To days Outline

1. To days Outline • Callbacks • MATLAB And Simulink • S-functions • Project suggestions Lecture 7

2. Callbacks • A callback is a MATLAB command that executes when a certain event occurs. • Opening a model • Double-click, moving etc of Simulink blocks • Callback are installed using the MATLAB command Set_param(object, parameter, value) • object:A MATLAB string containing the name of the model or a path to the block • parameter: A MATLAB string containing the name given to the event of interest. • value: A MATLAB string containing the callback. Lecture 7

3. Callbacks Lecture 7

4. Callbacks Example • Create a simple model in Simulink that contains • a gain • a sine wave • a scope. • When a user tries to run the model he should be prompted for a gain value Lecture 7

5. MATLAB and Simulink • When running a simulink model we have access to variables in the MATLAB workspace • What if we want to set variables from a function • All parameter values in the different simulink blocks can be set with the command: set_param Set_param(’Object’, ’parameter’, value’) • All parameter values in the different simulink blocks can be viewed with the command: get_param get_param(’Object’, ’parameter’,) Lecture 7

6. MATLAB and Simulink Example: • Set the gain value in the model: Mymod.mdl Lecture 7

7. MATLAB and Simulink • How can we set parameters in a closed model? • What if the model has several levels of subsystems? Lecture 7

8. MATLAB and Simulink Example: • Create a Graphical user interface and a simulink model of the double tank system. • A user should be able to set process parameters: • Bottom area • Area of the bottom hole • Pump constant. • The user should also be able to set gain values in the controller. Lecture 7

9. MATLAB and Simulink Lecture 7

10. S-functions • Allows us to define custom Simulink blocks • S-function represents a general Simulink block with: • input vector u • output vector y • state vector x • Continuous states xc • Discrete states xd Lecture 7

11. S-functions • We must define: • Initial values of each state • Define the size of the state vector • Define the size of the output vector • Define the size of the input vector • Set sample time if there is a discrete model. • S-function must compute the output • y=g(x,u,t,p) • Update the discrete states • xd(k+1)=fd(x,u,t,p) • Compute the derivatives • xc’=fc(x,u,t,p) Lecture 7

12. S-functions / m-file sfunc_name(t,x,u,flag,p1..pn) function [sys,X0,str,ts]=sfunc_name(t,x,u,flag,p1..pn) switch flag, case 0, [sys,x0,str,ts]=mdlInitializeSizes; case 1, sys=mdlDerivatives(t,x,u); case 2, sys=mdlUpdate(t,x,u); case 3, sys=mdlOutputs(t,x,u); case 4, sys=mdlGetTimeOfNextVarHit(t,x,u); case 9, sys=mdlTerminate(t,x,u); otherwise error(['Unhandled flag = ',num2str(flag)]); end Lecture 7

13. S-functions mdlInitializeSizes • Return the sizes, initial conditions, and sample times for the S-function. function [sys,x0,str,ts]=mdlInitializeSizes sizes = simsizes; sizes.NumContStates = 0; sizes.NumDiscStates = 0; sizes.NumOutputs = 0; sizes.NumInputs = 0; sizes.DirFeedthrough = 1; sizes.NumSampleTimes = 1; % at least one sample time is needed sys = simsizes(sizes); x0 = []; % initialize the initial conditions str = []; % str is always an empty matrix ts = [0 0]; % initialize the array of sample times return Lecture 7

14. S-functions mdlDerivatives • Return the derivatives for the continuous states. function sys=mdlDerivatives(t,x,u) sys = []; return Lecture 7

15. S-functions mdlUpdate • Handle discrete state updates, sample time hits, and major time step function sys=mdlUpdate(t,x,u) sys = []; return Lecture 7

16. S-functions mdlOutputs • Calculate the output function sys=mdlOutputs(t,x,u) sys = []; return Lecture 7

17. S-functionsmdlGetTimeOfNextVarHit • Return the time of the next hit for this block. • Note that the result is absolute time. • Note that this function is only used when you specify • variable discrete-time sample time [-2 0] in the sample time array in mdlInitializeSizes. • Example, set the next hit to be one second later. function sys=mdlGetTimeOfNextVarHit(t,x,u) sampleTime = 1; sys = t + sampleTime; return Lecture 7

18. S-functionsmdlTerminate • Perform any end of simulation tasks. function sys=mdlTerminate(t,x,u) sys = []; return Lecture 7

19. S-functions Example: • Create a continuous s-function that describes the double tank system. • Initial condition • Upper 0.1m • Lower 0.2m • Output should be the • difference between the two tanks. Lecture 7

20. S-functions • We must define: • Initial values of each state • Define the size of the state vector • Define the size of the output vector • Define the size of the input vector • Compute the derivatives • xc’=fc(x,u,t,p) • S-function must compute the output • y=g(x,u,t,p) Lecture 7

21. Exercises on this days topics • Work on the second laboration. • It’s time to start thinking about a project. Lecture 7

22. Project suggestions • Design of a Water Clock • Double Pendulum • DC and AC motors • Two Salty Tanks • Animate a bouncing ball • Search the internet and library for interesting projects. Lecture 7

23. Design of a Water Clock A 12-hour water clock is to be designed with the dimensions shown in the sketch. The shape of the clock is obtained by revolving the curve y = f(x) around the y axis. Define the shape function, f(x), and the radius of the circular hole at the bottom that gives a constant water level decrease of 4 in/hr. Lecture 7

24. Double Pendulum The position of the two masses The differential equation describing the movement Lecture 7

25. Two Salty Tanks Consider the cascade of two tanks as shown in the figure. Assume that the volumetric flow rate throughout the system is constant with q = 5 gal/s. With a constant flow rate the volumes of both Tank 1 and Tank 2 are also constant with V1 = 100 gal and V2 = 200 gal. If the inlet to Tank 1 is pure water and the initial masses of the salt dissolved in the tanks are m1 = m2 = 50 lbm, determine the amount of salt in each tank versus time. Also determine the time and magnitude of the mass in Tank 2 when m2 is at its highest value. Lecture 7

26. DC and AC motors • DC Motor • AC Motor • Change frequancy, magnetic field, view voltage, current and emc. Lecture 7

27. Animate a bouncing ball • Throw or drop an elastic ball with some initial velocity and angel • Simulate how the ball will bounce • A user should be able to set different parameters as • Elastic constant • Initial angle • Initial velocity Lecture 7