## 4 Simulation and Experimental Results
### Experimental Results  
The experimental verification of the PQ-MRAS estimator was carried out on the laboratory setup shown in Figure 16. The setup consisted of two induction motors coupled by a clutch--one motor was controlled by the DFOC algorithm, the other one worked as a load. The control algorithm and PQ-MRAS were implemented in a rapid prototyping unit dSPACE MicroLabBox (dSPACE Inc., Wixom, MI, USA) through the MATLAB/Simulink software (version 2015b, The MathWorks). The drive system was controlled in real-time by an application created in the ControlDesk software (version 5.4, dSPACE Inc., Wixom, MI, USA). Figure 14: Operation of the PQ-MRAS estimator: (**a**) estimated rotor resistance, (**b**) reference and estimated reactive power, (**c**) estimated stator resistance, (**d**) reference and estimated active power; (simulation results), (\(\omega_{m}\)\({}^{\prime\prime}\) = 0.5 \(\omega\)\(m\)\(N\), \(t_{L}\) = 0.75 \(t\)\(N\), \(R_{r}\) = var, \(R_{s}\) = var). Figure 15: State variables of the drive: (**a**) reference and measured rotational speed, (**b**) electromagnetic torque and stator current component \(i_{sy}\), (**c**) estimated rotor flux vector module and stator current component \(i_{xx}\), (**d**) stator current components \(i_{sa,\beta}\), (simulation results), (\(\omega_{m}\)\({}^{\prime\prime}\)\(=\) 0.5 \(\omega\)\(m\)\(N\), \(t_{L}\) = 0.75 \(t\)\(N\), \(R_{r}\) = var, \(R_{s}\) = var). During the experiments, the estimator was tested for the open-loop operation mode. The rotor flux vector was estimated by the current model, whereas an electromagnetic torque was calculated by:  
\[t_{e}{}^{est}=\frac{3}{2}p_{b}\frac{L_{m}}{L_{\tau}}\text{Im}\big{\{}\psi_{\bf r }^{\bf i*}\cdot\bf i_{s}\big{\}}. \tag{21}\]  
During the first test, the general performance of the PQ-MRAS was analyzed. It can be observed that the obtained results correspond with the simulation results (Figures 17 and 18). It should be noted, however, that neither of the estimated parameters exactly matched its nominal values. Nevertheless, the estimation error for rotor resistance was about 5% and for stator resistance it was about 10%. Figure 16: Photography of the experimental setup. Figure 17: Operation of the PQ-MRAS estimator: (**a**) estimated rotor resistance, (**b**) reference and estimated reactive power, (**c**) estimated stator resistance, (**d**) reference and estimated active power; (experimental results), (\(\omega_{m}{}^{mf}=0.5\)\(\omega mN\), \(t_{L}=0.75\)\(tN\)). The main aim of the second test was to check estimator robustness to load torque variations (Figures 19 and 20). The values of both estimated resistances fluctuated according to load variations but in limited ranges (3% for rotor resistance, 5% for stator resistance). Figure 19: Operation of the PQ-MRAS estimator: (**a**) estimated rotor resistance, (**b**) reference and estimated reactive power, (**c**) estimated stator resistance, (**d**) reference and estimated active power; (experimental results), (\(\omega_{m}{}^{rot}=0.5\)\(\omega mN\), \(t_{L}=\) var). Figure 18: State variables of the drive: (**a**) reference and measured rotational speed, (**b**) electromagnetic torque and stator current component \(i_{sy}\), (**c**) estimated rotor flux vector module and stator current component \(i_{xx}\), (**d**) stator current components \(i_{ax,g}\); (experimental results), (\(\omega_{m}{}^{ref}=0.5\)\(\omega mN\), \(t_{L}=0.75\)\(tN\)). Subsequently, a speed reversal test was carried out (Figures 21 and 22). The estimator operated stably, yet the fluctuations of estimated parameters were noticeable--especially during transients (about 5% for rotor resistance, \(\pm 10\%\) for stator resistance). Figure 21: Operation of the PQ-MRAS estimator: (**a**) estimated rotor resistance, (**b**) reference and estimated reactive power, (**c**) estimated stator resistance, (**d**) reference and estimated active power; (experimental results), (\(\omega_{m}{}^{n\!f}=\pm 0.5\)\(\omega mN\), \(t_{L}=\pm 0.75\)\(tN\)).