Speed Control of DC Motor Drives

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```							S-17.2030 Electromechanics and Electric Drives

Laboratory Exercise No. 2

Speed Control of DC Motor Drives

Speed Control of DC Motor Drives
This laboratory exercise deals with the speed and current control of a separately excited DC motor. The laboratory experiments are carried out using an industrial DC motor drive, which is based on a four-quadrant thyristor rectifier and is suitable for motoring and regenerative braking operation as well as for speed reversals.

Cascade Control of Speed and Current
The control structure is based on cascade1 control of rotational speed and armature current. The principle of cascade speed control is illustrated in Fig. 1. The control system consists of an outer control loop for rotational speed and an inner control loop for current. The output of the speed controller is an input (current reference) to the current controller. The block diagram of the control system is shown in Fig. 2. The current and voltage limits are not included in Fig. 2 – when these limits are active, they cause nonlinearity in the control system. The two controllers can usually be designed independently, since the mechanical dynamics of the system is usually much slower than the dynamics of the armature circuit. Controllers and Controller Design In both control loops, one time constant of the plant is dominating: the armature time constant τ a in the inner loop, and the electromechanical time constant τ m in the outer loop. In such cases, it is usual to utilize PI controllers. The transfer function of the PI controller is
⎛ 1 ⎞ G ( s ) = kp ⎜1 + ⎟ sτ i ⎠ ⎝

(1)

where k p is the proportional gain and τ i is the integration time constant. In general terms, the proportional (P) controller is responsible for dynamic response, and the integral (I) controller

Figure 1: Cascade speed control.

1

Cascade = a series of stages in the processing chain of an electrical signal, where each operates the next in turn.

2

Figure 2: Block diagram of cascade control. The transfer functions are denoted by following symbols: speed measurement Gmω(s), armature current measurement Gmi(s), speed controller Gn(s), current controller Gi(s) and rectifier GT(s). is responsible for steady-state accuracy. Ideally, the I-controller removes any steady-state error. It is to be noted that the P-controller gain also affects the I-controller gain if the PI controller parameters are defined as in Eq. (1). When designing the controller, various criteria can be used for minimizing the error between the reference and actual values of the variable to be controlled. The design of DC motor controllers is often based on two alternative design rules: optimum modulus criterion and optimum symmetry criterion. The modulus criterion is based on the system behavior when the reference value is changed. The goal is that the measured value follows the reference value as accurately as possible. The modulus criterion is suitable for control loops where no variation of disturbance quantities is present. The current control loop is typically of this type. The symmetry criterion is based on the system behavior when a disturbance quantity changes. The goal is that, after a disturbance, the output quantity is restored to its original value as soon as possible. In addition, it is required that there are pure integrators or very large time constants in the system. The speed control loop is typically designed by means of the symmetry criterion since the speed controller shall restore the speed after disturbances caused by changes in the load torque. It should be noted, however, that controller parameters are often calculated on the basis of roughly estimated plant data. The control loops are not ideal, and both the characteristics of mechanical loads and requirements on control system performance vary a great deal in different applications. Therefore, the controller parameters obtained by means of standard design rules can be used only as broad indicators of the values to be employed. In particular, the speed controller parameters must often be adjusted experimentally. The following quantities are needed for using the design rules mentioned above: • the largest open-loop time constant τ s • the sum of the other open-loop time constants τ Σ • the static open-loop gain k tot . 3

The modulus criterion is typically used if τ s < 4τ Σ . The PI controller parameters are defined as

τi = τs
kp = 2ktot τ Σ

(2)

τs

(3)

The symmetry criterion is typically used if τ s >> τ Σ . The PI controller parameters are defined

τi = 4 τΣ
kp = 2ktot τ Σ

(4)

τs

(5)

When the symmetry criterion is employed, the reference value must be low-pass filtered using the time constant τ i , i.e., by using the transfer function 1/(1 + sτ i ) .
Current Control Loop

When the current control loop is designed, it can be assumed that the rotor does not rotate. This assumption can be made because the time constants in the current control loop are usually much smaller than the electromechanical time constant, and the feedback caused by the induced motional voltage can be ignored. Therefore, the current control loop shown in Fig. 3 can be used for controller design. If the converter is a DC-DC chopper (whose switching frequency is high), the converter delay and the time constants of the current measurement are usually very small as compared with the armature time constant τ a of the motor. In those cases, the current controller design can be based on canceling the motor pole and choosing an appropriate bandwidth of the current control loop, as described in the lectures. When a thyristor rectifier is used, the delay of the converter is relatively long, and the modulus criterion is commonly applied to the current controller design. Usually, the largest time constant is τ s = τ a . The term τ Σ is the sum of all other open-loop time constants (i.e., time constants in the forward branch and the possible time constants in the feedback branch Gmi ). The static gain k tot is the product of the open-loop gains.

Figure 3: Armature current control loop based on a PI controller. Current controller gain is kp and its time constant is τ i .
4

The rules mentioned above are valid if the current of the converter is continuous. Discontinuous-current operation causes problems for the control. Therefore, a choke (inductance) is added to the armature circuit in many cases; this inductance can be included in the armature inductance La of the model. The inductance is determined so that the steady-state current does not become discontinuous in any circumstances. Usually, the choke is more important for avoiding current discontinuity than it is for smoothing the armature voltage of the motor.
Speed Control Loop

For designing the speed control loop, the current control loop can be modeled by an equivalent transfer function. Omitting the negative feedback caused by the induced motional voltage (back-emf), the speed control loop shown in Fig. 4 is obtained. In this laboratory exercise, the design of the speed control loop is not analyzed further since it often depends on the mechanical load to be driven by the motor. However, an empirical design method will be used in the laboratory.

Figure 4: Speed control loop based on a PI controller. Speed controller gain is kpn and its time constant is τin. The current control loop is modeled by an equivalent transfer function (gain ke and time constant is τe).

A four-quadrant drive allows the DC motor to be driven in both rotational directions both in the motoring mode and in the regenerative braking mode. For four-quadrant operation, the power electronics must allow the direction of the armature current to be changed2. Figure 5
Bridge 1 I d1 a b c I d2 a b c Bridge 2

Figure 5: Four-quadrant drive based on antiparallel six-pulse thyristor bridges.
It would also be possible to change the direction of the field-winding current, but this alternative causes a considerable delay since the time constant of the field winding is long.
2

5

illustrates the four-quadrant drive based on two antiparallel six-pulse thyristor bridges. It is assumed that only one of the bridges is operated at a time (i.e., no circulating-current operation). In Fig. 6, a speed reversal is illustrated in the DC current-voltage (I-U plane). At first, the operation point is A. Bridge 1 is in rectifying operation (control angle α1 ) and the motor speed is n > 0. No gate trigger pulses are given to Bridge 2. For the speed reversal, the current controller reverses the current direction (corresponding to a fast transition from point A to point C), after which it keeps the current constant (corresponding a much slower change from point C to point E when the speed is decelerated and then accelerated in the opposite direction.). When the speed reversal command is obtained, the control angle of Bridge 1 is increased, and the current starts to decrease. In point B (control angle α 2 ), the current equals zero. The zero current is observed, and the gate trigger pulses of Bridge 1 are suppressed. After a short pause (dead time) needed for avoiding a short circuit between the bridges, gate trigger pulses are ′ given to Bridge 2. Initially, the control angle has such a large value α7 that the DC voltage of Bridge 2 is higher than the induced motional voltage of the motor, and no current flows. As the control angle is reduced, the DC voltage equals the induced motional voltage of the motor ′ at α6 . A further reduction of the control angle causes a current in the direction opposite to the original one. The DC machine works as a generator (braking the mechanical load). As the ′ ′ control angle is changed from α6 to α5 , the absolute value of the current increases from zero to the reference value, which is obtained at operating point C. Braking at constant current results in moving from point C to point D. From now on, Bridge 2 works as a rectifier. A further reduction of the control angle, keeping the current constant as
U

α′ 7 α′ 6 α′ 5
C

Bridge 2 (I < 0)

Bridge 1 (I > 0)

B Inverter operation n>0

A

α1 α2

α′ 4
D

Rectifier operation

Control angle of Bridge 1 increases

n>0

α3
I

α′ 3
Control angle of Bridge 2 increases

Rectifier operation

n<0

Inverter operation

α4
n<0

α′ 2
′ α1 E

α5 α6 α7

Figure 6: Operation of four-quadrant drive in the four quadrants of DC current-voltage plane.

6

the motor speed changes, finally leads to operating point E. Now the DC machine works as a motor at the original speed, but in the opposite direction, and is driven by Bridge 2 in rectifier operation.

Laboratory Set-Up
The electric machines to be used in the laboratory are illustrated in Fig. 7. The DC machine (DMP 112-4L) is connected to an induction machine (HXR M2AA 160 M4), which is used to produce the load torque. There is also a flywheel for increasing the moment of inertia of the system, and a torque transducer (HBM TN30FNA) is used for torque measurement. The converters, and some control and measuring equipment, have been installed in a cabinet as shown in Fig. 8. The DC machine is fed from a four-quadrant rectifier (DCS 402.0075), and the induction machine is connected to a four-quadrant frequency converter (ACS 611-0025-5). Both converters are controlled from a PC by using Windows-based software. Some instructions for using the software are given in Appendix 1.

Induction machine

Flywheel

DC machine

Torque transducer

Figure 7: Rotating machine setup for laboratory exercises.

7

Measurement bay

Switch bay

AC80

Frequency converter bay

Rectifier bay

ACS611 DCS402

Figure 8: Converter, control and measurement setup for laboratory exercises.

8

Data of the Laboratory Equipment
Separately Excited DC Motor DMP 112-4L

Nominal power Nominal rotational speed Nominal armature voltage Nominal armature current Flux factor at nominal field current Armature resistance (at 20°C) Armature inductance Total moment of inertia (whole system)

PN = 11 kW nN = 1 500 rpm UaN = 345 V IaN = 39 A kφ = 1,895 Vs/rad Ra = 0,8706 Ω La = 15,7 mH J = 0,791 kgm2

Transfer Functions of the DC Motor Drive

Six-pulse thyristor rectifier and its gate trigger circuit
GT ( s ) ≈ kT 1 + s τT
kT = 1

τ T = 1, 67 ms

(6)

Armature current measurement and filtering Gmi ( s ) ≈ k mi 1 + s τ mi k mi = 1

τ mi = 3 ms

(7)

Angular speed measurement and filtering
Gmω ( s ) ≈ k mω (1 + s τ mω1 ) (1 + s τ mω 2 ) (1 + s τ mω 3 )

(8)

kmω

60 = 2π

τ mω1 = 0,6 ms τ mω 2 = 0,8 ms τ mω 3 = 1,67 ms

Current controller and its parameter limits
⎛ 1 ⎞ Gi ( s ) = k p ⎜ 1 + ⎟ s τi ⎠ ⎝ k p = 0 … 10

τ i = 0 … 1000 ms

(9)

Speed controller and its parameter limits
⎛ 1 ⎞ Gn ( s ) = kpn ⎜ 1 + ⎟ s τ in ⎠ ⎝ k pn = 0 … 15

τ in = 0 … 6553 ms

(10)

9

Pre-Report
Before the laboratory experiments, each student delivers a pre-report by answering the questions 1…8 below. The answers should be given to the assistant about one week before the laboratory measurements. The assistant may send some feedback or ask for corrections or improvements to the answers before the laboratory measurements. This will be done by sending an e-mail to the student.
Questions
1. Explain why cascade control is used for speed and current control. How is the armature current limited to the allowed maximum value when cascade control is used? 2. Design the armature current controller of the laboratory setup using the modulus criterion (i.e., calculate the controller parameters k p and τ i ). 3. Plot the open-loop Bode diagram of the current control loop, for the current controller parameter values calculated above, either manually or by using MATLAB. A tool for MATLAB plotting is described in Appendix 2. 4. Evaluate the gain and phase margins from the Bode diagram. 5. Is the current control going to be oscillatory or not? 6. Evaluate the electromechanical time constant τ m of the laboratory setup. 7. The rotational speed of the laboratory setup is changed from n = +1 500 rpm to n = −1 500 rpm . The armature current is kept at the nominal value ia = −39 A during the speed reversal. Calculate the time needed for reversing the speed when the load torque is TL ≈ 0 . 8. How do the rotational speed and the armature voltage vary during the speed reversal described above? What is the influence of the armature resistance Ra ? Draw the rotational speed and the armature voltage as a function of time. (The machine is assumed to run at no load before the speed reversal and after it.)

10

Laboratory Measurements
First, the group will become acquainted with the laboratory setup under the guidance of the assistant. Then, the following measurements are carried out: 1. Speed reversals are investigated. The current controller parameters calculated in the prereport are used. The speed controller parameters are set to the following values: proportional gain KP = 3 and integration time constant TI = 100 ms. An oscilloscope is used for registering the rotational speed, armature current, armature voltage and shaft torque. The motor is first running at n = −1 500 1/min , and a speed reversal command to n = +1 500 1/min is given. When the speed has achieved the value n = +1 500 1/min , a new speed reversal command to n = −1 500 1/min is given.
Question: Explain how the curves are related to the quadrants of the I -U plane shown in Fig. 6. When is the power flowing from the electric grid to the machine and vice versa? Why does the polarity of the armature voltage change before the speed reaches zero value? Why does the torque change stepwise at zero speed?

2. The influence of field weakening on the starting is investigated. The field weakening is used above the rotational speed n = 1 500 1/min , and the motor is started to the reference value n = 3 000 1/min .
Question: What happens during the starting, and how do the results correspond to the theory?

3. The influence of the current controller parameters is investigated. The motor is started to n = 1 500 1/min , and the armature current and the rotational speed are registered. Various parameter values are used in order to find out whether the current control can be improved.
Question: What happens if pure P-control is used? What is the influence of the proportional gain and the integration time constant on the accuracy, quickness and oscillatory behavior of the control? How does the nonlinearity of the control system affect the results? Is the modulus criterion a suitable design rule for this case?

4. The influence of a step change in the load torque is investigated. First, the parameter values calculated in the pre-report are used in the current controller. The speed reference is set to n = 1 500 1/min . A load torque TL , whose value is 50 % of the nominal torque of the motor, is switched on and off, and the armature current and the rotational speed are registered. The load torque is produced by an induction machine fed by a frequency converter. The proportional gain and the integration time constant of the speed controller are varied, and their influence on the quickness and steady-state error of the control is studied as follows: a) Pure P-control is applied to the speed controller by setting the integration time constant TI = 0. Various values of the proportional gain KP are experimented with (at least 3 values).

11

b) PI-control is applied to the speed controller. Various values of the proportional gain KP and the integration time constant TI are experimented with. (You can start with the value KP = 3 and use three values of TI for each value of KP.)
Question: How do the proportional gain and the integration time constant affect the accuracy, quickness and oscillatory behavior of the control? Which parameter values should be chosen?

Report
The group writes a (joint) report after the laboratory measurements, documenting the substantial measurement results and giving answers to the questions asked above. Write also a short comment on the learning result from this laboratory exercise. What was the main outcome? Could something be improved? There are no formal requirements on the report. The assistant may send some feedback, or ask for corrections or improvements to the report before it is accepted.

12

Appendix 1: Some Instructions for Using the Electric Drives in Laboratory Exercise 2
The laboratory setup consists of a DC drive (four-quadrant rectifier and DC machine) and an AC drive (four-quadrant frequency converter and induction machine). The operation of both drives can be monitored and controlled from a PC. The computer programs available are:
• •

DriveWindow Light 2 for the DC drive, DriveWindow 2 for the AC drive.

The user interfaces of both programs are rather similar. The electric drive to be controlled must be switched on before starting the computer program in question. Fig. 9 shows the display of the DriveWindow Light 2 program for the DC drive. This window can be used for

Figure 9: Display of the DriveWindow Light 2 program (DC drive).

13

Figure 10: Drive control panel of the DriveWindow Light 2 program. controlling and monitoring the operation of the drive, changing its parameters, reading the error file etc. In order to control the operation of the DC drive from the PC, the converter must first be in the online mode (default). The drive is operated using the drive control panel shown in Fig. 10. The local control mode is chosen in the program by clicking on the toolbar icon:

The icon becomes lighter when the PC has taken over the control of the drive. The DC drive is started by first closing the main contactor by clicking on the toolbar icon

in the drive control panel. Then the start command can be given by clicking on the toolbar icon:

The drive is stopped by clicking on the toolbar icon:

The main contactor of the DC drive is opened by clicking on the toolbar icon:

The reference value of the rotational speed is changed by first clicking on the numerical field

(on the left), then typing the value, and finally pressing the Enter button of the keyboard or clicking on the toolbar icon:

14

The arrow icons (on the right-hand side) can also be used for decreasing or increasing the reference value. The rotational direction of the DC drive is reversed by giving a negative value to the speed reference. Drive parameters (such as PI controller parameters) can be found by double-clicking the corresponding parameter group in the parameter browser, as shown in Fig. 9 (for the speed controller parameters). The parameter values can be changed by double-clicking on the parameter in question in the parameter list:

The new parameter value can be typed in the numerical field, finally pressing the Enter button of the keyboard. The DriveWindow 2 program is used for monitoring and controlling the AC drive. When the program is started, the default OPC Server software module is first accepted by clicking the OK button in the window shown in Fig. 11. The upper left corner of the DriveWindow 2 display is shown in Fig. 12. The four-quadrant frequency converter consists of two IGBT bridges (grid-side bridge and motor-side bridge), and the program considers them to be separate devices. When several devices are controlled by the program, one of them can be activated. The ACS 611 drive should be selected in the browse tree pane (see Fig. 12). The AC drive is operated using the drive control panel located at the bottom of the display. When the drive is configured for torque control, the panel looks like the one in Fig. 13. The local control mode is chosen in the program by clicking on the corresponding toolbar icon. To start the AC drive, it is sufficient to give the start command (without closing any main contactor). The drive control panel also has toolbar icons for the rotational direction of the AC drive.

Figure 11: Accepting the default OPC Server for the DriveWindow 2 program (AC drive).

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Figure 12: Display of the DriveWindow 2 program (upper lefrt corner).

Figure 13: Drive control panel of the DriveWindow 2 program.

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Appendix 2: Some Instructions for Using the MATLAB Tool Available
A simple MATLAB application can be downloaded from the WWW pages of the course. They are intended to make it easier to plot the Bode diagrams needed for the report. The application can be used at least in Windows systems with MATLAB, Control System Toolbox and Symbolic Math Toolbox, like for example the computers in the PC classes of the Faculty. There is no need to specially install the application. It is sufficient that the files have been copied to the work directory. The resulting figures can be saved in the FIG format, which can be opened by MATLAB. The figures can also be transformed to many other formats by choosing the Export command in MATLAB.

Bode Diagrams: boded
The application boded plots a Bode diagram and evaluates the gain margin and the phase margin for a series coupling of blocks (i.e., for a product of transfer functions). The transfer functions are fed to the application separately, and they can also be switched on or off individually. In order to use the application, the files boded.m and boded.fig must be downloaded and copied to the work directory. The application is started by writing the command boded on the MATLAB command line. The address for downloading the files is:

The transfer functions are fed in polynomial form so that the numerator and the denominator are separated by a slash (/). The Laplace variable is denoted by the letter s. The slash cannot be used as the division operator in the usual way because it is the separator, but other operators work as usual. Therefore, 1/s+1 is interpreted like 1/(s+1). The separator slash is always required even if the denominator is actually not needed, as illustrated in the following example.
Example: The feedback system in Fig. 14 consists of first- and second-order transfer functions and gain blocks. The gain margin and the phase margin of the system are obtained from the open-loop transfer function of the system, which can be fed to the application boded as shown in Fig. 15. The resulting Bode diagram, together with the gain margin and the phase margin, is shown in Fig. 16.

17

+–

10 s 2 + 100 s + 106

1500

1 10−4 s + 1

Figure 14: The example block diagram.

Figure 15: User interface of the boded application (Aktiiviset lohkot = Active blocks, Lohkojen siirtofuntiot = Block transfer functions).

Figure 16: Example Bode diagram with gain and phase margins. 18

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