## 4 Simulations and Analysis  
### Simulation Setups  
According to Equation (12), the highest deceleration a DDTV needs to achieve is \(-\)5.5 m/s\({}^{2}\), which means the emergency braking control strategy does not have to be triggered fundamentally when the vehicle runs on a high adhesion ground. Thus, simulations only need to be conducted under a muddy road, snow, and ice among the conditions shown in Figure 3.  
Except the braking control strategy proposed in this article, the other three strategies are also taken into simulations as comparison. All four strategies are respectively:  
* **FB (full braking)**: which is called \"full braking\" and is the most widely-used emergency braking control strategy in tracked vehicles. With this strategy, the hydraulic retarder and mechanical brake work separately to provide the largest braking torque whether the track is locked or not;
* **TABS (traditional ABS)**: which is transplanting a traditional ABS control strategy into tracked vehicles that need to add a PWM-driven solenoid valve in each wheel cylinder to realize the high-speed rise-hold-decline processes of braking pressure in it. The duty ratio of PWM is calibrated for each track-ground condition to achieve the best performance. The hydraulic retarder and mechanical brake also work separately.
* **SMSCM (sliding mode slip control without motor)**: which uses the output of the sliding mode slip ratio controller proposed in this article as the total demanded braking torque, but the PMSMs are not used in the process of emergency braking. The hydraulic retarder and mechanical brake works cooperatively to follow the demanded braking torque derived in Equation (20).
* **SMSCR (sliding mode slip control with regenerative braking)**: which is the emergency braking control strategy that the regenerative braking of PMSMs also participate in in the braking process proposed in this article.  
In addition, the hydraulic retarder obeys the rule of shutting down when the vehicle runs at a speed lower than 12 km/h in all these braking control strategies above.  
Three indicators are taken into the simulations to evaluate the performances of these strategies. The first one is the stopping time \(T\), and the second one is the stopping distance \(S\). The last indicator \(D\) is defined as Equation (26) to represent the deviation of the real slip ratio to the demanded value:  
\[D=\left\{\frac{1}{{\lambda_{d}}^{2}T_{q}}\int_{0}^{T_{q}}[\lambda(t)-\lambda_{d }(t)]^{2}dt\right\}\times 100\% \tag{26}\]  
where \(T_{q}\) is the duration from when emergency braking is triggered to achieve the speed of 5 km/h such that only mechanical brakes provide the braking torque.  
The simulations were performed in the environment of MATLAB/Simulink R2015b. The DDTV was braked at a speed of 80 km/h, and the brake pedal was set to increase from 0-100% with the accelerator pedal decreasing to zero in 10 milliseconds. The start point of plotting and calculating the indicators was defined as when the velocity of the track was equal to that of the vehicle to eliminate the effect of the slip of driving. The main parameters of the DDTV for the simulations are listed in Table 1.