Homework Answers
The derivation of getting A, B, C matrices in controllable canonical form is given below
PS: To avoid confusion, the input in the derivation is taken as U(S) as x is chosen as state variable.
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6. For the transfer function 5s2 +23s+81 H(s) = s3 +11s 43s +27 +11 s. (a) Sketch the DF2 (canoni...
10. Consider the following input-output transfer function. U(s) s3 6s 11s +4 Draw the CCF state d...
State space of transfer function
10. Consider the following input-output transfer function. U(s) s3 6s 11s +4 Draw the CCF state diagram of the system. Obtain the dynamic equations of the system in CCF. i.i Obtain the dynamic equations of the system in odr.
10. Consider the following input-output transfer function. U(s) s3 6s 11s +4 Draw the CCF state diagram of the system. Obtain the dynamic equations of the system in CCF. i.i Obtain the dynamic equations of the...
Problem 1: Convert the following transfer function model into state-space model and sketch its block diagram with x defined as the leftmost state variable. 2s2 +8s +6 s3 +8s2 +16s+6 Problem...
Problem 1: Convert the following transfer function model into state-space model and sketch its block diagram with x defined as the leftmost state variable. 2s2 +8s +6 s3 +8s2 +16s+6
Problem 1: Convert the following transfer function model into state-space model and sketch its block diagram with x defined as the leftmost state variable. 2s2 +8s +6 s3 +8s2 +16s+6
S+5 Consider a system where the transfer function is given as: G(s) -tS 3+6s2+11s+6 a. Sketch a r...
s+5 Consider a system where the transfer function is given as: G(s) -tS 3+6s2+11s+6 a. Sketch a root locus for static controller gain K b. Design a controller to meet the following specifictions: t, S 1s, 2 0.6, e(oo)Istep0
s+5 Consider a system where the transfer function is given as: G(s) -tS 3+6s2+11s+6 a. Sketch a root locus for static controller gain K b. Design a controller to meet the following specifictions: t, S 1s, 2 0.6, e(oo)Istep0
4. Block Diagrams (a) Consider a causal LTI system with transfer function H(s)2 Show the direct-form block diagram of Hi(s) (b) Consider a causal LTI system with transfer function 2s2 +4s -6 H(s)- Sh...
4. Block Diagrams (a) Consider a causal LTI system with transfer function H(s)2 Show the direct-form block diagram of Hi(s) (b) Consider a causal LTI system with transfer function 2s2 +4s -6 H(s)- Show the direct-form block diagram of Hi(s) c) Now observe that to draw a block diagram as a cascaded combination of two 1st order subsystems. d) Finally, use partial fraction expansion to express this system as a sum of individual poles and observe that you can draw...
100 H(s) 2. For the transfer function: s3+32s2260s+400 a) create a reduced order model by removing...
100 H(s) 2. For the transfer function: s3+32s2260s+400 a) create a reduced order model by removing the "high frequency" pole (Hints ... Use zpk() to find poles. Make sure the new transfer function has the same Kdc as the original model) b) Use MatLab to verify that the step response for the two models are "equivalent"
Select the correct transfer function for the block diagram below: R(s) C(s) C(s) R(s) s3+13s2+32s+(20s+k) C(s)...
Select the correct transfer function for the block diagram below: R(s) C(s) C(s) R(s) s3+13s2+32s+(20s+k) C(s) R(s) s3+13s2+32s+(20+k) b. C(s) R(s) s3+13s2+(32+k)s+(20+k) R(s) C(s) s3+13s2+20s+32 d.
5) (10 pts) The transfer function of a system is given by: S +1 H(s) =...
5) (10 pts) The transfer function of a system is given by: S +1 H(s) = $3+ 9s2 + 23s + 15 What is the steady state error of this system when the input is unit step function?
4. Block Diagrams (a) Consider a causal LTI system with transfer function Show the direct-form block diagram of Hi(s) b) Consider a causal LTI system with transfer function H282+4s -6 H (s) = 2 Show...
4. Block Diagrams (a) Consider a causal LTI system with transfer function Show the direct-form block diagram of Hi(s) b) Consider a causal LTI system with transfer function H282+4s -6 H (s) = 2 Show the direct-form block diagram of Hi(s) (c) Now observe that to draw a block diagram as a cascaded combination of two 1st order subsystems. (d) Finally, use partial fraction expansion to express this system as a sum of individual poles and observe that you can...
27. (a) The circuit below has transfer function H(s)--out . It is known that L =0.5...
27. (a) The circuit below has transfer function H(s)--out . It is known that L =0.5 H ist andRI = 4 Ω and R2=2Q. (i) Compute the transfer function. (ii) Compute the COMPLETE range of for which the circuit is BIBO stable. R2 out C : 0.25 F. Compute H(s)-out ) Determ ne the complete range of m for which Vin(s) (b) Let R= 2 Ω the circuit is BIBO stable in out mvtt) out
singal and system QUESTION 5 [20 marks] Given transfer function of a networks H(s) transfer function...
singal and
system
QUESTION 5 [20 marks] Given transfer function of a networks H(s) transfer function at w = 1000 rad/s. $10+ 52 +10005+7x106 - Evaluate the [10 marks) b) Simplify and obtain the frequency response (magnitude and phase plots) of the 100(5+10) following transfer function H(s) s+10000 [6 marks] Sketch the magnitude and phase plots from (b) using Bode Plot Technique. [4 marks]
State space of transfer function
10. Consider the following input-output transfer function. U(s) s3 6s 11s +4 Draw the CCF state diagram of the system. Obtain the dynamic equations of the system in CCF. i.i Obtain the dynamic equations of the system in odr.
10. Consider the following input-output transfer function. U(s) s3 6s 11s +4 Draw the CCF state diagram of the system. Obtain the dynamic equations of the system in CCF. i.i Obtain the dynamic equations of the...
Problem 1: Convert the following transfer function model into state-space model and sketch its block diagram with x defined as the leftmost state variable. 2s2 +8s +6 s3 +8s2 +16s+6
Problem 1: Convert the following transfer function model into state-space model and sketch its block diagram with x defined as the leftmost state variable. 2s2 +8s +6 s3 +8s2 +16s+6
s+5 Consider a system where the transfer function is given as: G(s) -tS 3+6s2+11s+6 a. Sketch a root locus for static controller gain K b. Design a controller to meet the following specifictions: t, S 1s, 2 0.6, e(oo)Istep0
s+5 Consider a system where the transfer function is given as: G(s) -tS 3+6s2+11s+6 a. Sketch a root locus for static controller gain K b. Design a controller to meet the following specifictions: t, S 1s, 2 0.6, e(oo)Istep0
4. Block Diagrams (a) Consider a causal LTI system with transfer function H(s)2 Show the direct-form block diagram of Hi(s) (b) Consider a causal LTI system with transfer function 2s2 +4s -6 H(s)- Show the direct-form block diagram of Hi(s) c) Now observe that to draw a block diagram as a cascaded combination of two 1st order subsystems. d) Finally, use partial fraction expansion to express this system as a sum of individual poles and observe that you can draw...
100 H(s) 2. For the transfer function: s3+32s2260s+400 a) create a reduced order model by removing the "high frequency" pole (Hints ... Use zpk() to find poles. Make sure the new transfer function has the same Kdc as the original model) b) Use MatLab to verify that the step response for the two models are "equivalent"
Select the correct transfer function for the block diagram below: R(s) C(s) C(s) R(s) s3+13s2+32s+(20s+k) C(s) R(s) s3+13s2+32s+(20+k) b. C(s) R(s) s3+13s2+(32+k)s+(20+k) R(s) C(s) s3+13s2+20s+32 d.
5) (10 pts) The transfer function of a system is given by: S +1 H(s) = $3+ 9s2 + 23s + 15 What is the steady state error of this system when the input is unit step function?
4. Block Diagrams (a) Consider a causal LTI system with transfer function Show the direct-form block diagram of Hi(s) b) Consider a causal LTI system with transfer function H282+4s -6 H (s) = 2 Show the direct-form block diagram of Hi(s) (c) Now observe that to draw a block diagram as a cascaded combination of two 1st order subsystems. (d) Finally, use partial fraction expansion to express this system as a sum of individual poles and observe that you can...
27. (a) The circuit below has transfer function H(s)--out . It is known that L =0.5 H ist andRI = 4 Ω and R2=2Q. (i) Compute the transfer function. (ii) Compute the COMPLETE range of for which the circuit is BIBO stable. R2 out C : 0.25 F. Compute H(s)-out ) Determ ne the complete range of m for which Vin(s) (b) Let R= 2 Ω the circuit is BIBO stable in out mvtt) out
singal and
system
QUESTION 5 [20 marks] Given transfer function of a networks H(s) transfer function at w = 1000 rad/s. $10+ 52 +10005+7x106 - Evaluate the [10 marks) b) Simplify and obtain the frequency response (magnitude and phase plots) of the 100(5+10) following transfer function H(s) s+10000 [6 marks] Sketch the magnitude and phase plots from (b) using Bode Plot Technique. [4 marks]
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