In+Lab+4 - EECS 216 Fall 2010 Lab 4 Control Part II In-lab...

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EECS 216 Fall 2010 Lab 4: Control Part II: In-lab & Post-lab Assignment The lab has been designed so that you can complete both in-lab and post-lab portions during the three-hour lab. Please plan on handing in your completed post-lab before you leave. 1 Laboratory Work (In-lab) All the circuits constructed as part of this laboratory use the 741 operational amplifier. 1.1 Circuit & Protoboard Layout The following three figures illustrate the circuits and their protoboard layout for the present lab. Figure 1.1.1 shows the op-amp circuit realization of the PD controller, where the plant, P ( s ) appears as a separate component in the circuit. Further details about P ( s ) are given in Figure 1.1.2, which provides the appropriate op-amp circuit. Finally, Figure 1.1.3 provides a schematic for the overall layout of the protoboard. x ( t ) R 1 - + Op-amp 1 R 1 p ( t ) R 2 A R 2 C - + Op-amp 2 - + Op-amp 3 R 3 w ( t ) P ( s ) y ( t ) Figure 1.1.1: Op-Amp Realization of PD Controller With 2-Degrees of Freedom 1
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Lab 4 Control - V i + R A C 1 B D R - + C 2 + - V o Figure 1.1.2: Op-Amp Circuit for Plant 1.2 Plant Response (a) Examine the circuit of the plant on your protoboard and fill in the values for the resistor and capacitors below: R = C 1 = C 2 = (b) Isolate the plant from the PD circuit. Use the signal generator to apply a unit step input, i.e., v i ( t ) = u ( t ), to the plant and observe on the oscilloscope both the input step (scope channel 1) and output step response, v o ( t ), (scope channel 2). Store these scope traces (plot and both channels of data) on the computer for later use. Note: The output step response should be of the form v o ( t ) = A + Be - αt cos( ω 0 t + φ ). (c) Using the oscilloscope, measure the oscillation frequency, ω , and the decay rate, α , of the step response signal v o ( t ).
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