Laboratory PID Tuning Based On Frequency Response Analysis. 2. be able to evaluate system performance for empirical tuning method;
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1 Laboratory PID Tuning Based On Frequency Response Analysis Objectives: At the end, student should 1. appreciate a systematic way of tuning PID loop by the use of process frequency response analysis; 2. be able to evaluate system performance for empirical tuning method; 3. understand the role of proportional, integral and derivative modes of control, in comparison with theory. 1 Introduction It is known that open-loop systems are difficult to control; closed loops are more stable but can, under certain conditions, become unstable. The purpose of control is to produce stability and it cannot be assumed that closing the loop will give the required stability to the system. A process and its controller consist of elements, many of which cause lags and also attenuate the control signals. These control signals are seldom constant for any appreciable period and will always consist of a wide range of sinusoidal signals at different frequencies and amplitudes, all present at the same time. If an open-loop system is tested to find the attenuation and time lag or phase shift for each of the frequencies to which it is capable of response, it should be possible to predict the performance when the loop is closed. It may be possible to have a set of conditions such that the phase shift between input and output and is 180 and the gain of the controller is equal to the attenuation of the system. Closing such a loop would produce the system providing its own input which would go into continuous oscillation, because there is a further 180 phase shift designed into the controller. The purpose of the following experiment is to predict such a set of condition and to adjust the controller by several practical methods to avoid instability and, at the same time, provide the necessary degree of control. After each controller setting, the system is checked to see if its performance is close to the predicted performance. 1.1 Integral Action Time If a step waveform is applied to a proportional plus integral controller, the proportional part of the output will increase in a step of amplitude u; and the integral part will start to increase as a ramp function (see Figure 1). After a time T i = t 2 t 1, the increase in the output due to the integral term will be equal to the step increase due to the proportional term. T i is the integral action time and it can be varied, i.e. the slope of the ramp can be INC 351-S. Wongsa PID Tuning Based on Frequency Response Analysis 1
2 changed, by the integral action control. Note that an increase in the integral action time decreases the effect of this term. Figure 1: Integral action time: e deviation; u controller output signal; u p controller output due to proportional action; u i controller output due to integral action; K 1 and K 2 are constnats. 1.2 Derivative Action Time If a ramp input is applied to a proportional plus derivative controller, the derivative part of the output increases in a step of amplitude u and the proportional part increases as a ramp function, as seen in Figure 2. After a time T d = t 2 t 1, the increase in the output due to the proportional term will equal the increase due to the derivative time. The time T d, in this case, is the derivative action and can be varied by the derivative action control. Note that an increase in the derivative action time increases the effect of this term. 2 Controller tuning Lab Equipment 1. PCS327 Process Control Simulator 2. Oscilloscope 3. Signal Generator INC 351-S. Wongsa PID Tuning Based on Frequency Response Analysis 2
3 Figure 2: Derivative action time. e deviation; u controller output signal; u p controller output due to proportional action; u d controller output due to derivative action; K 1 and K 3 are constants. 2.1 Task 1 Open Loop Frequency Response Procedure 1. Patch the front panel of the PCS 327 as in Figure 3 and set all controls and switches as indicated. 2. Disconnect point A and set % PB to 100% 3. Inject into the SET VALUE DISTURBANCE socket a sinusoidal input at 5 V peak to peak. Vary the input frequencies as specified in Table I. For each of these frequencies, measure V out /V in and the phase shift between V out and V in. Record these data in Table 1 4. Find the frequency and gain at phase lag = 180, i.e. the phase crossover frequency and the gain margin of the system, respectively Of special interest is the frequency at which the phase lag is exactly 180 : To determine this, it is possible to invert one channel and adjust channel gain on the oscilloscope until both amplitudes are equal. Then there will be exact coincidence of input and output waveforms when the output lag is Using the data obtained from 3. and 4. to plot the Nyquist plot (in Figure 5) and the Bode plot (Figure 6) of the open-loop system. You may do it at home. INC 351-S. Wongsa PID Tuning Based on Frequency Response Analysis 3
4 Figure 3: Patching for controller setting (open loop) 6. Remove the input test signal and close the loop by connecting Link A in Figure Increase the controller gain by reducing the percentage PROPORTIONAL BAND until, with a slight movement of the SET VALUE control, the system will go into continuous oscillation. Note the gain setting and the period of the oscillation, which will be referred as the ultimate gain (Po) and the ultimate period (To). Compare these values with phase cross-over frequency and the gain margin obtained in 4. INC 351-S. Wongsa PID Tuning Based on Frequency Response Analysis 4
5 Figure 4: Patching for controller setting (closed loop) 3 Nyquist Diagram 2 1 Imaginary Axis Real Axis Figure 5: Nyquist plot INC 351-S. Wongsa PID Tuning Based on Frequency Response Analysis 5
6 Table 1: -Open loop gain and phase shift FREQUENCY V out V in GAIN PHASE SHIFT (Hz) (volt) (Volt) (V out /V in ) (Degree) Figure 6: Patching for controller setting (closed loop) INC 351-S. Wongsa PID Tuning Based on Frequency Response Analysis 6
7 2.2 Task 2 PID tuning by using ZieglerNichols method All the following methods are based on two preliminary measurements, namely the percentage PROPORTIONAL BAND required to give continuous oscillation with proportional control only, and the PERIOD of such oscillation. For each of the methods the following terms are used: P o = % proportional band (PB) that causes oscillation with proportional control only. T o = Period of oscillation with proportional control only. T i = Integral Action Time. T d = Derivative Action Time. Procedure 1. Patch the panel of the PCS 327 according to Figure 4 Set all controls and switches as indicated. 2. Use the values of P o and T o obtained by TASK I as follow: ω 180 is the frequency that make 180 phase-lag and k 180 is the corresponding gain. The Ultimate gain is K u = 1/K 180 and the Ultimate period is T u = 2π/ω Apply to the SET VALUE DISTURBANCE socket a square wave input of 5V peak to peak at 1 Hz. Observe the MEASURED VALUE. 4. Set up the controller by each of the following method. Draw the output time response with respect to step input for each of the settings. Zeigler and Nichols Proportional - only mode (P) %PB = 2P o Proportional - plus - integral mode (PI) %PB = 2.2P o T i = T o 1.2 Proportional, integral and derivative mode (PID) %PB = 1.67P o T i = 0.5T o T d = T o 8 5. Varying each controller gain to observe their effect on the output response. INC 351-S. Wongsa PID Tuning Based on Frequency Response Analysis 7
8 2.3 Report 1. Your report should include: the Nyquist plot and the Bode plot of the open-loop system. discuss of some relevant issues of PID tuning based on frequency response analysis, for example the implication of P o and T o in the sense of the system s stability. the performance of the controller when set up by the Zeigler-Nichols tuning. explanation of proportional, integral and derivative modes of control and the advantage gained by using each mode in an industrial control situation. The discussion should be made in both theoretical and experimental perspectives. 2. Data may be photocopied, but do not photocopy the graph. Each student should plot his or her own. 3. The report is due before you arrive for the next lab, which is usually a week after the lab. Late reports will not be accepted. 4. Duplicate reports are totally unacceptable and no mark will be given to all responsible students. INC 351-S. Wongsa PID Tuning Based on Frequency Response Analysis 8
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