AN EXPERIMENTAL INVESTIGATION OF THE PERFORMANCE OF A PID CONTROLLED VOLTAGE STABILIZER J. A. Oyedepo Department of Computer Engineering, Kaduna Polytechnic, Kaduna Yahaya Hamisu Abubakar Electrical and Electronics Engineering Department, Kaduna Polytechnic Gyang Chorji Rwang Power Holding Company of Nigera isjamoye@yahoo.com Abstract This study presents the design and construction of a PID controlled voltage stabilizer with single input and single output voltage. The purpose of the study is to carry out an experimental investigation on the performance of a PID control voltage stabilizer. The PID controller is known to have the ability to filter out overshoots, oscillations and improved rise and settling time. The PID control voltage stabilizer was constructed and tested by taking voltage readings at the output of the controller before connecting the PID controller. And measurement of voltage readings was repeated after connecting the PID controller. The output of the controller was also monitored on an Oscilloscope. The result of the experiment shows that for stabilizer input voltages between the ranges of 160-220V, a stable output of 200v was obtained. The result also shows that there is an explicit relationship between the performance parameters specified before the design and the coefficients of the controller polynomials. Even though there are inherent errors in any system that is designed, the PID controller has reduced the overall error and cause the stabilizer to move closer to its set-point as observed on both the measurement taken and the oscilloscope display. Keywords: PID controller, Stabilizer, Experiment, Performance. Introduction A voltage stabilizer is an electrical device that is designed and constructed so that it will maintain a fixed, stable output voltage level even with fluctuations in the input voltage level [1]. If the network shows voltage surges, over voltages, or under voltages, this piece of equipment offers compensation, holding the output voltage fixed and stable at a 200V ac therefore protecting electrical appliances. It is unfortunate that most voltage stabilizers cannot properly protect equipment they allow some voltage fluctuations through to the electrical appliances. Fluctuations in the network or switching cause oscillations in the appliances. Hence the appliance tends to overshoot. Now the rise time and settling time needs to be reduced to almost zero, since they cannot be completely eliminated. This study focuses on the design, construction and experimental investigation of the performance of PID controlled voltage stabilizer with the task of improving the accuracy, relative stability and speed of response of the voltage stabilizer. PID controller design If a mathematical model of a plant can be derived. Then it is possible to apply various design techniques for determining parameters of the controller that will meet the transient and steady state specifications of the closed loop system. If the plant is complicated then the mathematical model cannot be easily obtained and as such an analytical approach to design a PID controller is not possible [3]. Therefore we must resort to experimental approach to design the PID controller. The voltage supplied by the power amplifier to the line has a phase difference of Ǿ [5] and given as; 293
[ ( )] (1) Where Vo = Instantaneous steady state output voltage. Vm = RMS input voltage of the line V = RMS voltage output from the power amplifier Vo = RMS output voltage Let and To correct the maximum main fluctuation of 10% (2) (3) Where is the output that can be corrected on both sides of Vs by Vs as goes from 0o to 180o or from +90o to - 90o Vs represents the voltages of equation (1), (2) and (3) β = gain constant of the sensing circuit. K1 = gain constant of the phase control circuit. Vref E ψ Vo s + a + s - α Vs ki Sin ψ β S/H Ti Fig. 1. Transfer function block diagram of the plant. By replacing the integrator with phase advance circuit, for better transient response and steady-state error, the transfer function becomes: ( ) ( ) (4) Where a is the location of zero From equation (3) we see that the system is non linear and solution of such discrete time non linear control system is beyond the scope of this project. Now the system is linearised to have an idea of its stability and transient (assuming ) and the conditions for stability are determined [2]. The transfer function of the sample and hold is ( ) ( ) (5) where T1 is the sampling period The gain constants K1, β and Vs are lumped up together to give the loop gain K since the system is discrete. Z Transforms are used to give the transfer function 294
( ) [ ( )( ) ] (6) The PID controller has a transfer function expressed as; ( ) [ ] (7) Where Gc(s) = Controller transfer function Kp = Proportional gain TiS = Integral time TdS = derivative time Let us apply Ziegler Nichols tuning rule (first method) aimed at obtaining 25% maximum overshoot in step response [4]. 200v L = 0ms T = 3ms t(s) 1 2 3 4 5 6 Figure 2. The voltage stabilizer output graph before the PID. PID controller tuned by the first method of Ziegler Nichols rule gives; ( ) [ ] (8) [ ] ( ) From Table 1. Of first method the zeigler Nichols tuning rule based on step response of PID plant is [4]; 295
Table1. Zeigler Nichols tuning rule based on step response of plant [4]. Type Controller P PI PID of KP Ti Td T L 0.9 T L 1.2 T L 0 L 0 0.3 2L 0.5L Therefore, ( ) (9) From eqn. (9) the PID controller may be represented with the block diagram shown in fig. 3 R(s) 1.8(s+1) 2 S PID controller K(s + a)(1- e -T 1 s ) S 2 Voltage stabilizer Figure 3. Block diagram of the system with PID controller designed by use of Zeigler Nichols tuning rule (first method). The PID controlled stabilizer was constructed and the pictorial view of the implemented work is as shown in fig. 4. This hardware was tested and readings were taken with and without the PID controller. Figure 4. Pictorial view of the PID controlled voltage stabilizer. 296
Results The results obtained are shown in tables 2 and 3. Table 2 shows the stabilizer output voltage (v) at different time (ms) before the PID controller was connected. As observed the output voltage ranges from -160 to 220 volts. On the other hand, table 3 depicts the stabilizer output voltage (v) at different time (ms) after the PID controller was connected. Careful observation shows that the output voltage is constant and is stabilize between -200 to 200 volts. While, fig. 5 is the scope output voltage waveform of the PID control voltage stabilizer before the PID was connected and fig. 6 is the scope output voltage waveform of the PID control voltage stabilizer after the PID was connected. Furthermore, Fig. 7 shows the Plot of output voltage (v) against time (ms) before the PID controlled voltage stabilizer was connected and figure. 8 is the Plot of output voltage (v) against time (ms) after the PID controlled voltage stabilizer was connected. 297
Table2. Readings before the PID controller was Table3. Readings after the PID controller was connected to the stabilizer connected to the stabilizer TIME (ms) VOLT (V) TIME (ms) VOLT (V) TIME (ms) VOLT (V) TIME (ms) VOLT (V) 5 160-0.2-160 5 200-0.2-200 4.8 160-0.4-160 4.8 200-0.4-200 4.6 160-0.6-160 4.6 200-0.6-200 4.4 160-0.8-190 4.4 200-0.8-200 4.2 160-1 -200 4.2 200-1 -200 4 160-1.2-200 4 200-1.2-200 3.8 175-1.4-200 3.8 200-1.4-200 3.6 180-1.6-200 3.6 200-1.6-200 3.4 190-1.8-200 3.4 200-1.8-200 3.2 190-2 -200 3.2 200-2 -200 3 195-2.2-200 3 200-2.2-200 2.8 195-2.4-200 2.8 200-2.4-200 2.6 200-2.6-200 2.6 200-2.6-200 2.4 200-2.8-200 2.4 200-2.8-200 2.2 200-3 -200 2.2 200-3 -200 2 200-3.2-200 2 200-3.2-200 1.8 200-3.4-200 1.8 200-3.4-200 1.6 200-3.6-200 1.6 200-3.6-200 1.4 195-3.8-200 1.4 200-3.8-200 1.2 195-4 -200 1.2 200-4 -200 1 195-4.2-200 1 200-4.2-200 0.8 195-4.4-220 0.8 200-4.4-200 0.6 195-4.6-220 0.6 200-4.6-200 0.4 195-4.8-220 0.4 200-4.8-200 0.2 100-5 -220 0.2 200-5 -200 0 0 0 0 298
Fig. 5 Scope output voltage waveform of the PID controlled voltage stabilizer before the PID was connected Fig. 6 Scope output voltage waveform of the PID controlled voltage stabilizer after the PID was connected 299
Output Voltage (v) with PID Output voltage (v) without PID JORIND 11(2) December, 2013. ISSN 1596-8303. www.transcampus.org/journals; www.ajol.info/journals/jorind 250 200 150 100 50 0-6 -4-2 -50 0 2 4 6-100 -150-200 -250 Time (ms) Series1 Fig. 7 Plot of output voltage (v) against time (ms) before the PID controlled voltage stabilizer was connected 250 200 150 100 50 0-6 -4-2 -50 0 2 4 6-100 -150-200 -250 Time (ms) Series1 Fig. 8 Plot of output voltage (v) against time (ms) after the PID controlled voltage stabilizer was connected Discussion As stated in our introduction, this study focuses on the design, construction and experimental investigation of the performance of PID controlled voltage stabilizer, with the task of improving the accuracy, relative stability and speed of response of the voltage stabilizer. Observations from the scope output (figure. 5) indicate that the output response before the PID controller has rise time (delay) of 3 ms and an overshoot 10 percent. While, figure. 6 show the output response after the PID controller without the time delay and the overshoot thus improving the accuracy, relative stability and speed of response of the voltage stabilizer. On the other hand, Figures. 300
7 and 8 shows the plot of output voltage (v) against time (ms) before the PID controlled voltage stabilizer was connected and figure. 8 is the Plot of output voltage (v) against time (ms) after the PID controlled voltage stabilizer was connected. The results obtained in figures 7 and 8 have further confirmed the result from the scope output. Conclusions The paper presented the design and construction of a PID controlled voltage stabilizer with a single input and single output. The purpose of the study is to carry out an experimental investigation on the performance of a PID control voltage stabilizer. The PID controller is known to have the ability to filter out overshoots, oscillations and improved rise and settling time The result of the experiment shows that the stabilizer can stabilize voltages between the ranges of 60-220V to produce a stable output of 200v. The result also shows that there is an explicit relationship between the performance parameters specified before the design and the coefficients of the controller polynomials. Even though there are inherent errors in any system that is designed, the PID controller has reduced the overall error and cause the stabilizer to move closer to its set-point as observed on both the measurement taken and the oscilloscope display. References Lowe, J.F, (1986), Electronics for electrical trades, 4th Edition, McGraw-Hill book Maddock, R.J, (1988), Electronics a Course for Engineers 2nd Edition, Longman Nigeria. Pp, 55-58. Ogata, K, (1986), Modern Control engineering, 2nd Edition, Prentice Hall Oroge, C.O, (1986), Control system engineering, University Press Limited, Ibadan Theraja, B.L, (1999), Electrical technology, 3rd Edition, S. Chard & Company Ltd. 301