# Modified Smith Input-Shaper Crane-Controller for Position Control and Sway Reduction
## 4 Experimental and Simulation Results
### Experimental Verification of the Proposed Control Structure  
To see the impact of the proposed control structure on the crane dynamics and to identify the validity of the proposed control structure, several experimental setups were made and compared with the simulation results:  
* Case 1: the PD position controller without sway reduction. * Case 2: PD-ZV position control. * Case 3: the proposed control structure without the error controller. * Case 4: the proposed control structure with the error controller  
For all cases, the same reference waveform \(x_{r}\) shown in Figure 14 was used to compare the obtained responses. This reference waveform can have a positive or negative influence on the cargo sway. That depends on the moment the change of the reference waveform occurs. The reference waveform \(x_{r}\) was chosen to ensure the maximum sway of crane cargo and see the impact of the sway reduction on the cargo sway. The cargo was transferred multiple times between distances of 1 meter in time intervals of 11.64 s, 21.5 s, 31.0 s, 42.77 s, and 53.5 s. These moments of reference change were measured from the first positive edge of the reference. In all cases, the same PD position controller \(G_{PD}\big{(}q^{-1}\big{)}\) was used, which can be seen in Figures 2, 3 and 6. The parameters of the PD position controller given in Table 2 and used in all cases were obtained to achieve the maximum positioning speed of the cargo and the robustness and stability of the position control loop. In Case 2, the input-shaping technique was incorporated within the positioning control loop, while the parameters of the PD position controller were left the same as in Case 1. The ZV method was used for the input shaper technique, and its parameters are given in Table 3. From these responses, Figures 18-21, the impact of the input shaper on the position control loop dynamics can be seen by comparing them with the responses of Case 1. It can be seen that the given PD controller cannot be used with the input shaper technique because it introduces a negative effect on the closed control loop. It decreases phase reserve and gives oscillatory responses. Adjusting the parameters of the position controller, specifically by reducing the positioning speed, can mitigate oscillatory responses that can occur during operation. This adjustment improves the position system's stability. However, while achieving stable responses is beneficial, this approach may not fully meet the requirements for effective crane positioning. This is because similar stability could be achieved using a position PD controller without incorporating a sway reduction algorithm. The difference between the measured and simulated position responses resulted from the cart's wheels skidding because of inadequate friction between the wheels and the surface during operation. These differences were particularly pronounced because the position sensor is mounted directly on the motor shaft, which does not account for the slippage occurring on the wheels. Consequently, this misalignment led to inaccurate readings of the cart's actual position compared to the expected simulated data. While the position response exhibits oscillatory behavior due to the input shaper, it positively influences cargo sway reduction, as seen in Figures 16 and 20. To achieve the same cargo transfer speed as the control structure of Case 1 and to incorporate the shaper technique in the closed control loop, the proposed control structure shown in Figure 6 without the error controller was used in Case 3. The proposed control structure's responses are in Figures 22-25. The speed of position control, as illustrated in Figures 14 and 22, remains consistent with the parameters established in Case 1, indicating stable performance across both  
Figure 17: Control PD position controller signal measured \(u_{m}\) and simulated \(u_{s}\) without the sway reduction algorithm.