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日期：2024-12-12 09:28

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Control of an Electric Drive in Simulink

Introduction

Simulink is a dynamic simulation environment of Matlab, in which complex

physical systems can be modelled through differential equations and their

behaviour can be analysed. An electric drive can also be modelled in Simulink

through the equations governing its operation. However, as the electric drive

consists of different subsystems, such as an electric motor, a power electronic

converter, a mechanical load, each of these subsystems can be modelled

separately before combining them into a single model to emulate the behaviour

of a complete electric drive.

Fig. 1 shows the basic structure of an electric drive. The type of the motor

determines the configuration of the power converter, the number of sensors,

and the control algorithm. For example, if the motor is a dc machine, then the

power converter would be a half-bridge (two-quadrant drive) or a full H-bridge

(four-quadrant drive), there will be one current sensor and one dc-link voltage

sensor. The position/speed of the rotor is acquired through a shaft-mounted

position sensor.

Fig. 1 A typical electric drive

Using the blocks and tools offered by Simulink, the physical behaviour of the

blocks shown in Fig. 1 can be emulated. The scheme of Fig. 1 in terms of Simulink

blocks is shown in Fig. 2. The highlighted areas represent different subsystems

of Fig. 1. The area labelled ‘Display’ shows a scope on which different quantities

can be plotted as a function of time to visualize the time evolution of different

variables. The subsystems are briefly described below.

Motor Load Power

Converter

Control

algorithm

User set

points

Sensors

Conversion

to digital

domainControl of an Electric Drive in Simulink

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Fig. 2 Simulink block diagram of a dc motor drive

The motor

In Fig. 2, a dc motor is shown as the actuator, but it can also be any other

electrical machine, such as a three-phase permanent magnet synchronous

motor. The details of the ‘Motor’ subsystem are shown in Fig. 3. As observed,

they are the electrical and mechanical state equations of a separately excited

constant flux dc motor. The applied armature voltage is the electrical actuation

signal and the torque produced by the machine acts as the mechanical actuation

signal. The load torque is shown as a separate input, which can be either a

constant, a step function or any other load torque profile depending on the

application being analysed. The outputs of the dc motor block are the armature

current and the rotor mechanical position. The user can choose to have the

mechanical speed as another output.

The parameters of the dc motor can be set/changed by double clicking on the

block and just inputting the new values in the dialog box. Fig. 4 shows the dialog Control of an Electric Drive in Simulink

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box for the dc motor parameters. Since all the parameters shown in Fig. 4 are in

their standard SI units, the inputs (voltage and load torque) and the outputs of

(current and angle) of the motor block should also be interpreted in their

standard SI units.

Fig. 3 Simulink block implementation of the state equations of a constant flux dc motor

Fig. 4 Parameter dialog box for a constant flux dc motor Control of an Electric Drive in Simulink

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The power converter

For a dc motor drive, the power electronic converter can consist of a half-bridge

or a full H-bridge depending on whether the motor is required to rotate in one

direction only (half-bridge) or in both directions (full-bridge). To preserve

generality of the implemented drive system, a full H-bridge is simulated to give

maximum flexibility to the user. The power converter block also includes a pulse

width modulation (PWM) scheme that converts the duty cycles for the two legs

of the H-bridge (da and db) into pulses of varying widths. The dc-link voltage is

defined as a constant input decided by the user. The modulator block’s

parameter dialog box is shown in Fig. 5, which requires the user to input the

switching frequency in Hz. The details of the modulator block are shown in Fig. 6.

Fig. 5 Parameter dialog box for the modulator

Fig. 6 H-bridge modulation scheme Control of an Electric Drive in Simulink

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Sensors and ADCs

In electric drives, voltage, current and position sensors are used to measure the

dc-link voltage, the load currents and the shaft position respectively. Since these

quantities are in the analog domain while the control, in modern electric drives,

is in digital domain, an analog to digital conversion is necessary. Analog to digital

converters (ADCs) do this conversion and provide the controller with

measurements at a fixed sampling frequency (decided by the drive designer).

The sensors measuring the voltage and current also introduce noise on the

measurements, which is normally a zero-mean, constant variance white noise.

In addition to the white noise on the analog signal, the noise due to the

quantization effect of the ADCs impacts the measurement in the digital domain

further. All these effects are simulated inside the ‘Sensing subsystem’ of Fig. 2

as detailed in Fig. 7.

For the shaft position measurement, incremental or absolute position sensors

are normally used in electric drives. The resolution of the position signal

available to the controller depends on the number of pulses per revolution of

the incremental encoder or the bit resolution of the absolute encoder. The fixed

resolution of the position sensors introduces a quantization noise on the

position signal. This quantization noise is emulated in the simulation for an

incremental encoder.

Fig. 7 Sensor subsystem structure Control of an Electric Drive in Simulink

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It can be noticed from Fig. 7 that there is only one input current ia but two other

currents ib and ic are included to allow the user to simulate a three-phase

system. For a three-phase machine, the currents ib and ic must also be added as

inputs to the block rather than constants as shown in Fig. 7.

Fig. 8 shows the parameter dialog box for the sensing subsystem. The range of

the current and voltage measurement must be set such that this range is not

exceeded at any time. The resolution of the ADCs is usually 12-bit in commercial

electric drives but can also be 14 to 16-bit in case of high-end drives. The pulseper-revolution

(ppr) value for incremental encoders starts from as low as 12ppr

for very low-cost encoders and can be in excess of 10,000ppr for devices used

for precision applications.

Fig. 8 Sensor subsystem parameters

Control algorithm

The control algorithm for the electric drives is normally executed on a digital

signal processor (DSP) at a fixed control execution frequency, usually at the

switching frequency of the power converter. The control routines are normally

written in a high-level language such as C. The block labelled ‘Control’ in Fig. 2

emulates the behaviour of a DSP that samples the input data at a fixed frequency

and outputs the duty cycles for the power converter after one execution cycle.

The details of the block are shown in Fig. 9. Control of an Electric Drive in Simulink

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This block consists of a Matlab s-function. S-functions (system-functions)

provide a powerful mechanism for extending the capabilities of the Simulink

environment. An S-function is a computer language description of a Simulink

block written in MATLAB, C, C++, or Fortran. The block labelled ‘simple_control’

is like any other Simulink block but its behaviour can be fully controlled by the

user by modifying the program that describes it.

Fig. 9 Details of the block labelled ‘Control’ in Fig. 2

In electric drives, the control algorithm is executed on a DSP that can be

programmed in C, BASIC and assembly languages with C being the most

commonly used language. The s-function feature of Simulink is therefore used

to program the functionality of the block ‘simple_control’ in C.

The program describing an s-function block must follow a certain structure and

must contain some pre-defined functions and definitions. To program the

s-function block properly, it is recommended to start with an example code such

as ‘sfuntmpl_doc.c’ or ‘sfuntmpl_basic.c’ available from Matlab and modify

according to the requirements of the application. The available templates are

for a level 2 s-function.

The number of inputs, outputs and parameters of the s-function block are

defined inside the C program and they must match the inputs and outputs in Control of an Electric Drive in Simulink

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Simulink. The parameters passed by Simulink to the s-function are listed in the

dialog box of the s-function as shown in Fig. 10. In Fig. 10, the only parameter

that Simulink passes to the s-function is Ts, the sampling time. Inside the C

program describing the s-function, this parameter Ts is used to define the

execution sample time of the s-function block i.e. the block is executed every Ts

seconds.

Since the execution time of the s-function must match the switching period of

the power converter and the sampling frequency of the current, voltage and

position measurements, the parameter Ts is defined as a global constant for the

simulation. To change this parameter, go to: File->Model Properties->Model

Properties, click on the tab Callbacks and then click InitFcn.

Fig. 10 Parameter dialog box for the s-function shown in Fig. 9

Some screenshots from the C code for the s-function ‘simple_control’ are shown

below with a brief explanation of the functions, variables and parameters.

S_FUNCTION_NAME: this constant defines the name of the s-function and it

must correspond to the name of the file (without the extension .c) which is also

used as the s-function name in the block (see Fig. 10). Control of an Electric Drive in Simulink

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The header files, such as aux_funcs.h and Constants.h are user-defined .h files

that contain definitions of functions and constants used in the code. The two

header files are included as an example, others can be defined and included as

necessary.

Fig. 11 Code lines defining the type of the s-function, inputs, outputs and parameters

U(element): this function macro gets a pointer to the vector of inputs from

Simulink and allows to get the inputs to local variables.

NUM_INPUTS, NUM_OUTPUTS, NUM_PARAMS: these must correspond to the

inputs, outputs and parameters of the s-function block in Simulink. If these

constants do not match the s-function block’s conditions, Matlab will generate

an error and will not compile the code for execution.

The parameters passed by Simulink to the function can be accessed as elements

of the parameter array starting from 0. For example, the first parameters will be

read in as: (mxGetPr(ssGetSFcnParam(S,0))[0]). The second parameter can be

read in as: (mxGetPr(ssGetSFcnParam(S,0))[1]).

The global variables should be defined outside of any functions so that they’re

accessible to all the functions. In Fig. 11, TS, TS_INV and thm_prev are global

variables. Variables that must hold their values between executions can be

declared as global, although it is not strictly necessary.

In Fig. 12, the sizes of the inputs, outputs, sample times, and other arrays are

defined. It is important to set the number of sample times to 1 through the Control of an Electric Drive in Simulink

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function ssSetNumSampleTimes(S, 1); as the s-function is intended to be a

single-execution-rate block in our application of an electric drive. The sample

time of the s-function is then set by calling ssSetSampleTime(S, 0, Ts); as shown

in Fig. 13. The figure also shows the initialization conditions that the user can

set, for example, assigning initial values to the global variables.

Fig. 12 Definition of the s-function code array sizes

Fig. 13 s-function sample time and initialization conditions Control of an Electric Drive in Simulink

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The outputs for the model are calculated through the function mdlOutputs

shown in Fig. 14. First, the inputs from the Simulink environment are read into

the local variables and arrays. The calculations necessary for the control of an

electric drive are performed on these local variables before passing the outputs

to Simulink. This is the function where almost all of the code related to the

drive’s control should reside.

Fig. 14 Some code lines for mdlOutputs function

To complete the process of building a Simulink block from a C program, the code

must be compiled into a Matlab executable file. The command used for this is

mex (that stands for Matlab executable). This command must be called in the

Matlab command window by ensuring that the folder in which the code files are

located is selected as the ‘current folder’ in Matlab (see Fig. 15). All the .c and .h

files that contain the functions used inside the main file ‘simple_control.c’

should be within the current folder and all .c source files must be included as Control of an Electric Drive in Simulink

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input arguments of the mex command as shown in Fig. 15, where aux_funcs.c is

the second .c source file that must be compiled along with simple_control.c.

Every time anything is changed in the code (e.g. changing a parameter in a .h file

or adding/deleting a line in any .c file of the project), the mex command should

be repeated before expecting a change in the behaviour of the s-function block.

This process is similar to compiling and building the project files in a DSP code.

Fig. 15 Instructions for compiling the C code into a mex file

A C compiler will be needed to compile the code into a mex file. There are

several compilers available from Mathworks, any of these can be used for

compiling the code.

Once successfully mexed, the current folder will have a mexw file with the name

of the s-function e.g. simple_control.mexw64. This file will be accessed by

Simulink during simulation as the contents of the S-function block shown in

Fig. 9. Control of an Electric Drive in Simulink

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The task

Your task is to understand the model and the basic project you are provided.

Simulate it with different conditions to enhance your understanding and be

familiar to the model and the C code. Then, starting from the basic project as

described above, develop the model and C code for the following objectives:

1) Armature current control of the dc motor

2) DC motor’s speed control

3) Apply different load torque profiles to test your speed control

4) DC motor’s position control (optional)

5) A model to simulate a three-phase PMSM drive (advanced)

6) Simulate vector control of a three-phase PMSM (advanced)