How-to use Frequency response widget

Introduction

This section describes example of frequency response scada widget. The frequency response complements time domain analysis. Typhoon HIL frequency response scada widget provides a way to tune the controller and measure the system small signal performance on the fly without starting a new simulation every time.

Model description

This example builds upon one of the Induction Machine speed control examples. It demonstrates one way the widget can be used to tune and enhance control performance by measuring loop gains and sensitivity transfer functions.

Figure 1: Induction machine example

Modify speed controller for frequency response

We can refer to the simple control system illustration that defines some of the interesting system transfer functions:

Figure 2: Control system illustration

After including the disturbance and some measurement signals, the modified control system is illustrated in the figure below, showing inputs for reference disturbance, load disturbance, and output disturbance.

Figure 3: Setup for measuring loop gain

Simulation

After compiling the model and loading the custom user interface (scada), the frequency response widget should be visible.

Figure 4: Setup for measuring loop gain

Ensuring high open loop gain is a common method used to improve the system closed loop performance. Referring to this example, the loop gain is the negative of the transfer function represented by "X/E". To measure the loop gain, set the peturbing source as "Inverter control.out_dist.Vs1", the input signal as "Inverter control.E", and the output as"Inverter control.X". The figure below shows the negative loop gain for 3 different combinations of Kp and Ki. In general, higher loop gain increases the speed of response at the expense of reducing stability margins (more oscillations).

Figure 5: Measured loop gain for different controller parameters

The sensitivity transfer function complements the loop gain. To obtain the sensitivity frequency response, select the input as "N" and output as "Y". In general, the sensitivity peak should be between 1.0dB and 2.1dB for a balance between performance and sensitivity. Also the sensitivity should ideally be low at low frequency so that the closed loop system can track slow-moving reference correctly.

Figure 6: Sensitivity transfer function for different controller parameters

Based on the sensitivity analysis, Kp=1, and Ki=10 shows adequate performance with a peak of about 2.1dB around 15Hz. This result can be confirmed by the time-domain analysis. As shown in the figure below, using step responses at the different Kp, and Ki parameters we can confirm that Kp=1 and Ki=10 provides the best balance between speed of response and damping as predicted by the frequency response.

Figure 7: Time domain response

Table 1. Minimum requirements
Files
Typhoon HIL files Available on request
Minimum hardware requirements
No. of HIL devices 1
HIL device HIL402
Device configuration 1