## 5 Simulations and Experimental Results
### Experimental Results  
In order to validate the effectiveness of the proposed velocity estimator and control method in practice, a gear-shifting test bench was developed. Figure 12 shows the layout and the main components of the experimental set up. It mainly consists of an induction motor, transmission, actuator, sensors, controller and other support mechanisms. Figure 13 shows the structure of the control system. The position of the actuator is monitored by a high-accuracy position sensor (KTM-25 mm). The current through the moving coil is measured with a closed-loop Hall-effect current sensor (TBC20 SY). The actuator is controlled by an IGBT H-bridge drive. TMS320F2812 Digital Signal Processor (DSP) with a clock frequency of 150 MHz is applied as the main controller. Sensor signals are transmitted to A/D ports after being processed by interface circuits. The sampling frequency of the DSP is set to 10 kHz, the switching frequency of the Pulse Width Modulation (PWM) inverter is set to 30 kHz. Experimental data is transmitted to the personal computer via an Ethernet cable for display and analysis.  
Taking the gear-shifting disengaging phase that only needs position control as an example, the initial position is limited by the synchronizer and actuator, and can be considered as zero. The target position is 9 mm, and the settling time of the reference position is set as around 20 ms. In this phase, the sleeve of the synchronizer should be controlled to the target neutral position precisely within the desired settling time. Figure 14a shows the test results of the position with the proposed controller, and the position sensor is used in the position loop to provide a feedback signal. It can be seen that the controlled position track the reference trajectory with a small delay, this is because the computing power of the fixed-point TMS320F2812 DSP and the measurement accuracy of the sensors are limited. Similarly, the estimated position also lags behind the measured value. The derivative of the measured position and the estimated velocity is shown in Figure 14b. It is quite obvious that the derivative of the measured position is affected by the measurement noise, but the velocity estimator can observe the velocity effectively and removes undesirable spikes existing in the velocity observation.  
Next, the velocity estimator replaces the position sensor in the control system, i.e., the measurement of the position sensor is just used for comparison. As shown in Figure 15, the test results display a small overshoot of 2.2% due to the effect of the velocity estimate. As stated in [PERSON] et al. (2010), this overshoot can be accepted and will not affect the gear-shifting performance. Therefore, the sensorless control of an independent gear-shifting actuation system with the model-assisted reduced-order ESO based cascade controller is technically feasible.  
Figure 12: The experimental set up.  
Figure 14: Experimental results for the control system using a position sensor: (**a**) Position; and (**b**) Velocity.  
Figure 13: The structure of the control system. ADC: Analog to Digital Converter; CAP: Capture Unit.  
Figure 15: Experimental results for the control system using a velocity estimator.