 20: Experimental input commands on the x\(-\)axis. robustness than the ZVD and EI shapers, which exhibit residual deflections throughout the evaluation range of \(L/L_{m}\). The ZVD\({}_{\text{AL}}\) shaper was characterized by zero residual deflection at \(L/L_{m}=1\) whereas the ZVD shaper exhibits the same feature in the case of an ideal actuator. Furthermore, the EI\({}_{\text{AL}}\) shaper produces one hump and two zero-residual deflections, which are observed for the EI shaper in the case of an ideal actuator. Therefore, the residual deflection reduction performances of the ZVD\({}_{\text{AL}}\) and EI\({}_{\text{AL}}\) shapers are predictable, whereas the ZVD and EI shapers produce large residual deflections in the case of acceleration-limit actuators. Figure 23 depicts the numerical and experimental robustness performances as a function of actuator parameter ratio \(\kappa_{a}/\kappa_{am}\). The classical ZVD and EI shapers are unaffected by the actuator parameter as expected.