DC SERVO MOTOR CONTROL SYSTEM

Transcription

1 DC SERVO MOTOR CONTROL SYSTEM MODEL NO:(PEC - 00CE) User Manual Version 2.0 Technical Clarification /Suggestion : / Technical Support Division, Vi Microsystems Pvt. Ltd., Plot No :75,Electronics Estate, Perungudi, Chennai ,INDIA. Ph: , Mail : service@vimicrosystems.com, Web :

2 CONTENTS CHAPTER PAGE NO. A Description of A.1 Hardware Description 1 A.2 Front Panel Diagram 2 A.3 Specifications 3 A.4 Front Panel Identification 3 1 CONTROL SYSTEM COMPONENTS 1.1 Introduction Open Loop and Closed Loop System Components of Closed Loop System DC Servo Controller Transfer Function of the DC Motor Conclusion TRANSFER FUNCTION OF CLOSED LOOP CONTROL SYSTEM 2.1 Introduction Closed Loop Control of the DC Motor with Proportional Speed Controller Closed Loop Transfer Function with Proportional Controller Effect of Load Torque (Disturbance input) with P-Controller Transient Performance and steady state performance Disturbance Rejection Closed Loop System with PI Controller Closed Loop Transfer Function with PI Controller Conclusion Experimental Section 2-15

3 PEC - 00CE A. DESCRIPTION OF : A.1 HARDWARE DESCRIPTION: The DC servo motor speed control system consists of the following. 1. Regulated DC Power supplies to supply to the control circuits and to the power amplifier - the chopper. 2. MOSFET based single quadrant chopper (PWM Power Converter), through which the armature voltage is controlled. 3. Proximity Sensor and Speed feedback circuitry for measurement of speed and closed loop control of the motor. 4. Speed sensor - Proximity sensor is provided to sense the speed 5. Speed controller - Either proportional (P) or Proportional + Integral (PI) Controller can be selected 6. DC Servo motor fixed on a separate frame. A tacho generator disk is fixed at one end of DC Servo motor All the control elements are fixed in a sleek box and the mimic diagram is screen printed on the Front plate. Vi Microsystems Pvt. Ltd., [ 1 ]

4 PEC - 00CE A.2 FRONT PANEL DIAGRAM Vi Microsystems Pvt. Ltd., [ 2 ]

5 PEC - 00CE A.3 SPECIFICATIONS 1. Input to the DC servo motor control unit is 230V ±10%, 50Hz, AC, single phase. 2. DC Power supply to the motor is 12V, by a PWM power converter. 3. DC Motor: 12V, Permanent Magnet DC motor Max. Current : 1.5Amp. Max Torque : 1.5 Kg-cm Max Speed : 1500 rpm at rated voltage (12V) and current (1.5A) 4. One 3½ Digit display of set speed / actual speed: A.4 FRONT PANEL IDENTIFICATION 1. 3½ digit LED Display-1: To display set speed and actual measured speed of motor. 2. Toggle Switch S 1 : To select between set speed and actual measured speed. 3. Toggle switch S 2 : To release the PWM pulse. 4. Switch: Power switch to ON or OFF the power. 5. Potentiometer-1: This is to set the Reference voltage corresponding to the speed in rpm. 6. Connectors: 2 connectors available at the front panel. One is connected to the ground and 2nd is connected to the reference voltage V r to facilitate for measurement of various voltage by a multimeter. 7. Connector point : To take the reading of error voltage at the output of error amplifier. Vi Microsystems Pvt. Ltd., [ 3 ]

6 PEC - 00CE 8. SPDT Switch i) S1-To select between open loop and closed loop system. ii) iii) S2-To select between Optocoupler & Proximity Sensor. S3-To select between Dc-Tachogenerator and other. 9. Connectors: To connect the armature winding of the DC motor Pin `D' Connector. To connect to the sensor of the motor. 11. Patch Connector : This is to patch the two connectors available on the front panel for open loop or closed loop. Vi Microsystems Pvt. Ltd., [ 4 ]

7 CHAPTER - 1 PEC - 00CE 1.1. INTRODUCTION: CONTROL SYSTEM COMPONENTS In general a system is defined as the one which gives an output signal in response to an input signal, as shown in fig.1.1. Fig.1.1. System Systems are classified based on their characteristics, as linear system, Non-linear system, casual system, time-invariant system, memory systems, Memory less systems etc. Here we consider only the class of systems that are linear. A linear system obeys the superposition and homogeneity (scaling) principle. The behaviour of a linear system can be described by linear differential equations, relating the input and the output variables. This gives a mathematical model for the system concerned. When the mathematical model of the system is solved for various input conditions, the result represents the dynamic response of the system. A system can be purely mechanical, comprising mass, spring and dashpot, or it can be purely electrical comprising Resistance, inductances and capacitances or a combination of mechanical and electrical components such as DC/AC motor. All these systems can be described by linear differential equations, making relevant simplifying assumptions. The differential equations describing a linear time invariant system can be reshaped into different forms for the convenience of analysis. For example, the transfer function representation forms a useful model for transient response analysis of single-input-single output linear systems. The transfer function of a linear time invariant system is defined to be the ratio of the Laplace Transform of the output variable to the Laplace transform of the input variable under the assumption that all initial conditions are zero. Vi Microsystems Pvt. Ltd., [ 1-1 ]

8 PEC - 00CE 1.2. OPEN LOOP AND CLOSED LOOP SYSTEM: An open-loop system is represented by the block diagram of fig.1.2. The system is controlled or activated by a single signal at the input for a single input - single output system. There is no provisions within the system for supervision of the output and no mechanism is provided to correct the system behaviour for any lack of proper performance of the system due to change in environment or loading conditions. Fig.1.2. Open-Loop System A closed loop system (feedback system) is represented by the block diagram of fig.1.3. It is driven by two signals (more signals can also used), one the input signal and the other or feedback signal derived from the output of the system. The feedback signal gives the system the capability to act as the self correcting mechanism through the controller. Fig.1.3. Block diagram of a Closed Loop System 1.3. COMPONENTS OF A CLOSED LOOP SYSTEM: The Closed Loop system consists of the following components i) error amplifier, ii) controller iii) power amplifier iv) the feedback element Vi Microsystems Pvt. Ltd., [ 1-2 ]

9 PEC - 00CE i) ERROR AMPLIFIER: Which compares the reference signal V r with the feedback signal Vf The output is a voltage proportional to the difference between the two signals. ii) CONTROLLER: The controller processes the error signal and gives an output voltage signal V C known as the control voltage. This suggests the necessary corrective measures required in the actuating signal V a to be applied to the system. iii) POWER AMPLIFIER: Which takes the input as the control voltage signal V C from the controller and produces the necessary actuating input signal to be applied to the system to achieve the desired output. iv) FEEDBACK: This constitutes the tacho generator and the associated amplifier. The feedback signal V f is a voltage proportional to the output variable of the system DC SERVO CONTROLLER (As a Simple Closed Loop Control System) For the study of the closed loop control system, a DC motor is used as the system to be controlled. The DC motor can be modelled as a linear system, if the magnetic saturation is neglected and the field flux is assumed to be constant. For this purpose, a permanent magnet DC motor is used. Here the flux is produced by the permanent magnets which is constant TRANSFER FUNCTION OF THE DC MOTOR: The DC motor can be represented by the equivalent circuit of fig.1.4. The armature resistance and inductance are represented as lumped parameters as R a and L a. The field current is assumed to be constant. This sets the constant flux in the machine. Vi Microsystems Pvt. Ltd., [ 1-3 ]

10 PEC - 00CE Fig.1.4. Armature Controlled DC Motor R a - Armature resistance (ohms) L a - Armature inductance (Henrys) V a - Voltage applied to the armature (volts) i a - Armature current (Amps.) e b - back emf (volts) i f - field current (amps) - Assumed as constant for wound field motor. - angular speed of the motor in Rad/sec. N - angular speed of the motor in RPM J - Equivalent moment of inertia of the motor and load (kg-m 2 ) B - Equivalent viscous friction coefficient of the motor and the load (Nm/rad/sec) The equations governing the behaviour of the motor are given below. The electromagnetic torque developed by the motor is (1.1) If the flux is assumed to be constant (1.2) Vi Microsystems Pvt. Ltd., [ 1-4 ]

11 PEC - 00CE when (1.3) The back emf developed is (1.4) where k b - back emf constant volts / rad / sec. The differential equation governing the armature circuit is (1.5) The differential equation governing the mechanical system comprising armature and load is (1.6) where T L = Load torque. N.m Taking Laplace transform, assuming zero initial condition for equations (1.2), (1.4), (1.5) and (1.6) (1.7) (1.8) Vi Microsystems Pvt. Ltd., [ 1-5 ]

12 PEC - 00CE (1.9) (1.10) From equation (1.9) (1.11) From equation (1.10) (1.12) Using equations (1.11) and (1.12) the DC motor with constant flux, can be represented by the block diagram of fig.1.5. Fig.1.5 Block Diagram of DC Motor The transfer function between the output variable - the speed (s) and the input variable V a (s) is obtained by setting T L (s) - the load torque to zero. The simplified block diagram is shown in fig.1.6. Vi Microsystems Pvt. Ltd., [ 1-6 ]

13 PEC - 00CE The transfer function Fig.1.6. Block diagram of the DC motor with T L =0 (1.13) where T a = L a /R a - the armature electrical time constnat m = J/B - the mechanical time constant (1.14) Vi Microsystems Pvt. Ltd., [ 1-7 ]

14 PEC - 00CE Generally the armature electrical time constant is much smaller than the mechanical time constant is therefore assuming a =0, by letting L a =0, equation (1.14) can be simplified as (1.15) (1.16) where (1.17) (1.18) Usually R a and B are very small and hence R a B << k b k t (1.19) Vi Microsystems Pvt. Ltd., [ 1-8 ]

15 PEC - 00CE and (1.20) In a similar way one can derive the transfer function between the torque (s) and T L (s) and is given by (1.21) The above transfer functions of the motor are used to study the closed control system. The closed loop transfer function between the reference input and the speed is derived in the following chapters CONCLUSION: The general closed loop control system is described in this chapter. The various control system components and their functions are explained. The transfer function of the DC motor is derived systematically. The DC motor offers itself as a linear system, when certain simplifying assumptions are made. The system is of first order and types zero. Therefore it makes it convenient to study the closed loop control system. Vi Microsystems Pvt. Ltd., [ 1-9 ]

16 CHAPTER INTRODUCTION: TRANSFER FUNCTION OF CLOSED LOOP CONTROL SYSTEM The closed loop transfer function of the system is derived systematically in this chapter. The system / plant to be controlled is the DC motor. The objective is to vary the speed through a reference setting. The simplest control system is represented as shown in fig.2.1 Fig.2.1. Simple Closed Loop Speed Control System The reference speed is compared with the actual speed of the motor sensed through a optical speed sensor. The error is processed through the speed controller. The speed controller sets the required voltage to be applied to the motor. Although the system would achieve the desired speed, it has a drawback. The armature of the motor presents a very low impedence to the applied voltage. Under steady state condition most of the applied voltage is balanced by the back emf and only the remainder drives the armature circuit. However during the transient, there is a mismatch between the applied voltage and the back emf as the speed changes slowly. Therefore excessive current may be drawn from the converter. Vi Microsystems Pvt. Ltd., [ 2-1 ]

17 2.2 Closed Loop Control of the DC motor with proportional speed controller: The closed loop control of the DC motor, using the speed controller is shown in fig.2.1. The system consists of i) An Error Amplifier Which compares the reference speed (set speed/speed command), with the actual speed. The output is a voltage proportional to the differences between the set speed and the actual speed. ii) A Controller- Known as the speed controller. The controller processes the error signal and gives an output, that sets the required voltage to be applied to the motor through the "PWM power controller", to achieve the set speed. The output of the controller is called the control voltage signal. The controller can be of a simple proportional controller or a proportional plus integral controller or a Proportional + Integral controller. iii) A PWM Power Controller Which takes the input as the control voltage signal V c from the controller and produce the required voltage to be applied to the motor. The power amplifier is a chopper whose average output voltage depends on the duty cycle ratio. The duty cycle ratio is adjusted by the control voltage set by the controller. iv) Speed Feedback Circuit This constitutes the speed sensor and the associated amplifier. The speed sensor can be a Proximity sensor, which can produce a voltage proportional to the speed of the motor. The speed signal is processed through a feedback circuit and applied to the error amplifier. In this DC Motor control system, speed is sensed through an Proximity Sensor consisting of a starter disk. Proximity sensor produce a pulses which is converted into analog voltage signal using frequency to voltage converter. The output F / V converter is 0 to 5 Volts which correspondents to rpm. Vi Microsystems Pvt. Ltd., [ 2-2 ]

18 v) DC Servo Motor: A DC Servomotor of 1500 rpm of 0.25 HP rating is used in this experiment. A slotted disk is provided with a optical sensor to sense the speed. The control elements together with the motor can be represented as a feedback control system as shown in the block diagrams of fig.2.2. In the block diagram, the controller, the power amplifier, and the feedback circuit are represented as gains and the motor is represented by its transfer function. The various gains in the block diagram of fig.2.2 is explained below. k p - The gain of the proportional controller. The error signal when it passed through the controller is amplified by k p. The gain k p can be varied to achieve optimum performance. The steady state error can be reduced by increasing the gain k p. If a proportional plus an integral (P.I) controller is used, it can be replaced by its transfer function, given by (2.1) G - The gain of the power amplifier. It is defined as (2.2) where, V pst - Peak value of the ramp used for pwm control. For example, If V dc = 24V, and V pst = 10 V, then k - The speed feedback gain. This gain translates the speed signal into a voltage signal whose level is compatible with speed reference signal. It is defined as Vi Microsystems Pvt. Ltd., [ 2-3 ]

19 (2.3) where V r - Reference voltage level for rated speed - 2 N/60 radians per sec. N - rated speed in rpm The motor is represented by its transfer function (2.4) where k m = 1 / k b = motor gain constant k b = Back emf constant = Effective motor time constant Vi Microsystems Pvt. Ltd., [ 2-4 ]

20 Fig.2.2.Transfer function model of the speed control system with proportional speed controller 2.3. Closed Loop Transfer function with proportional controller: Fig.2.3. Feedback Control System with proportional controller In order to derive the closed loop transfer function between the speed (s) and the reference input V r (s), the block diagram of fig.2.2 can be reduced as shown in fig.2.3, in which the gain of the controller k p and that of the power amplifier G are combined into a single gain k A = k p G. The disturbance input, the load torque, T L is set to zero. The closed loop transfer function is given by (2.5) (2.6) Vi Microsystems Pvt. Ltd., [ 2-5 ]

21 The closed loop transfer function is same as that of a first order type zero system. The steady state and transient performance of the system can be easily studied from the transfer function of equation (2.6) Effect of Load Torque (Disturbance input) with P-Controller: When the motor is running at a steady speed, the application of load would reduce the speed. In a closed loop control system, effect of load torque on the change in speed will be less. This is because the change in speed, due to load torque, will either increase or decrease the error. The controller would then respond to the new error signal and set a new control voltage V C which in turn, change the output voltage of the power amplifier. The motor speed will therefore track the reference speed. The closed loop transfer function between the speed and the load torque can be derived by setting the reference input to zero. The block diagram fig.2.2 can then be reduced as shown in fig.2.4. Fig.2.4. Transfer function model for deriving (s) / T L (s) (2.7) (2.8) Vi Microsystems Pvt. Ltd., [ 2-6 ]

22 2.5 Transient and Steady State Performance: i) Transient Performance: For a step input of V r (t) = V R, the speed (s) from equation (6) can be obtained as (2.9) Taking Inverse Laplace Transform, (2.10) (2.11) (2.12) Fig.2.5. Speed Response for a step input of Reference Signal Vi Microsystems Pvt. Ltd., [ 2-7 ]

23 Equation (10) shows that the speed increases slowly depending on the time constant 1/a, as shown in fig.2.5. The steady state speed is proportional to V R, the set reference (command) speed. ii) Steady State Performance: From the transfer function of equation (2.6), the steady state error can be deduced. Under steady state condition, s=0, and the steady state speed is given by (2.13) Equation (2.13) shows that actual speed is less than the command value. The steady error is given by (2.14) The quantity is defined as position error constant K p (2.15) Vi Microsystems Pvt. Ltd., [ 2-8 ]

24 Therefore (2.16) Equation (2.16) shows that the steady state error can be reduced by increasing the gain k A = k P G i.e. by increasing the gain of the proportional controller. 2.6 Disturbance Rejection: From the transfer function of equation (2.8) for a step input of load torque T L, (2.17) The steady state speed is given by (2.18) Equation (2.18) indicates that the steady state speed will be less by an amount given by equation (2.18) when compared to the no load steady state speed given by equation (2.13). Equation (2.18) also indicates that the change in speed can be reduced by increasing the gain k A, i.e. by increasing the proportional gain of the controller, k P as K A = k P G Determination of Motor Time Constant: The motor transfer function, from equation (4) is Vi Microsystems Pvt. Ltd., [ 2-9 ]

25 where k m - motor gain constant - motor time constant (2.19) where J - moment of inertia of the motor R a - armature resistance k b - motor back emf constant = 1/k m k t - motor torque constant = k b when the speed is expressed in radians per sec. The motor gain constant k m can be obtaianed by measuring the motor back emf constant, k b. The measurement of k b is explained in the experimental work 1. Armature resistance of the motor can be measured using a multimeter. For small motor, measurement of moment of inertia is little difficult and is therefore obtained from the manufacturer. Knowing the value of J, the motor time constant can be calculated as given by equation (2.19). From the closed loop transfer function of equation (2.6) the effective time constant is given by (2.20) Knowing the values of, k A, k m and k, e can be calculated. Hence the transient response of the motor for a step input in reference can be obtained from equation (2.20). 2.7 CLOSED LOOP SYSTEM WITH PI CONTROLLER: The proportional controller can work only with a certain steady state error. The error can be reduced by increasing the gain of the proportional controller. However, the gain is increased the performance of closed loop system becomes more oscillatory and takes longer time to reach the steady state. The steady state error can be reduced by using a PI controller. The equation describing the PI controller is Vi Microsystems Pvt. Ltd., [ 2-10 ]

26 (2.21) (2.22) here K p - Proportional gain of the PI controller T I - Integral time or reset time e(t) - Error signal Equation (2.22) gives the PI controller transfer function From equation (2.21) it is seen that the PI controller has two adjustable or tuning parameters k p and T I. The integral or reset action of the PI controller removes the steady state error. However, the integral mode of control has a considerable destabilising effect which in most of the situations can be compensated by adjusting the gain k p, 2.8 CLOSED LOOP TRANSFER FUNCTION WITH PI CONTROLLER: Figure 2.6 below shows the block diagram of the speed control loop with PI controller Fig.2.6. Block Diagram of the DC servomotor with PI Controller From the block diagram, setting T L =0, we can derive the transfer function for speed as follows. (2.24) Vi Microsystems Pvt. Ltd., [ 2-11 ]

27 (2.23) Under steady state condition s=0, (2.25) Equation (2.25) shows that the steady state error with PI controller is zero. Vi Microsystems Pvt. Ltd., [ 2-12 ]

28 2.9 CONCLUSION: The transfer function of the closed loop system with P, PI controllers are derived systematically. It is shown that the steady state error depends on the proportional gain kp. With PI controller the steady state error is Zero. The dynamic response of the system for a step input will be faster with P controller. The transfer function of the closed loop system with the disturbance input ( In this case the load torque) is derived. Experimental studies on the control system both on open loop and closed loop are described in the following chapters. Vi Microsystems Pvt. Ltd., [ 2-13 ]

29 Vi Microsystems Pvt. Ltd., [ 2-14 ]

30 EXPERIMENTAL SECTION EXPERIMENT - 1 AIM : Study of open loop response using P Controller. APPARATUS REQUIRED i. PEC - 00CE Trainer Kit. ii. Motor setup. iii. Multimeter. PROCEDURE 1. Connections are made as per the connection diagram shown above. 2. Keep the Open / Closed loop switch in open loop position. 3. Do not connect the feed back circuit. 4. Vary the input speed and note down the values as per the tabulation. 5. Vary the speed to different positions and tabulate the readings. TABULATION S. No. SP(V) PV (V) N (rpm) RESULT Thus the open loop response using P controller was studied. Vi Microsystems Pvt. Ltd., [ 2-15 ]

31 Vi Microsystems Pvt. Ltd., [ 2-16 ]

32 EXPERIMENT - 2 AIM Study of Closed loop response using PI Controller. APPARATUS REQUIRED i. PEC - 00CE Trainer Kit. ii. Motor setup. iii. Multimeter. PROCEDURE 1. Connections are made as per the connection diagram shown above. 2. Keep the Open / Closed loop switch in closed loop position. 3. Connect the feed back circuit. 4. Vary the input speed and note down the values as per the tabulation. 5. Vary the speed to different positions and tabulate the readings. TABULATION S. No. SP(V) PV(V) N (rpm) RESULT Thus the closed loop response using PI controller was studied. Vi Microsystems Pvt. Ltd., [ 2-17 ]

33 EXPERIMENT - 3 AIM To study the characteristics of armature voltage Vs set speed in open loop and closed loop system. APPARATUS REQUIRED i. PEC - 00CE Trainer Kit. ii. Motor setup. iii. Multimeter. PROCEDURE 1. Interface the DC servo motor in to the PEC00-CE unit. 2. Initially, Pulse / Release switch should be in OFF condition. 3. Connect the multimeter in (Volt - DC) mode across A - AA 4. Release the pulse, set the speed of ( ) RPM. 5. Measure the armature voltage of the motor across A - AA in open loop / closed loop mode. 6. Note down the armature voltage for different set speed. TABULATION Set speed in (RPM) Armature Voltage (Open Loop) Armature Voltage (Closed Loop) RESULT Thus the characteristics of armature voltage Vs set speed in open loop and closed loop system was studied. Vi Microsystems Pvt. Ltd., [ 2-18 ]

34 EXPERIMENT - 4 AIM To study the characteristics of speed sensor output Vs set speed in open loop and closed loop system. APPARATUS REQUIRED i. PEC - 00CE Trainer Kit. ii. Motor setup. iii. Multimeter. PROCEDURE 1. Interface the DC servo motor in to the PEC00-CE unit. 2. Initially, Pulse / Release switch should be in OFF condition. 3. Connect the multimeter in (Frequency) mode across F - GND 4. Release the pulse, set the speed of ( ) RPM. 5. Measure the speed sensor of the motor. Across F - GND in open loop / closed loop mode. 6. Note down the speed sensor output for different set speed. TABULATION Set speed in (RPM) Frequency Output (Open Loop) Frequency Output (Closed Loop) RESULT Thus the characteristics of frequency output Vs set speed in open loop and closed loop system was studied. Vi Microsystems Pvt. Ltd., [ 2-19 ]

35 EXPERIMENT - 5 AIM To study the characteristics of signal conditioner output Vs set speed in open loop and closed loop system. APPARATUS REQUIRED i. PEC - 00CE Trainer Kit. ii. Motor setup. iii. Multimeter. PROCEDURE 1. Interface the DC servo motor in to the PEC00-CE unit. 2. Initially, Pulse / Release switch should be in OFF condition. 3. Connect the multimeter in (Volt - DC) mode across PV- GND 4. Release the pulse, set the speed of ( ) RPM. 5. Measure the speed sensor of the motor. Across PV- GND in open loop / closed loop mode. 6. Note down the signal conditioner output for different set speed. TABULATION Set speed in (RPM) Signal Conditioner Output (Open Loop) Signal Conditioner Output (Closed Loop) RESULT Thus the characteristics of signal conditioner output Vs set speed in open loop and closed loop system was studied. Vi Microsystems Pvt. Ltd., [ 2-20 ]