23 CHAPTER 2 PID CONTROLLER BASED CLOSED LOOP CONTROL OF DC DRIVE 2.1 PID CONTROLLER A proportional Integral Derivative controller (PID controller) find its application in industrial control system. It is a generic loop feedback mechanism and used as feedback controller as shown in Figure 2.1. PID working principle is that error value is calculated from the processed measured value and the desired reference point. The controller minimizes the changing error in the inputs of the system. PID controller provides the best results if it is tuned properly by keeping parameters of the systems according to the nature of system in the case of unknown system. Figure 2.1 PID controller block diagram The PID controller includes three parameters namely the proportional, the integral and derivative part which are called as P,I and D part. The output response of PID controller in time domain is given below;
24 () () ) ) (2.1) Where K p = Proportional gain constant, K i = Integral gain constant, k d = Derivative gain constant. P term obtains the reaction to current error. I term obtain reaction to the sum of recently appeared errors. D term obtains reaction according to the rate current error changing. The addition of all three parts contribute the control mechanism such as speed control of DC motor in which P value depends upon current signal of error, Integral on the accumulation of previous error and Derivative controller predict future error based on the current rate of change. As derivative action is sensitive to noise and it is not possible for a system without disturbance and so mostly the controllers are PI controller rather than PID as P part increases overshoot and the integral part helps the system to reach onto its target value. The P term takes the output proportional to error value. Its response can be adjusted by multiplying the error by a constant Kp which is called proportional gain. If proportional gain is larger, then it creates a high overshoot and makes the system unstable where a small change in output makes small control action. The integral term contributes error and duration of error proportionally. The calculated error is multiplied by integral gain and then added to the controller output. Finally it is reduced to steady state error. The effects of the controlled parameters on the output response of the system are summarized as shown in Table 2.1.
25 Table 2.1 Effects of the PID gains in the Response of the system Gain Rise Time Maximum overshoot K P Decrease Increase K I Small change Decrease Settling Time Small change Increase Steady state error Decrease Small change K D Decrease Increase Decrease Eliminate 2.2 PID TUNING METHODS Today P-I-D is used over 90% of the control loops in control engineering world. Actually if there is control, there is an analog P-I-D or P- I-D in digital forms. In order to achieve optimum solutions Kp, Ki and Kd gains are obtained according to the system performance. The most common tuning methods are as given below: Manual tuning method (Trial and Error). Ziegler- Nichols tuning method. Cohen - Coon tuning method. 2.2.1 Manual Tuning Method (Trail And Error) The most effective tuning method is that in which a model is developed and selecting P, I and D gain values. Every tuning method has some advantages and disadvantages which are listed below. Trail and error method is way of tuning in which controller is tuned by increasing its Proportional value(p) until output of the system get oscillation at the same time keeping I and D value set to zero. Then
26 increasing I value selecting the value in optimum range as increases of I value to certain limit cause instability, and then D value is increased if it is required. Advantages and Disadvantages It is very simple method to find parameters of controller but it needs a lot of time and experience. 2.2.2 Ziegler-Nichols Tuning Method More than six decades ago, P-I controllers were mostly used than P-I-D controllers. Though the P-I-D controller is faster and has no oscillation, it tends to be unstable in the condition of any disturbance to the process and even small changes in the input set point than PI controllers. Ziegler Nichols method is one of the most effective methods which increase the usage of P-I- D controllers. Figure 2.2 PID controller Ziegler - Nichols tuning method
27 The logic is from neutral heuristic principle. Firstly, checking is done whether the desired proportional control gain is positive or negative. To obtain this, step input is manually increased a little and if the steady state output increases as well, it is negative, otherwise it is positive. Then K i and K d are set to zero and only increasing K p value till it creates a periodic oscillation at the output response. This critical value is ultimate gain Kc and the period where the oscillation occurs is Pc ultimate period. Hence the whole process depends on two variables and the other control parameters are calculated according to the table. Table 2.2 Ziegler - Nichols PID Controller Tuning Parameter Control Type K P T I T D P 0.50Ku 0 0 PI 0.45Ku Tu/1.2 0 PID 0.60Ku Tu/2 Tu/8 Advantages Experiment is easy need to change the P controller only. Includes dynamics of whole process, describing the more accurate picture of the behaviour of the system. Disadvantages Experiment is time consuming. It can venture into unstable regions while testing the P controller, which makes the system to become out of control. It might result in aggressive gain and overshoot in some cases.
28 2.2.3 Cohen Coon Tuning Method The process reaction curve is obtained first, by an open loop test as shown in Figure 2.3, in this method and is approximated by a first order plus dead time model with the following parameters. = ( ) (2.2) (2.3) Where t 1 = time at which C=0.283 CS t 2 = time at which C=0.683 CS C = output the plant Figure 2.3 Cohen - coon PID Tuning method This method is proposed by Smith et al (1985) which provides a good approximation to process reaction curve by first order plus dead time model. After determining the three parameters K m, and d m, the controller parameters can be obtained, using Cohen-Coon (Seborg et al 1989) relation given in Table 2.3. These relations were developed with a ¼ decay ratio empirically to provide closed loop response.
29 Table 2.3 Tuning Parameter Cohen -coon method Controller type Kc I D P 1 1 + - - 3 PI 1 9 10 + 12 30 + 9 + - PD 1 5 4 + - 6 6 22 + PID 1 4 3 + 4 32 + 13 + 4 11 + Advantages Good process models. Disadvantages It is only good for first-order processes. Compared to all the tuning method, Ziegler Nichols tuning methods is very effective to find the controller parameters and which can implement first order to third order system but Cohen-coon only applied to first order system.
30 2.3 DESIGN AND IMPLEMENT OF PID CONTROLLER GAINS FOR CONTROLLING DC MOTOR SPEED USING ZIEGLER NICHOLS TUNING METHOD The target of this project is to control the speed. So the speed is sent back to check the system in closed loop DC motor with PID controller. Ziegler Nichols method is used for tuning the PID controller parameters and Simulink model of DC motor system with P - controller is shown in Figure 2.4. According to Ziegler-Nichols tuning method Figure 2.4 Simulink model of DC motor system with P- Controller Simulating the DC motor system with P controller. Increasing gain of P controller until sustained oscillations. Then noting the controller gain and time period (tu). The variation gain of P controller and the corresponding simulated wave forms for various gain values of P controller are shown from Figures 2.5(a) to 2.5 (e).
31 For Ku = 10 1 0.9 K=10 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 1 2 3 4 5 6 7 8 9 10 Time in seconds Figure 2.5(a) Step response of DC motor with P- controller (K=10) For Ku=50 1.2 K=50 1 0.8 0.6 0.4 0.2 0 0 1 2 3 4 5 6 7 8 9 10 Time in seconds Figure 2.5(b) Step response of DC motor with P- controller (K=50)
32 For Ku= 70 Figure 2.5(c) Step response of DC motor with P- controller (Ku=70) For Ku=80 8000 6000 K=80 4000 2000 0-2000 -4000-6000 -8000 0 2 4 6 8 10 Time in sec Figure 2.5(d) Step response of DC motor with P- controller (K=80)
33 For Ku=74.08 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0-0.2 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 Time in sec Figure 2.5(e) Step response of DC motor with P- controller(k=74.08) The above Figure shows that ku=74.08, the DC motor output has constant amplitude and period of the one cycle is calculated which is tu=0.09.by using Table 2.2 different controller gains are calculated which is shown in Table 2.4. Table 2.4 PID Parameters gains Type of controller K P T I T D P 37.04 PI 33.34 0.075 PID 44 0.0485 0.012
34 2.4 PROPOSED PID - PWM FULL BRIDGE DC-DC CONVERTER FED DC DRIVE 2.4.1 Circuit Description and Operation The block diagram representation of the proposed system is shown in Figure 2.6. It consists of single phase diode bridge rectifier, full bridge DC- DC converter, DC motor and closed loop PID mechanism such as speed and current controller. This system has two control loops, outer loop is speed control loop and inner loop is current control loop. Figure 2.6 Block diagram of PID - PWM Full bridge DC-DC converter fed DC motor The primary purpose of the PID control is to provide speed response without maximum overshoot and steady state error. Full bridge DC- DC converter provides four quadrant operations to the DC motor ie forward motoring, forward braking, reverse motoring and reverse regenerative braking. Here four MOSFET switches are controlled by PWM voltage switching techniques. Switching techniques are explained in previous chapter. Detailed explanation about speed and current controls are in the following subheadings.
35 2.4.2 Speed Controller The speed control is shown in outer loop of Figure 2.6. DC motor provides the speed feedback.to the speed error amplifier the actual and required speeds are fed. The difference between actual and desired speed is amplified, and the output obtained serves as the input to current loop. For example, if the actual motor speed is less than the desired speed, the speed error will be proportion to the current demanded by the speed amplifier, and to minimize the speed error the motor will accelerate. The inner loop will be called for more current when the load increases there will be an immediate deceleration and the speed error signal increases. The acceleration produced due to increased the torque and the speed error will be reduced until equilibrium is reached. At the point a motor current produces a current reference that gives a torque which is equal and opposite of the load torque. The speed controller shown is simple proportional amplifier, for a finite speed error; there will be a steady state error of that is the target speed cannot be achieved by P-Controller. The speed controller having an integral and proportional (P) term is used to eliminate steady state speed error. When the input to the PID controller is zero the finite output is obtained, that is by using PID control zero steady state error can be achieved. 2.4.3 Current Controller The heart of the drive system is indicated by the shaded region in the closed loop controller is give in current loop. The actual motor current follows the current reference signal is the main purpose of the current loop.
36 To control the duty cycle () and the output voltage of the converter is done by comparing the current reference signal with the feedback signal of the actual rotor current here the amplified current error signal is used to control the duty cycle. From the rectifier the feedback signal is obtained in the main supply. The reference and the actual current signal are compared and obtained error signal is amplified by the current error amplifier. With the high gain current error amplifier the actual motor current will be equal to the current reference signal compared to motor speed the current error will be small. To make the actual motor current to follow the current reference signal the armature is automatically adjusted by the controller regardless of the speed the current has exact value. The control system cannot be perfect but the current error amplifier may be PID type in which the demanded and actual current will be equal in steady-state period. The motor current never exceed the reference value until the current control loop function properly. The current reference signal magnitude is limited so that the motor current is always within the specified value. 2.5 CLOSED LOOP CONTROL OF DC DRIVE WITH BIPOLAR VOLTAGE SWITCHING 2.5.1 Circuit Description and Operation The detailed circuit diagram of diode bridge rectifier, DC-DC converter and DC motor are shown in Figure 2.7.
37 Figure 2.7 Schematic diagram of PID - PWM Full bridge DC-DC Converter fed DC motor with Bipolar voltage switching The single phase AC supply is applied to a diode rectifier and a LC filter with braking resistor, such that a constant amplitude DC link voltage is established. DC motor load is powered through full bridge DC DC converter which consists of four MOSFET switches (M1, M2 M3 and M4) and their respective anti-parallel diodes (D1, D2, D3 and D4). These switches are controlled by PWM technique with PID controller. The diagonally opposite switches M1, M4, and M2, M3 are considered as two switch pairs. These two switch pairs are turned on and off simultaneously such that the motor voltage is referred to bipolar voltage switching. Conventional PID controller is used as a speed controller for recovering the actual motor speed to the reference. The reference and measured speed are the input signals to the speed PID controller. Here K P, K I, and K D values of controller are determined by Ziegler-Nichols tuning method. Further, this controller output is limited to give the reference signals for one input of current controller and other one as measured current taking from the motor. The difference of signals (i.e. current error) is amplified through this controller and emerged as a control voltage (Vc). This control voltage (Vc) is
38 limited and compared with a triangular signal, to generate PWM pulses to turn on the MOSFET switches. 2.5.2 Switching Patterns of Bipolar Voltage Switching. The proposed PID-PWM technique is established by comparing a carrier triangular wave (V tri ) at relatively high frequency (fc) with control voltage Vc i.e, output of the current PID controller. The switching frequency of carrier triangular wave is 1 khz. The switching patterns are generated in such a way that when Vc > V tri, switch M1 and M4 are turned on otherwise, M2 and M3 are turned on. The switching patterns are shown in Figure 2.8. Figure 2.8 Switching patterns of bipolar voltage switching Powering mode and Regenerative modes of operation are obtained. In powering mode, the motor current is carried by either switch pairs M1, M4 or M2, M3 according to the polarity of the motor voltage. The energy stored in the reactive element is returned back to the supply from the motor through either diode pairs D1, D4 or D2, D3. in the regenerative mode.
39 2.6 CLOSED LOOP CONTROL OF DC DRIVE WITH UNIPOLAR VOLTAGE SWITCHING 2.6.1 Circuit Description and Operation The proposed single phase DC motor controlled by PID-PWM full bridge DC-DC Converter with unipolar voltage switching technique is shown in Figure 2.9. Here, the switches in each leg are controlled by independent of other leg, so it is called as unipolar voltage switching technique. Figure 2.9 Schematic diagram of PID - PWM Full bridge DC-DC Converter fed DC motor with unipolar voltage switching 2.6.2 Switching Patterns of Unipolar Voltage Switching In this control technique, the switches in each leg are controlled independently of the other leg.the switching patterns are such that when V c >V tri. M1 is on, and when -V C >V tri.m3 is on and switching in the same leg
40 have compliment switching patterns. The switching patterns are illustrated in Figure 2.10. The duty ratio of the switches M1 and M2 are same as the bipolar voltage switching scheme which is given below and the average voltage is also same and it varies linearly with control voltage. The converter output voltage is in the motoring mode 0 to V dc and in the reverse motoring mode 0 to -V dc. Figure 2.10 Switching patterns of unipolar voltage switching The following modes of operation can be defined. The motor current is carried by switch pair M1 and M4. in the powering mode. For free Wheeling mode, the motor current continues to flow in an anti-parallel diode when the conducting switch is turned off as in M1, D3 andm4, D2. A regenerative mode may arise during light loading.
41 2.7 SIMULATION RESULTS AND DISCUSSION 2.7.1 Simulation of Closed Loop Control DC Motor with Bipolar Voltage Switching The single phase D.C motor drive system controlled by PID-PWM with full bridge DC-DC converter have been simulated by using the software package MATLAB/SIMULINK. The Simulink model of the proposed PID-PWM full bridge DC-DC converter is illustrated in Figure 2.11 and the simulation results of the proposed system are represented in Figures 2.12 to 2.16, which indicate performance of DC motor for four quadrant operation. Figure 2.11 Simulink model of PID - PWM Full Bridge DC-DC converter fed DC motor with bipolar voltage switching
42 Figure 2.12(a) Load voltage - Forward motoring Mode Figure 2.12(b) Load voltage Reverse Motoring Mode The above Figure 2.12(a) and 2.12(b). Shows that the average motor voltage varies linearly with input signal.also the D.C Motor voltage jumps between +V dc and - V dc so that this switching strategy is referred as the bipolar voltage switching.
43 It has to be noted that the duty ratio of the switches ( 1 ) can be varied between 0 and 1, depending on the magnitude and polarity of the control voltage. Therefore Vo can be continuously varied in the range of +V dc to - V dc,while motor current can be either positive or negative such that the motor can operate four quadrants of the Vo Io plane. Figure 2.13 Load Current response - Four Quadrant Figure 2.14 Load Torque response - Four Quadrant
44 Figure 2.15 Speed Response - Four Quadrant Figure 2.16 Average output load Voltage - Four Quadrant 2.7.2 Simulation of Closed Loop Control DC Motor with Unipolar Voltage Switching The simulink model of proposed PID-PWM full bridge DC-DC converter is shown in Figure 2.17 and the performance characteristics of DC motor simulated wave form which are illustrated from Figure 2.18 to 2.26
45 Figure 2.17 Simulink model of PID-PWM Full Bridge DC-DC converter fed DC motor with unipolar voltage switching Figure 2.18 Input voltage and current waveform without LC filter
46 Figure 2.19 Input voltage and current waveform with LC filter Figure 2.20(a) Load voltage-forward motoring mode Figure 2.20(b) Load voltage-reverse motoring mode
47 Figure 2.21 Load current responses Four quadrant 40 Torque in NM 20 0-20 -40 0 0.5 1 1.5 2 Time in Sec Figure 2.22 Load Torque response Four quadrant Figure 2.23 Speed response Four quadrant
48 2.7.3 Comparison of Open Loop and Closed Loop Speed Response with PID Controller Figure 2.24 Open loop and Closed Loop Speed Response of DC motor From the Figure 2.24, it can be concluded that a PID Ziegler Nichols method is suitable to design gain values for D.C. Motor, where the overshoot in the closed loop response is reduced to zero and steady state error is minimized. Figure 2.25 FFT Analysis of Open loop system
49 Figure 2.26 FFT Analysis of Closed loop system. From Figures 2.25 and 2.26 shows that total harmonics distortion of the supply line current is reduced to a great extent in the closed loop system when compared to open loop system. 2.7.4 Four Quadrant Torque - Speed Characteristic The simulation results of four quadrant DC motor torque and speed are shown in Figures 2.22 and 2.23. At initial conditions, the motor is operated in first quadrant (forward motoring mode).when negative speed step signal command is issued, the machine undergoes braking operation in forward braking operation with motor speed tending to zero and starts rotating in reverse direction as soon as the speed of the motor is zero which is shown in Figure 2.23.when again speed reversal command is given, motor undergoes in reverse braking and operates in forward motoring. In the motoring mode, the magnitude of motor output voltage increases until the steady state is reached and in braking mode voltage starts decreasing towards zero. Figure 2.16 shows the change of motor output voltage from forward braking mode to reverse motoring mode. In the forward and reverse motoring mode, the motor average voltage and armature current
50 is in phase. In braking mode both are out of phase as shown in the Figures 2.16.and 2.21. Torque- speed characteristic is shown in the Figure 2.27. In the Figure arrows indicate the travel of torque- speed from (forward motoring mode)first quadrant to( reverse motoring mode) Third quadrant via (reverse braking mode) second quadrant in four quadrants. Figure 2.27 Torque - Speed Characteristics (Four quadrant ) 2.8 DISCUSSION OF BIPOLAR VOLTAGE SWITCHING AND UNIPOLAR VOLTAGE SWITCHING This chapter discusses about PID controller, different tuning methods and its advantages and disadvantages. First comparison has been done between speed performance of PID controller for DC motor by open loop and closed loop with PID controller using Ziegler - Nichols tuning method. It is observed from simulation results that PID controller with Ziegler-Nichols tuning method performs better speed response and steady state period than the open loop system.
51 We have studied about PWM switching techniques and implemented to closed loop speed controlled separately excited DC motor. Next comparison has been done between PWM with bipolar and uniploar voltage switching techniques. The performance of closed loop DC motor with PWM switching techniques based on PID controller whose MATLAB simulation results are shown 2.12a and 2.12b, 2.20a and 2.20b. From the figure the output voltage changes from +V dc to V dc in the bipolar voltage switching Technique and 0 to +V dc or 0 to V dc in the uniploar voltage switching technique. It is clear from figures that in unipolar voltage technique better performance of output voltage is obtained because the switching frequency is doubled and also less rms ripple content in torque,voltage and current. The performance of separately excited DC motor has been successfully controlled by PID controller with uniploar switching technique and power factor has been improved from 0.63 to 0.93 by using LC filter connected across the diode bridge rectifier. Finally it is concluded that closed loop DC motor is successfully operated Vo -Io in four quadrants.