Question

Department of Engineering Technology EET 441/GET 431 Controls Lab Spring, 2024 Lab #3: 1st Order Systems: Open-loop/Closed-loop harmonic response of an RC circuit Due Date: Laboratory #3 compares the open-loop and closed-loop response of a first order system to harmonic input. A range of frequencies are applied and the results used to construct Bode plots. The goal of this laboratory is to verify the measured responses with theory, observe the differences between the open-loop and closed-loop responses, and show how the time constant can be estimated from the amplitude and phase data. Harmonic Response Procedure. 1. Measure the resistance and capacitance of the plant. 2. Monitor the input on oscilloscope channel 1 and output on channel 2. Set up the measurement functions on the oscilloscope to measure channel 1 and channel 2 peak-to- peak voltage and the phase shift between channels. The oscilloscope screen should have these measurements displayed across the bottom of the screen as shown in figure 1. RIGOL TD 160ml TTTTTTTTIT VPF(2)= 2.984 UPP(1)= 5.12V CH1= 1.00V Pha_A= 14º Time 1.000ms 0+0.0000s 4-365 500ml Figure 1. Oscilloscope screen showing channel measurements and phase. 3. Adjust the feedback circuit to obtain an open-loop gain of 0.5. Measure and record the open-loop input amplitude, output amplitude and phase at each frequency of the attached datasheet. 4. Reattach the feedback to the circuit to provide a closed-loop control system. Repeat the measurements over all frequencies as listed on the datasheet. 5. Repeat steps 3 and 4, adjusting the open-loop gain each time to values of 1.0, 2.0, and 4.0. Report 1. Prepare a written report in memorandum format (short report format) that describes the experiment goal, equipment, procedure, and results. Present the underlying mathematical models and describe how well the model fits the experimental data. Describe any errors observed and deviations of experimental data from the expectations predicted in the model. Prepare your figures carefully. Make sure the axes are labeled correctly with units and a legend to identify the curves. Each figure must be numbered, have a description, and be referenced in the body text. 2. Include a Bode plot with amplitude and phase figures for the open-loop and closed-loop test results. Determine the break frequency (time constant) from each curve in each figure. Explain the process for these calculations and compare these results with the measured value of the plant time constant (RC) and the response time constant, [T/(1 + Kp)]. Discuss your results.

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