Workshop Matlab/Simulink in Drives and Power electronics Lecture 3

Transcription

1 Workshop Matlab/Simulink in Drives and Power electronics Lecture 3 : DC-Motor Control design Ghislain REMY Jean DEPREZ 1 / 29

2 Workshop Program 8 lectures will be presented based on Matlab/Simulink : 1 Introduction to Matlab 2 Introduction to Simulink 3 DC-Motor Control design 4 DC-Motor Chopper design SimPowerSystems 5 Introduction to Stateflow/Statechart 6 Induction Motor Inverter Control 7 Synchronous Motor Modeling 8 Synchronous Motor Control Two system applications (four quadrants electric drives of mechanical systems) will be used as "conducting lines" during the workshop. 2 / 29

3 Drives and Power Systems Presentation of the Structure of Industrial Drives and Power Systems Large domains of application DC-Motor, Synchronous Motor and Induction Motor Power Electronics (IGBT, MOSFET ) Classical Control Algorithm (Cascaded Control Loop, Scalar control, Vector Control ) 3 / 29

4 Problems with Traditional Development Solution Model-based design 4 / 29

5 Advantages of Model-based design 5 / 29

6 Design of Mechatronics System Model-based design Simulation of the system is essential Multi-domain modeling Matlab/Simulink is a very good tool for this kind of approach. Many useful Toolboxes in Matlab/Simulink: SimPowerSystems / SimScape StateFlow Real-Time Workshop 6 / 29

7 Summary Overview of the Control System Toolbox Building Models Analyzing Models: Introduces the LTI Viewer Designing Compensators: Introduces the SISO Design Tool Using an application to the DC-Motor Control design 7 / 29

8 Hand Tuning Control Systems Hand tuning refers to iterative, manual tuning of control systems Disadvantages of hand-tuning: Tuning on a real system can be costly (test cell) Tuning requires significant knowledge, experience or both Impossible to tell that you are at optimal solution 8 / 29

9 Overview of the Control System Toolbox The Control System Toolbox product provide functions designed for control engineering. This product is a collection of algorithms, written mostly as M-files, that implements common control system design, analysis, and modeling techniques and convenient graphical user interfaces (GUIs). Control System Toolobox specificities : Model can be Transfer functions, in zero-pole-gain or state-space form, allowing you to use both classical and modern control techniques. You can manipulate both continuous-time and discrete-time systems. Conversions between various model representations are provided. Time responses, frequency responses, and root loci can be computed and graphed. Other functions allow pole placement, optimal control, and estimation. 9 / 29

10 Some examples of the Control Toolbox Various tools for the Model Analysis using Bode Diagram, Pole-Zero Map, Nyquist Diagram, Step Response Graphical User Interface for an easy controller design Example: rlc_gui 10 / 29

11 1: Building Models Describes how to build linear models, interconnect models, determine model characteristics, convert between continuous- and discrete-time models, and how to perform model order reduction on large scale models. This chapter develops a DC motor model from basic laws of physics. Firstly: Creating Continuous-Time Models 11 / 29

12 LTI Model Types Palestine Polytechnic University LTI Model Types Control System Toolbox provides functions for creating four basic representations of linear time-invariant (LTI) models: Transfer function (TF) models Zero-pole-gain (ZPK) models State-space (SS) models Frequency response data (FRD) models These functions take model data as input and create objects that embody this data in a single MATLAB variable. 12 / 29

13 Creating Transfer Function Models Transfer functions (TF) are frequency-domain representations. A SISO transfer function is a ratio of polynomials: Transfer functions are specified by their numerator and denominator polynomials A(s) and B(s). In MATLAB, a polynomial is represented by the vector of its coefficients, for example, the polynomial is specified as [1 2 10]. To create a TF object representing the transfer function: specify the numerator and denominator polynomials and use tf to construct the TF object: num = [ 1 0 ]; % Numerator: s den = [ ]; % Denominator: s^2 + 2 s + 10 H = tf(num,den) Transfer function: s s^2 + 2 s Model can also be defined as an expression of the Laplace variable s: s = tf('s'); % Create Laplace variable H = s / (s^2 + 2*s + 10) Transfer function: s s^2 + 2 s / 29

14 A simplified model of the DC motor The torque Td models load disturbances. You must minimize the speed variations induced by such disturbances. For this example, the physical constants are: R = 2.0; % Ohms L = 0.5; % Henrys Km = 0.1; Kb = 0.1; % torque and back emf constants Kf = 0.2; % Nms J = 0.02; % kg.m^2/s^2 First construct a state-space model of the DC motor with two inputs (Va,Td) and one output (w): h1 = tf(km,[l R]); % armature h2 = tf(1,[j Kf]); % eqn of motion dcm = ss(h2) * [h1, 1]; % w = h2 * (h1*va + Td) dcm = feedback(dcm,kb,1,1); % close back emf loop 14 / 29

15 Creating State-Space Models State-space (SS) models are time-domain representations of LTI systems: dx = Ax + Bu dt y = Cx + Du ( t) ( t) ( t) ( t) ( t) where x(t) is the state vector, u(t) is input vector, and y(t) is the output trajectory. State-space models are derived from the differential equations describing the system dynamics: For example, a simple electric motor: 15 / 29

16 DC Motor in State-Space Models For example, consider a simple electric motor: di U = RA i+ LA + e dt e = Ke w c = Ke i dw J = c BM w T dt L dx = Ax + Bu dt y = Cx + Du To create this model, specify the state-space matrices A, B, C, D and use ss to construct the SS object: A = [ Ra/La Ke/La ; Ke/J -Bm/J]; B = [ 1/L ; 0 ]; C = [ 1 1 ]; D = [ x x]; H = ss(a,b,c,d) ( t) ( t) ( t) ( t) ( t) i x( t) = w i y( t) = w U u( t) = TL 16 / 29

17 LTI Viewer from Simulink 17 / 29

18 Analyzing Models: Introduces the LTI Viewer Analyzing Models: Introduces the LTI Viewer, a graphical user interface (GUI) that simplifies the task of viewing model responses. This chapter also discusses command-line functions for viewing model responses. 1- Select the Plot Type 2- Export Models to the Workspace Model reduction 18 / 29

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20 Define a Controller Use a Controller as a Simple gain 1/1, It will be tuned by the control toolbox 20 / 29

21 Designing Compensators: Introduces the SISO Design Tool, a GUI that allows you to rapidly iterate on compensator designs. You can use this tool to adjust compensator gains and add dynamics, such as poles, zeros, notch filters 21 / 29

22 Tune Blocks 22 / 29

23 Configuring Design and Analysis Plots 23 / 29

24 The SISO Design Tool The SISO Design Task in the Control and Estimation Tools Manager, a user interface (UI) that facilitates the design of compensators for single-input, single-output feedback loops through a series of interactive pages The Graphical Tuning window, a graphical user interface (GUI) for displaying and manipulating the Bode, root locus, and Nichols plots for the controller currently being designed. This window is titled SISO Design for Design Name. The LTI Viewer associated with the SISO Design Task 24 / 29

25 The SISO Tool : Graphical window Using the Graphical Tuning Window Toolbar The toolbar can performs: Add and delete real and complex poles and zeros Zoom in and out Invoke the SISO Design Tool's context-sensitive help 25 / 29

26 Opening the SISO Design Tool This section shows how to open the SISO Design Tool with the DC motor example developed in Building Models Examples of the DC motor model, type load ltiexamples This loads a collection of linear models, including the DC motor. To open the SISO Design Tool and import the DC motor, type sisotool(sys_dc) This command opens both the SISO Design Task node on the Control and Estimation Tools Manager and the Graphical Tuning window with the root locus and open-loop Bode diagrams for the DC motor plotted by default. 26 / 29

27 SISO Design Task Node (Architecture Page View) Right Click to Add Pole/Zero Feedback Structure G - plant H - sensor dynamics F - prefilter C - compensator 27 / 29

28 Graphical Tuning Window : The DC Motor Right - click in any of these regions to see design options This status bar shows useful tips about how to use this window and information about the status of your design 28 / 29

29 Loop Responses As you select different compensator designs, you may find it convenient to be able to examine the various loop responses (for example, step or impulse responses) for a particular design. To view, for example, the closed-loop step response, click the Analysis Plots tab This opens the Analysis Plots page containing the list of available responses, with none initially selected. 29 / 29