# New Stable Non-Vector Control Structure for Induction Motor Drive
## 5 Simulation of the IM Drive in Basic Operation States
The time course of the angular speed \(\omega_{m}\) (the output variable) for the considered operation cycle is shown in Figure 5. It is obvious that the angular speed of the IM drive practically tracks the reference angular speed prescribed by the reference model (Figure 5a) during the entire operation cycle, even during the step disturbance \(T_{L}\) as is shown in Figure 5b. This is also observed on changes of the variable \(\mathrm{d}\omega_{m}/\mathrm{d}t\approx T_{D}\) (corresponding to the acceleration) in Figure 5b, where the considered disturbance torque \(T_{L}\) is settled with high dynamics. This experiment verifies that the proposed control structure is invariant against the additive disturbances. The robustness of the proposed control structure has been verified at the change of the two most important parameters of the controlled system significantly affecting its properties. In the case of IM, they are the rotor resistance \(R_{2}\) and the moment of inertia \(J\). In the majority of the control systems for IM, the precise speed control depends on knowledge of the rotor resistance value that usually is identified by various types of observers. Figure 6 shows the time response when the rotor resistance \(R_{2}\) was increased to twice its original value. The dynamics of the controlled system are almost identical to the dynamics of the reference model during the entire operation cycle (Figure 5b). The time courses of the variables in Figure 6 confirm the controlled system robustness for the considered variation of the parameter \(R_{2}\). Figure 5: Time courses of the IM control during the operation cycle: (**a**) prescribed by the reference model, (**b**) achieved by the motor at its starting and loading. Another parameter that considerably influences the motor dynamics is the moment of inertia \(J\) applied to the motor shaft. Its value can vary during the operation cycle, which is the case for many industrial applications of the IM drives (e.g., winding machines, robotic and transportation systems). As it follows up from the time courses in Figure 7a,b, the increase of the moment of additional inertia to a half/or double that of the motor's nominal moment of inertia does not influence the motor dynamics. This fact presents a very significant advantage in the control of nonlinear systems with an oscillating character. The effect of the load torque \(T_{L}\) is again compensated with high dynamics also at a significant change of the motor inertia, which confirms the high robustness against the parameter variations in the proposed control structure. The simulations have confirmed that the proposed controller ensures a high quality angular speed control of the IM drive during the entire operation cycle according to the prescribed dynamics. Moreover, the controller satisfies all basic control objectives: the drive is invariant against the disturbances (the load torque) and robust against changes of the motor parameters (the rotor resistance and additional moment of inertia connected to the rotor shaft). Figure 6: The effect of change of rotor resistance \(R_{2}=2\)\(R_{2N}\) on control dynamics at motor starting and loading. Figure 7: The effect of change of additional moment of inertia to the value: (**a**) \(J=0.5\)\(I_{N}\); (**b**) \(J=2\)\(I_{N}\) on control dynamics at motor starting and loading.