# A Novel Robust Control System Design and Its Application to Servo Motor Drive
## 7 Practical Experiment and Discussion  
The experimental system is shown in Figure 9, where the permanent magnet DC motor is axis-connected to the brake and inertia load. The brake is a piece of external voltage-controlled equipment that applies the external torque to the motor. The inertial load changes the overall system inertia by adding or removing the counterweight. The DC motor is driven by an H-bridge converter with a 24 V DC voltage source. The inner-current loop is controlled by a proportional and integral (PI)-type controller with the controller parameters \(K_{p}=20\) and \(K_{i}=10\) and a sampling frequency of 20 kHz. The proposed integral state feedback plus sliding mode control system controls the outer position and velocity loop. The linear control law is \(u_{L}=-\mathbf{k_{1}^{T}z}=-[0.7\quad 0.005\quad 0.1]\mathbf{z}\) and \(u_{smc}=-q\frac{\sigma}{|\sigma|+\varepsilon}=-3\frac{\sigma}{|\sigma|+0.001}\) and is run at a 2 kHz sampling frequency. The position and velocity signals are from the encoder with 2500 p/rev. Figure 10 is the block diagram of the developed system. Table 2 displays the parameters of the experimental system. The controllers are implemented on the chip PIC 32 MK DSP, which works using a 120 MHz clock. Finally, the controlled parameters, position and velocity, are shown on the oscilloscope by a digital-to-analog converter (DAC). The position command is shown in Figure 11a. The total experimental time is 20 s, and the displacements are nine revolutions, which are subjected to the trapezoidal velocity profile with acceleration \(\pi\ rad/s^{2}\), deceleration \(-\pi\ rad/s^{2}\), and maximum speed \(3\pi\ rad/s\). Two kinds of inertial values, which are 0.021675 Nm/s\({}^{2}\) and 0.036125 Nm/s\({}^{2}\), are built as the variations, and the brake supplies an external load of 0.002 Nm to the system periodically including 1 s ON and 2 s OFF.  
Figure 10: The block diagram of the motor drive system.  
Figure 9: The experimental platform for the DC motor drive system.  
Three cases are used to practically test the proposed control structure, as shown in Table 3. Case 1 is a nominal condition with the inertia of 0.021675 Nm/s\({}^{2}\) and without the external load added. Case 2 is the condition with the exact inertia value, but the external load is ON and OFF control to be added to the system. In Case 3, the inertia is increased to 0.036125 Nm/s\({}^{2}\), and the load exists with ON and OFF control. The experimental results are shown in Figure 11b-d. They show that the controlled position and velocity responses under the perturbations still meet the required performance.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter Name** & **Value** & **Variation Range** \\ \hline Normal inertia \(J_{m}(\text{Nm}/\text{s}^{2})\) & 0.021675 & 0.01445 \\ Viscous friction \(B_{m}(\text{Nm}/\text{s})\) & 0.003724 & 0 \\ Torque constant \(K_{t}(\text{Nm}/\text{A})\) & 0.01041 & 0 \\ Feedback gain \(\text{K}_{1}\) & \([-0.7,-0.005,-0.1]\) & \\ \(q\) & 3 \\ Position/speed loop sampling frequency & 2 kHz \\ External load & 0.002 Nm \\ Current PI controller & \(20+10/\text{s}\) \\ Current loop sampling frequency & 20 kHz \\ \hline \hline \end{tabular}
\end{table}
Table 2: The parameters of the practical experimental system.  
Figure 11: The experimental results: (**a**) the position command; (**b**) Case 1; (**c**) Case 2; and (**d**) Case 3.