Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege

1. Engr/Math/Physics 25 Chp4 MATLABProgramming-4 Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

2. Learning Goals • Write MATLAB Programs That can MAKE “Logical” Decisions that Affect Program Output • Write Programs that Employ LOOPing Processes • For→ No. Loops know a priori • while → Loop Terminates based on Logic Criteria

3. The conditional statements (if, else, elseif) we learned last time allowed us to determine at run-time whether or not to execute a block of code. What these Decision Statements Do NOT do is to allow us to execute a block more than once The TWO Things that Computers Do Better than People STORE Massive Amounts of Data REPEAT operations Loop Structures

4. A “LOOP” is a Program Structure that REPEATS Until some CONDITION is MET The NUMBER of Loops may Be Known a priori (ahead of time) No. of Loops Determined by simple COUNTING Determined Dynamically No. of Loops Determined by a DECISION statement The Loop consists of A Condition Test A Repeated Statement-Block Repetition → LOOPs

5. PreTest Loop Test vs Statement Locations • The key feature → we test to see whether or not to continue before executing the body of the loop. • i.e., The Loop May Not Execute at All • Good if Potential Zero Executions is Desired • a.k.a. “While DO”

6. PostTest Loop Test vs Statement Locations • The Key feature → Do Not Test Until the Block Executes at Least Once • Use if Design Calls for at Least-One Repetition • a.k.a. “DO While”

7. MidTest Loop Test vs Statement Locations • The generalization of both the pre-test and the post-test loops • Empty Block-1 → PreTest Loop • Empty Block-2 → PostTest Loop

8. A PreTested, COUNTED Loop for Loop Statement Start Set k = m • No. Repetitions Known • MATLAB Syntax • forCounter = Start : Increment: Endstatements • end k ≤ n? Increment kby s True Statements-1 False end Statements

9. Given for Loop Counting Variable: k=m:s:n The step value s may be negative Example: k = 10:-2:4 produces k = 10, 8, 6, 4 If s is omitted, the step value defaults to +1 If s is positive, the loop will not be executed if m is greater than n If s is negative, the loop will not be executed if m is less than n If mequalsn, the loop will be executed only once If the step value s is not an integer, round-off errors can cause the loop to execute a different number of passes than intended for Loop Rules

10. The continue statement passes control to the next iteration of the loop in which it appears, skipping any remaining statements in the body of the loop. The Following Code Uses a continue The continue Statement statement to avoid taking the log of a negative number. x = [10,1000,-10,100]; y = NaN*x; for k = 1:length(x) if x(k) < 0 continue end y(k) = log10(x(k)); end • The Result: y = 1, 3, NaN, 2

11. Let’s Fine Tune the No-Neg-Log Code by COMMENTING OUT the if-continue Commands Remove continue Statement x = [10,1000,-10,100]; y = NaN*x; for k = 1:length(x) %if x(k) < 0 %continue %end y(k) = log10(x(k)); end • The Result: y = 1.0000 3.0000 1.0000 + 1.3644i 2.0000

12. The use of loops and branching can often be avoided, thus creating simpler and faster programs by using a logical array as a mask that selects elements of another array. Any elements not selected will remain unchanged. The following session creates the logical array D from the 3x3 numeric array B Use of a Logical MASK

13. Logical Mask Session Use of a Logical MASK cont >> B = [0, -1, 4; 9, -14, 25; -34, 49, 64] B = 0 -1 4 9 -14 25 -34 49 64 >> D = (B >= 0) D = 1 0 1 1 0 1 0 1 1 Mask Array →a Logical that “masks out” Negative numbers

14. Original B = 0 -1 4 9 -14 25 -34 49 64 Logical MASK cont • Logical Mask Session cont >> B(D) = sqrt(B(D)) B = 0 -1 2 3 -14 5 -34 7 8 >> B(~D) = B(~D) + 50 B = 0 49 2 3 36 5 16 7 8 Negative Values Unchanged → Masked OUT by D(m,n) = 0 Positive Values Unchanged → Masked OUT by D(m,n) = 1

15. The while loop is used when the looping process terminates because a specified condition is satisfied, and thus the number of passes is not known in advance. A simple example of a while loop is while Loops x = 5; while x < 25 disp(x) x = 2*x - 1; end • Results from the disp statement are 5, 9, and 17.

16. A PreTested DYNAMIC Loop Start while Loop Statement Set Loop VarInitial value LogicalDecision • No. Repetitions UNknown • MATLAB Syntax • whileLogical Expression • statements • end True Statements(MUST IncrementLoop Variable) False end Statements

17. For the while loop to function properly two conditions must occur Start while Loop Statement Set Loop VarInitial value LogicalDecision • The loop variable must have a value before the while statement is executed • The loop variable must be changed somehow by the statements Inside the Loop True Statements(MUST IncrementLoop Variable) False end Statements

18. A simple while loop k = 1 x = 9 k = 2 x = 17 k = 3 x = 33 while Loop Example • The Results x = 5;k = 0; while x < 25 k = k + 1 y(k) = 3*x; x = 2*x-1 end >> y y = 15 27 51 • The loop variable x is initially assigned the value 5, and it keeps this value until the statement x = 2*x - 1 is encountered the first time. Its value then changes to 9. Before each pass through the loop, x is checked to see if its value is less than 25. If so, the pass is made. If not, the loop terminates

19. Write a .m- file to determine The min. number of terms required for the sum of the series 5k2 – 2k; k = 1, 2, 3, … to exceed 10,000. the sum for this number of terms The .m-file and the Results Another while Loop Example tot = 0;k = 0; while tot < 10e3 k = k + 1; tot = 5*k^2 - 2*k + tot; end disp(‘No. terms = ') disp(k) disp('The Sum = ') disp(tot) No. Terms = 18 Sum = 10203

20. The switch structure provides an alternative to using the if, elseif, and else commands. Anything programmed using switch can also be programmed using if structures. However, for some applications the switch structure producesmore readable code than when using the if structure. The switch Structure

21. switch input expression (which can be a scalar or string). case value1 statement group 1 case value2 statement group 2 . . . otherwise statement group n end MATLAB switch Syntax

22. This switch Block displays the High School Class-Name that Corresponds to a Given Grade Level switch Example grade_level = input('Hi-School Grade Level.: '); switch grade_level case 9 disp(' Freshman') case 10 disp(' Sophomore') case 11 disp(' Junior') case 12 disp(' Senior') otherwise disp(' NOT a Hi-Schl Grade Lvl') end

23. switch Example Results Hi-School Grade Level.: 9 Freshman Hi-School Grade Level.: 11 Junior Hi-School Grade Level.: 13 NOT a Hi-Schl Grade Lvl Hi-School Grade Level.: 10 Sophomore

24. Consider an Electrical Diode → I V REALBehavior IDEALModel OFFSETModel LINEARModel Example: Prob 4.24 • We can MODEL the V-I Behavior of this Device in Several ways

25. Problem-24 cont • The Diode exhibits a form of RECTIFICATION • i.e., It allows current to Flow in the FORWARD direction, But NOT in the REVERSE direction • Think of a diode as a “Check-Valve” for Electrical Current”

26. Problem-24 cont • Now Let’s Connect the Diode to • A Power Source, Vs • A Useful Load, RL +VL • Next Assume that Vs is a Decaying Sinusoidal, Alternating Current (AC) Voltage-Source modeled mathematically as

27. Problem-24 → Plot Vs +VL % Bruce Mayer, PE * 08Jul05 % ENGR25 * Problem 4-24 % file = Prob4_24_Vs_plot.m % INPUT SECTION tmax = input('Max time in sec = '); Vmax = input('Max Supply Potential in V = '); %CALCULATION SECTION % use linspace command to generate 500 time pts t = linspace(0,tmax,500); % Use for-Loop to generate plotting vector, vs for k = 1:500 % Calc SUPPLY V-Level vsup = Vmax*exp(-t(k)/3)*sin(pi*t(k)); vs(k) = vsup; end % PLOT SECTION plot(t,vs),ylabel('Load Voltage (V)'),xlabel('Time (sec)'),... title('Ideal-Diode Rectifier'), grid disp('Plot Complete')

28. Problem-24 → Plot Vs +VL

29. Recall the Ideal-Diode Model → IDEALModel Prob 24 cont • With This Diode Behavior weExpect Load a Voltage in this form +VL • Write a MATLAB Program to Plot VL vs t for: 0 t  10s

30. Problem-24 → Plot VL Ideal % Bruce Mayer, PE * 08Jul05 % ENGR25 * Problem 4-24a % file = Prob4_24a_ideal_diode.m % INPUT SECTION tmax = input('Max time in sec = '); Vmax = input('Max Supply Potential in V = '); % CALCULATION SECTION % use linspace command to generate 500 time pts t = linspace(0,tmax,500); % Use for-Loop to generate plotting vector, vL for k = 1:500 % Calc SUPPLY V-Level at the current t(k) vs = Vmax*exp(-t(k)/3)*sin(pi*t(k)); % chk Fwd or Rev condition by if-else if vs > 0 vL(k) = vs; else vL(k) = 0; end end plot(t,vL),ylabel('Load Voltage (V)'),xlabel('Time (sec)'),... title('Ideal-Diode Rectifier'), grid +VL VS

31. IDEALModel Problem-24 → Plot VL Ideal

32. Recall the OffSet-Diode Model → OFFSETModel Prob 24 cont • With This Diode Behavior weExpect Load Voltage in this form +VL • Write a MATLAB Program to Plot VL vs t for: 0 t  10s

33. Problem-24 → Plot VL Offset % Bruce Mayer, PE * 08Jul05 % ENGR25 * Problem 4-24b % file = Prob4_24b_offset_diode.m % INPUT SECTION tmax = input('Max time in sec = '); Vmax = input('Max Supply Potential in V = '); % CALCULATION SECTION % use linspace command to generate 500 time pts t = linspace(0,tmax,500); % Use for-Loop to generate plotting vector, vL for k = 1:500 % Calc SUPPLY V-Level at current t(k) vs = Vmax*exp(-t(k)/3)*sin(pi*t(k)); % chk Fwd or Rev condition by if-else if vs > 0.6 vL(k) = vs-0.6; else vL(k) = 0; end end plot(t,vL),ylabel('Load Voltage (V)'),xlabel('Time (sec)'),... title('Offset-Diode Rectifier'), grid +VL VS

34. OFFSETModel Problem-24 → Plot VL Offset

35. Compare Plots Side-by-Side +VL Prob 24 Analysis • 0.6V Offset has a large affect when the Vs amplitude is only 3V • OffSet is 20% of amplitude

36. Plots for 24V amplitude Prob 24 Analysis +VL • Makes less difference • Note different vertical scales

37. All Done for Today SinusoidalHalfWaveRectifier

38. Engr/Math/Physics 25 Appendix Time For Live Demo Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu