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Figure 2 Back view of the Bristol controller friction disc JARTEC motor-driven cam Figure 3 Motor-driven cam The system consists of a pneumatic servomechanism controlled by a double- nozzle-flapper valve, the recorder and the variable speed drive. All elements of the
complete feedback system are visible and when the control loop is closed, a system described by a first order transfer function is obtained. The sinusoidal input is provided by a motor driven cam (Figure 3). Control of the input frequency is implemented by the use of a friction drive disc which in turn is driven by a 3-speed belt drive. By turning the frequency control wheel which adjusts the signal take-off position on the friction disc and also the belt drive, different frequencies of the sinusoidal input can be obtained. The nozzle-flapper control valve controls the air pressure difference across the piston in the cylinder of the pneumatic controller which in turn controls the displacement of the output link. The air supply is set at 120kPa. A 2-channel recorder is used to record the input and output motions on a constant speed paper chart using colour pens which are directly coupled to input and output via a pulley wire system mounted off the back plate. Shown in Figure 4 is the schematic diagram showing how the system works. 8 Output ei Input Figure 4 Schematic diagram of the Bristol controller (a first order system) Eq. (2) can be re-written as Piston 3. Theoretical Background The Bristol controller is designed in such a way that it is a first order control system with transfer function -Linear Flapper Valve (1) 0₁ The time constant T can be obtained by using the frequency response 0 () of the system. The amplitude ratio of the output and input c can be calculated from = 1 To+1 (2)
(3) Taking lef as the vertical axis and ² as the horizontal axis, Eq. (3) is obviously a straight line with a slope of 7². Hence, the time constant is the square root of the slope. 4. Input and Output of Position Control System The input frequency is determined with the use of a stopwatch. For each frequency, the magnitudes of input and output signals and the phase lag are recorded on the paper in the chart recorder as shown in Figure 5. From the recorded information and the various input frequencies, the amplitude ratios and the phase lag can be calculated. mxxxxxx tot >2002|0i| = = T²0² +1 5. Experimental Data Figure 5 Recorded input and output sine waves 4= (5) x 360° Both experimental and calculated results should be tabulated in the table below W w² A.R Phase L No. rad/s (rad/s)² 00/0₁ Lag º tan mm 8 mm b mm 1/(A.R)² (0/00)²
6. Calculations
7. Derived Results (Based on the results in the table, plot a graph of w² vs (0/0)². We should be able to get a straight line the slope of which is the time constant T of the position control system.)
8. Discussions iscuss the results, their accuracy, their significance, any abnormalities or restrictions that existed in the experiments.)
9. Conclusions (What conclusions were drawn from the experiment?)
10. Student Reflections (Students are to state their learning from the experiment and ways in which it could be improved.)