# Optimization Procedure for Computing Sampling Time for Induction Machine Parameter Estimation
## 4 Simulation and Experiment
### Application to the Experimental Data  
The optimal sampling time procedure is tested on measurement data, and parameter identification procedure is conducted to compare the effectiveness of the procedure with optimal sampling time and original sampling time.  
The motor used for the test is the Koncar 5 AZ112M-4B3, nominal power is 4 kW, and nominal speed 1420 rpm. The motor is delta connected with 380 V/50 Hz line voltage applied directly. The measurements are completed using the IOTECH WaveBook 512 data acquisition system, with Iotech WBK61 voltage sensors and Tektronix A622 current clamps. The initial sampling time is set to the fastest possible sampling with the mentioned hardware configuration, to \(T_{s,min}=0.1\) ms. The measured quantities are shown in Figure 3. It can be seen that the measured data is contaminated with noise which is expected to reduce the quality of the results.  
The procedure for obtaining optimal sampling time is tested on measured current \(i_{d}\) (voltage oriented reference frame \(v_{q}=0\)). The results of fitting the damped complex exponential series to the data is displayed in Figure 4a. Clearly the fit is less accurate than in the noiseless data and the optimal decimation of the measured data is large. The optimal decimation is \(\hat{d}=59\) that decimates the optimal interval size of \(\hat{q}_{int}=2985\) to the \(q_{d}=51\). Large decimation also results in the long sampling time for the damped complex exponentials fit to the data (namely \(T_{s,fit}=5.9\) ms). The system estimated discrete poles are shown in the Figure 4b. The figure shows that the heavy decimation of the measured data effects the pole locations so they are scattered even to the left half plane of the \(z\)-plane. It is not expected that the discrete IM model can correspond to the continuous for this sampling time. With the estimated motor poles, the procedure for obtaining the optimal sampling time is conducted. The result for optimal sampling is \(T_{s,opt}=1.4981\) ms, and the optimal motor poles are also shown in Figure 4b. The optimal sampling time in this case contracts the poles towards the (1,0) point in the \(z\)-plane, thus retaining the possibility of discrete approximation of the IM model while keeping them spread far enough to remain computationally robust.  
It can be seen that the optimal sampling time for the experimental IM is much higher than the original sampling time used for recording the transient, but it is lower than the decimated sampling time that is used for fitting the data with Prony exponential series. This shows that even if the initial sampling is too slow, one can calculate if the faster sampling is needed as long as the Prony exponential series approximates the data.  
In the case of experimental data, where the initial number of samples used for computing is lower and more realistic in regards to applications with IM, the total time to compute the optimal sampling time is averaged at 32.5 s based on 20 repeated runs. This is significant reduction compared to seven minutes in the simulation case that demonstrates realistic expectations of the algorithm demands.  
Figure 2: Optimal poles obtained with optimal sampling time and original estimated poles from simulated data.  
Figure 4: (**a**) Damped complex exponential fit to measured data (\(i_{d}\)) in the 1 st interval, with \(\boldsymbol{\Gamma}=\hat{\boldsymbol{\Gamma}}\); (**b**) Optimal poles obtained with optimal sampling time and original poles from Prony approximation.  
Figure 3: Real measured data.