## 5 RT Real-Time Simulation and Experimental Validation  
The proposed control mechanism is constructed by using six PI controllers; the speed controller is configured with an anti-wind-up to provide a smooth dynamic change for the whole range of speed operation, especially when the speed has a sluggish variation compared with the other electrical variables. Simulations using Matlab/Simulink software and hardware RT simulation tests are performed for the system, which involves the state observation as a feedback variable in order to compute the parameters of the PI controllers. Moreover, the singular perturbation (SP) technique affords a manner to disintegrate the two-time-scale arrangement into slow and fast dynamics in different time scales,which remarkably facilitate their architectural reasoning. Correspondingly, the original system is divided into lower-order subsystems with each subsystem has its own control-observer unit, and then the responses of all subsystems are combined to formulate the response of the complete main system. Thus, the concept of combining SP method and SM strategy forms an excellent choice to realize the standard control objectives of the systems, which are characterized by an imprecise model, parametric uncertainties, or parasitic dynamics. For this purpose, the following tests are performed considering the variation of rotor resistance. The general layout of the proposed control system is illustrated in Figure 1. The indirect rotor field oriented control (IRFOC) is considered as the base principle upon which the proposed control strategy is formulated. Under IRFOC, the rated rotor flux is totally aligned with the direct-axis of the rotating reference frame \((\lambda_{r}^{*}=\lambda_{m})\). In this topology, the load torque is constrained within a definite value and considered as unknown quantity. The designed SMO observer is implemented using the expression (24). The block of adaptive SMO estimates the rotor speed and rotor resistance simultaneously using the adaptive control laws described by Equations (52) and (53), respectively. A low-pass filter described by Equation (54) is utilized to smooth the signal of the estimated speed as the speed signal is containing high frequency components as mentioned earlier. The block of park angle estimation is used to estimate the synchronous frequency \(\hat{\omega}_{s}\), which is then used to calculate the synchronous angle \(\hat{\theta}_{s}\) needed for the transformation between the coordinate systems. Moreover, all motor parameters are assumed to be constant and known except the speed and rotor resistance. The control parameters and the motor data are listed in Table 1, whereas the parameters of the sliding observer are shown in Table 2.  
Figure 1: Complete system configuration. The selected observer parameters must ensure the overall stability of the nonlinear closed-loop system. One must use a high gain for the observer (fast dynamics to be neglected) and a constrained state feedback control (predominate slow dynamics), then the separation between the observer design and state feedback can be achieved [54; 55; 56; 57]. To validate the effectiveness of the proposed SMO, the control system shown Figure 1 has been tested using Matlab/Simulink, within which the static Runge-Kutta fourth-order method is utilized to solve the equations which describe the system operation. The estimations of stator currents and rotor fluxes are obtained by solving the relationship (24). To attenuate the chattering, the sampling time is selected as 50 \(\upmu\)s. A PWM technique is used to provide the switching signals to 10 IGBT VSI, with a switching frequency of 10 kHz. Under assumptions of availability of all parameters and all states including rotor flux, the estimated values of rotor speed, rotor flux, and rotor resistance are compared with their actual ones.