From NIS Chapter 5 Experiment 1 Objectives To verify the equivalency of the basi

Question

From NIS Chapter 5 Experiment 1 Objectives To verify the equivalency of the basic forms, including cascade, parallel and feedback forms. To verify the equivalency of the basic moves, including moving blocks past summing junctions, and moving blocks past pickoff points. Minimum required software packages MATLAB, Simulink, and the Control System Toolbox Prelab 1. Find the equivalent transfer function of three cascaded blocks, GI(s s 3 s-t 1 G20s) and G3 (s) s 4 s 5 2. Find the equivalent transfer function of three parallel blocks, Gi(s)- T. s 3 and G3(s) G2 (s) s 4 s 5 3. Find the equivalent transfer function of the negative feedback system of Figure P5.42 s+ 1 s 3 if G(s) and H(s) s(s 2) s 4 R(s) COs) G(s) H(s) Figure P5.42 4. For the system of Prelab 3, push H(s) to the left past the summing junction and draw the equivalent system 5. For the system of Prelab 3, push HOs) to the right past the pickoff point and draw the equivalent system

Explanation / Answer

1.

syms s;
G1=1/(s+1);
G2=1/(s+4);
G3=(s+3)/(s+5);
T1=G1*G2*G3

T1 = (sym)

           s + 3        

(s + 1)(s + 4)(s + 5)

2.

T2=G1+G2+G3

T2 = (sym)

s + 3                   1                   1
     +     +
s + 5                s + 4              s + 1

3.
G=(s+1)/(s*(s+2));
H=(s+3)/(s+4);
T=G/(1+G*H)

                s + 1             

                       (s + 1)(s + 3)        
           s1 + (s + 2)
                      s(s + 2)(s + 4)

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