## 3 Simulation Result and Analysis
The simulation results are shown in Figure 1(a)-d.  
In the process of the gradual zero error, the normal constraint conditions shall at least ensure that \(\|e(k+N)\|<\|e(k+N-1)\|\); the simulation results are shown in Figure 2(a)-d.  
If the constraint range is set outside of the allowable range, \(0.62\|e(k+N-1)\|\leq\|e(k+N)\|\leq 0.76\|e(k+N-1)\|\), although the range is set smaller, the loss is large and exceeds the control input range. The simulation results are shown in Figure 3(a)-d.  
Figure 2: \(Cont\). Figure 2: The simulation results of the predictive tracking with the constraint range 0.78 \(\parallel e(k+N-1)\parallel\leq\parallel e(k+N)\parallel\)\(\parallel\)\(\parallel\)\(\parallel\). Figure 3: Cont. Figure 4: \(Cont.\)  
Figure 3: The simulation results of the predictive tracking with the constraint range \(\parallel e(k+N)\parallel<\parallel e(k+N-1)\parallel\). it can be seen that in the first scenario, the specific numerical constraints were clarified, the state incremented, the tracking error quickly converged, the output quickly reached the expected goal, and the control input increment was within the allowable range. The second and third cases indicated that there was no specific numerical constraint range, but only a separate upper or lower bound was determined. The state increment and tracking error could not converge quickly, the output could not achieve the expected goal quickly, and the control input increment was within the allowable range. The fourth case indicated that the constraint conditions were not within a specific numerical range. Although the state increment, tracking error, and output converge quickly, achieving the expected goal faster than the first case, the control input increment was not within the allowable range, and the control loss increased. The fifth case indicated that for the method with disturbance parameters, the specific numerical constraints were specified, the state incremented, tracking error quickly converged, the output quickly reached the expected goal, and the control input increment was within the allowable range, which was basically the same as the first case. Based on the simulation results of the above five scenarios, it can be seen that the method determined the upper and lower bounds of the constraint conditions, as shown in Figure 1. Compared with other scenarios, only the upper or lower bounds of the constraint conditions were determined, as shown in Figures 2 and 3, and the upper and lower bounds of the constraint conditions were arbitrarily set, as shown in Figure 4. This indicates that the state variable increment, tracking error, control increment, and performance index function in Figure 1 were shown in Figure 6a-d, which can converge more quickly and output variables can be quickly tracked, and it can meet the requirements of the performance index functions and control inputs not exceeding the range. In order to illustrate the effectiveness of the proposed method and compare it with the solution of the traditional model predictive control, it can be seen from the simulation in Figure 7a-d that the solution of the traditional model predictive control, without adding optimization constraints, had an unstable convergence of state increment and tracking error, large fluctuation, slow rate of convergence, and the convergence did not reach the predetermined accuracy. Figure 5: \(Cont\). Figure 5: The simulation results of the error tracking predictive control with the parameter perturbations and constraint range 0.78 \(\parallel e(k+N-1)\parallel\leq\parallel e(k+N)\parallel\leq\) 0.968 \(\parallel e(k+N-1)\parallel\).