Frequency Response Essay

3298 words - 14 pages

This lab deals with the concept of frequency response. During steady state, sinusoidal inputs to a linear system will generate sinusoidal responses of the same frequency, but of different amplitude and phase angles. This is due to a time lag between input and output generated. These differences are functions of frequency.
In this experiment, the frequency response test is used to identify the (linear) dynamics of a plant. It is performed by inputting a sinusoidal signal and comparing it with the sinusoidal output.

Objective of Experiment
1. To perform a frequency response test on an aircraft electro-hydraulic servo-actuator, hence determining the phase and gain margins ...view middle of the document...

When an error signal is detected, the displaced LVDT core causes current to increase in one coil and to decrease in the other: The net differential current causes the motor to move.
The servo-actuator consists of a servo motor, a valve spool, and actuator and a linear potentiometer.

As the motor reacts based on the input signal, it tends to block one nozzle and unblock the other. This causes an increase in oil pressure behind the former, and a decrease behind the other. This differential is applied at the ends of the main valve spool that consequently moves a distance proportional to the electrical/mechanical input. As the spool moves, pressurized oil is supplied to one chamber of the main actuator, while oil in the other flows back to the return. The piston rod of the actuator moves and this movement is converted to a voltage by the potentiometer.

The summing amplifier receives the error between input and output and the error voltage is applied to the power amplifier.

Summary of Experimental Procedure
1. We set sine wave frequency at 0.5 Hz, and fixed the amplitude of the function generator output at 5V peak-to-peak for the whole experiment.

2. We opened the hydraulic supply valve to allow the actuator to move in and out.

3. We measured and recorded the frequency (, voltage input Vi, voltage output Vo and (time in Table 1. The data was used to derive the gain and phase angle. We then repeated measurements for increasing frequencies of 1Hz.

4. We used the data to plot on the Nichols chart at each frequency, and read off the gain and phase margins.

5. We reset the function generator for 5V peak-to-peak square wave at about 0.5 Hz. We gradually increased the loop gain K by increasing the summing amplifier feedback resistor, until the system reached the point of instability. We converted K to (dB) using Gain = 20 log10 K, and compared this value of gain margin with that obtained from the Nichols chart.

6. From the Nichols chart, we read off the values of the open loop transfer function in Table 2. We used the data to draw the Bode gain plot and Bode phase plot on the same graph. From the resultant graph we estimated the order of the system and its time constants and discussed our results.

Experimental Data

For Table 1:
Sample : Frequency, f = 5.0 Hz
Input voltage, Vi = 5.2 V
Output voltage, Vo = 1.44 V
Time, Δt = 0.062s

• ω (rad/s) = 2πf
= 2π x 5.000
= 31.42 rad/s

• Closed-loop Gain (dB) = 20 log (Vo / Vi)
= 20 log (1.44/5.2)
= -11.15 dB

• Phase angle (°) = - Δt x f x 360°
= - (0.062) x 5 x 360°
= -111.6°

From Nichols Chart For Table 2:

Sample : Frequency, f = 5.0 Hz
Input voltage, Vi = 5.2 V
Output voltage, Vo = 1.44...

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