# High-Performance Flux Tracking Controller for Reluctance Actuator
## 4 Simulation Analysis
### Simulation  
In Figure 16, to suppress the effect of hysteresis, a novel control strategy is applied as follows:  
Actually, in the application of the reluctance actuator, with the desired flux trajectory as an input signal, the DO-DSMC will generate an estimated current, after the inverse hysteresis model and hysteresis model, and driving current. Ideally, the estimated current is equal to the driving current. Under the driving current, the actual flux trajectory is obtained. Hysteresis is the essential characteristic of a reluctance motor, that is, the input current and output flux are nonlinear. If the control strategy is effective, the input flux and output flux will be linear. Therefore, the accuracy of the proposed control strategy can be described by the flux tracking error. In the simulation, \(i=0.25(\sin(2\pi f_{1}t)+\sin(2\pi f_{2}t)+\sin(2\pi f_{3}t))\) is the inputting signal, and \(f_{1}=12 Hz;f_{2}=40 Hz;f_{3}=80 Hz,d(t)=0.025\times\sin(2\times pi\times 5 \times t)\). The control law (7) is adopted, and the sliding mode parameter is adjusted to \(c=9900\), q = 0.79, \(g=3.99\), \(\eta=0.4531\). Figure 17 shows the flux tracking effect of the reluctance actuator. Specifically, the proposed control strategy, which consists of inverse model compensation and the discrete sliding mode rate based on the disturbance observer, is applied in the reluctance actuator. Figure 17a depicts the input and output trajectories of the reluctance motor. In addition, Figure 17b is the control signal, which implies that the sliding surface is smooth and the chattering effect is suppressed. As seen in Figure 17c, the width of the hysteresis loop has been reduced, which means that the hysteresis effect has been compensated significantly. Moreover, the flux tracking error is described in Figure 17d. Obviously, the novel control method is effective in alleviating hysteresis. Further, in order to evaluate the effectiveness of the proposed control strategy in this paper, two existing control strategies, which are widely used at present, are also implemented. Namely, the composite control strategy of inverse model compensation and PI control (PI), as well as the compound control strategy of inverse model compensation and discrete sliding mode control (SMC). Figure 18 shows the flux tracking error curves under the three control strategies. Table 4 gives the experimental result of flux tracking control in different control strategies. The simulation results are shown in Figure 18. Figure 18a describes the input trajectory and the output trajectory under the three controllers. Figure 18b is the tracking error under the three controllers, which implies the tracking performance in different controllers. Where the red line, green line, and purple line are the tracking error under PI, DSMC, and DO-DSMC controller, respectively, we can see that the purple tracking error is the minimum; that is, the tracking performance of DO-DSMC is higher than DSMC and superior to PI controller. In practice, compared with the PI controller, DSMC has better disturbance rejection ability, whereas, when the disturbance is large, the system will be unstable, and the disturbance has an influence on tracking error. From Figure 18b, the green curve described the phenomenon, that is, after the green curve reaches stability, the  
Figure 16: Application diagram of control strategy in reluctance motor. overall error is also affected by disturbance. DO-DSMC, which is more stable than DSMC due to the introduction of a disturbance observer, is shown in purple in Figure 18b, where the disturbance observer compensates for the disturbances in the system, which improves the convergence and stability of the system. Further, in order to evaluate the control performance of the three controllers, some indexes, including VAR, MSE, and RE, were introduced, reflecting the change degree of