# Optimization Procedure for Computing Sampling Time for Induction Machine Parameter Estimation
## 3 Optimal Induction Machine Poles and Sampling Time
### Summary of the Procedure and Computational Complexity  
The whole procedure for computing the optimal induction machine sampling time is now summarized:  
1. Record the line start transient in voltage oriented reference frame, \(v_{q}=0\), with the fastest possible sampling time
2. Determine the optimal induction machine poles by solving optimization problem (Equation (24)) using the current \(i_{d}\) as the observed variable.
3. Determine the optimal sampling time factor \(K\) by numerical solution of Equation (26), and compute the optimal sampling time \(T_{s,opt}\).  
Solving of an optimization problem by metaheuristic algorithm (MIDACO Solver in our case) and iterative numerical solving of the nonlinear Equation (26) is required for the computation of the optimal sampling time.  
The optimization problem also requires solving of Equation (12) by means of singular value decomposition. This is the computationally most demanding step since it is repeated for each interval of the data segmented by the optimization procedure and for each iteration of the optimization. Therefore the requirements crucial to reducing the computation time is limiting the search area of the optimization procedure to reasonable intervals.  
Another aspect that seriously impacts the computation time is the original sampling time of the data and the duration of the recorded transient. This determines the total number of the original data samples. Depending on the stage of the optimization and the selected optimization variables, the original sampling time and transient duration alter the dimensions of the Hankel matrix Equation (8). This in turn affects the computational burden of the singular value decomposition solution of Equation (12). Naturally, lower initial sampling time and longer transient duration increase the computation demands.  
This paper suggests using the fastest possible sampling time for the best accuracy. However, the sampling times using FPGA based implementations can be reduced to nanosecond intervals which could lead to demanding computation of this procedure, so lowering the initial sampling frequency to commonly used 1-15 kHz is considered good initial sampling from the computation standpoint.  
In the examples presented in the following section the boundaries of the optimization are selected very wide. To test the diversity and applicability of the procedure, the simulation example uses large power and inertia motor (132 kW) that has longer line start transient duration. This motor is expected to have the poles in different locations in the \(z\)-plane than 4 kW motor used in the experimental example. However, the main reason to simulate 132 kW machine is to obtain the worst case scenario for the computational burden of the algorithm. The computational burden of the procedure is pointed out in the simulation and experiment subsections respectively.  
In the simulation, the original sampling time is set to microsecond level which, together with the long transient duration, demonstrates the largest expected computation time of the algorithm. In the measured data application, lower initial sampling (10 kHz) is selected, but the procedure still uses wide boundaries for the optimization variables. This demonstrates the actual computational time for practical use, that could be further reduced using narrower boundaries for the optimization based on experience.