MATLAB CHAPTER 9 Simulink

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MATLAB ??CHAPTER 9 Simulink

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Simulation Diagram

• Simulation diagram (block diagram)
• Consider the equation
• ?
• ?
• Simulation diagrams for

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Introduction to Simulink

• Type Simulink
• in the MATLAB
• Command window
• to start window.

Type simulink In the Command Window
? The Simulink Library Browser
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Introduction to Simulink

• Create a new model
• Click on the icon that resembles a clean sheet of
  paper, or select New from the File menu in the
  Browser.

Or
Click this icon
File ? New
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Introduction to Simulink

• ? Double-click appropriate library.
• ? See a list of blocks within that library.
• ? Click on the block name or icon.
• ? Hold the mouse button, and drag
• it to the new model window.
• ? release the button.

click, hold, drag, and release
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Introduction to Simulink

• ? Use the File menu in the model window to Open,
  Close, and Save model files.
• ? To print, File ? print
• ? Edit to copy, cut and paste blocks.
• ? you can also use mouse for these operations

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Introduction to Simulink

• Example
• Simulink Solution of
• Use Simulink to solve the following problem for
  0 t 13.
• The exact solution is

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Introduction to Simulink

• ? Start Simulink and open a new model window.
• ? Select and place the Sine Wave block from the
  Source library.

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Introduction to Simulink
? Double-click to open the Block Parameters
window. Make sure that Amplitude 1,
Frequency 1, Phase 0, Sample time 0 Then
click OK.
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Introduction to Simulink

• ? Select and place the Gain block from the Math
  Operations library.
• the Block Parameters window the Gain value
  10.
• Note that the value 10 then appears in
  the triangle.
• ? Select and place the Integrator block from the
  Continuous library.
• Initial condition0 (because y(0)0)

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Introduction to Simulink

• ? Select and place the Scope block from the Sinks
  library.
• ? Connect each input and output port.

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Introduction to Simulink

• ? Click on the Simulation menu, and click the
  Configuration Parameters item.
• (If you use MATLAB 6.5 or earlier, click
  Simulation parameters instead of
  Configuration Parameters.)
• Click on the solver tab, and enter 13 for
  the stop time.
• Make sure the Start time is 0.

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Introduction to Simulink

• ? Run the simulation by clicking on the
  Simulation menu,
• and clicking the Start item.

OR
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Introduction to Simulink

• ? After the simulation, double-click on the Scope
  block .

Double-click!
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Linear State-Variable Models

• State-variable models can have more than one
  input and more than on output.
• Simulink has the State-space block that
  represents the linear state-variable model

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Linear State-Variable Models

• Example
• Simulink Model of the Two-Mass System
• m15, m23, c14, c28, k11, and k24
• The equations of motion are
• These equations can be expressed in
  state-variable form as

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Linear State-Variable Models

• Vector matrix form

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Linear State-Variable Models

• Initinal conditions
• Output equation

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Linear State-Variable Models

• ?Create a new model window
• ?Select and place the Step block from the Sources
  library.
• Step time0, Initial and Final values 0 and
  1, Sample time0

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Linear State-Variable Models

• ?Select and place the State-Space lock. Enter
  A,B,C,D. Then enter initial condition.

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Linear State-Variable Models

• ?Select and place the Scope block.
• ?connect each port.

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Linear State-Variable Models

• ?experiment with different values of the Stop
  time until the Scope shows that the steady-state
  response has been reached.
• Ex) when stop time 25

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Piecewise-Linear Models

• Closed-form solutions are not available for most
  nonlinear differential equations, We must solve
  such equations numerically.
• Ex)
• Piecewise-linear models are actually nonlinear,
  although they may appear to be linear.
• Ex) a mass attached to a spring and sliding on a
  horizontal surface with Coulomb friction.

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Piecewise-Linear Models

• These two equations can be expressed as the
  single, nonlinear equation.
• Solutions of models that contain piecewise-linear
  functions are very tedious to program. However,
  Simulink has built-in blocks that represent many
  of the commonly-found functions such as Coulomb
  friction. Therefore Simulink is especially
  useful for such applications. One such block is
  the Saturation block in the Discontinuities
  library.

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Simulink Model of a Rocket-Propelled sled

• A rocket propelled sled
• Compute the sleds velocity v for 0t6 if v(0)
  0
• The rocket thrust is 4000N and the sled mass is
  450kg.
• The sleds equation of motion is

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Simulink Model of a Rocket-Propelled sled

• To obtain ?(t)
• Thus the equation of motion becomes
• The solution is formally given by

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Simulink Model of a Rocket-Propelled sled

• (a) Create a Simulink model to solve this problem
  for 0t10s.
• (b) Now suppose that the engine angle is limited
  by a mechanical stop to 60 , which is 60p/180
  rad. Create a Simulink model to solve the
  problem.
• Solution
• (a)
• ?create ?(t) by integrating the constant
  twice.
• ?Constant block from the Sources library.
  Constant valuepi/50.
• ?Trigonometric block from the Math Operations
  library. Functioncos.

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Simulink Model of a Rocket-Propelled sled

• ? Set the Stop time 10, run the simulation, and
  examine the result in Scope.

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Simulink Model of a Rocket-Propelled sled

• (b)
• ?modify the model as follows.
• ?the Saturation block from the Discontinuities
  library.
• Upper limit 60pi/180,
• Lower limit0.
• ?mux

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Simulink Model of a Rocket-Propelled sled

• Scope window

T0
T?0
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The Relay Block

• The Simulink Relay block is an example of
  something that is tedious to program in MATLAB
  but is easy to implement in Simulink.
• A graph of the logic of a relay.
• The relay switches the output between two
  specified values, named On and Off in the figure.

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Model of a Relay-Controlled Motor

• The model of an armature-controlled dc motor

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Model of a Relay-Controlled Motor

• x1i, x2?
• R0.6?, L0.002H, KT0.04Nm/A, Ke0.04Vs/rad,
  c0.01Nms/rad, and I610(-5)kgm2
• Suppose we have a sensor that measure the motor
  speed, and we use the sensors signal to activate
  a relay to switch the applied voltage v(t)
  between 0 and 100V to keep the speed between 250
  and 350rad/s.
• SwOff250, SwOn350, Off100, On0

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Model of a Relay-Controlled Motor

• Given parameter values
• To examine the speed ? as output, we choose

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Model of a Relay-Controlled Motor

• ?Create a new Simulink model.
• ?Select and place a Step block from the Sources
  library. Label it Disturbance Step.
• Step time0.05, Initial and Final time0 and 3,
  Sample time0
• ?Select and place a Relay block from the
  Discontinuities library.
• Switch-on and Switch-off points350 and 250,
• Output when on and Output when off0 and 100.

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Model of a Relay-Controlled Motor

• ?Select and place the Mux block from the signal
  Routing library.
• Display option to Signals.
• number of input2.
• ?Select and place the State-Space block from the
  Continuous library.
• enter the A,B,C,D.
• enter 00 for the initial conditoin.
• B tells 2 input, C and D tells 1 output.

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Model of a Relay-Controlled Motor

• ?Select and place the Scope block from the Sinks
  library.
• ?connect each port.
• ?Stop time0.1 and run the simulation. (the plot
  of ?(t) in the scope.)

Note Connect signal1(first input) to the output
of the Relay block Connect signa2(second input)
to the output of the Disturbance Step
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Model of a Relay-Controlled Motor

• Relay logic scheme keeps the speed within the
  desired limits of 250 and 350 before the
  disturbance torque starts to act.
• Speed oscillates.
• When V0, the speed decrease because back emf,
  and viscous damping.
• The speed drops below 250 when the disturbance
  torque starts to act, because the V0.
• As soon as the speed drops for the speed to
  increase because the motor torque must now work
  against the disturbance.

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Model of a Relay-Controlled Motor

• Speed becomes constant
• V100, the system achieves a steady-state
  condition in which the motor torque equals the
  sum of the disturbance torque and the viscous
  damping torque. Thus the acceleration is zero.

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Model of a Relay-Controlled Motor

• ?If you want examine the current i(t), change
  the matrix C to 1,0, and run the simulation
  again.