R(S)' a. Controller s+1 s+6 V₁(s) S-2 V(s) Fig.1b: Block diagram of the shock absorber Y Posi Find the transfer matrix of the system. Then draw the block diagram of the state-space system in an observable canonical realization form.
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![R(S)
Controller
s+1
s+6
V₁(s)
S-2
V(s)
Fig.1b: Block diagram of the shock absorber
-15
Y(s)
Position
a. Find the transfer matrix of the system. Then draw the block diagram of the state-space
system in an observable canonical realization form.
b. Obtain the solution of homogenous and nonhomogeneous state equations of the system for a
unit
ramp input.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95c39ab9-3b37-46f1-a8c4-1dbfb16acfca%2Fecc1aea6-091c-43bd-a70d-51d605105fc2%2Fjavisq_processed.png&w=3840&q=75)
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- Q5) An LTI system is characterized by the differential equation below: d² d = y(t)+ = y(t)+16.25y(t) == x(1) dt² dt dt a) Write the characteristic equation. b) Find the characteristic roots. c) Write the form of the zero-input response. d) Write the final zero-input response if yzı(0)=0 and dyzi(0)/dt=2. e) Plot the final zero-input response in Matlab/Octave and select the correct graph on the side: f) What are the characteristic modes for this system? 0 0.5 0 -0.5 0 0 5 (1) 5 (3) 10 10 0.5 -0.5 0.1 0 -0.1 -0.2 Am 0 0 5 (2) 5 (4) 10 10Q4) An LTI system is characterized by the differential equation below: d² = y(t) + 5 = y(t)+6y(t) = x(t) dt2 dt a) Write the characteristic equation. b) Find the characteristic roots. c) Write the form of the zero-input response. d) Write the final zero-input response if yzı(0)=2 and dyzi(0)/dt=-1. e) Plot the final zero-input response in Matlab/Octave and select the correct graph on the side: f) What are the characteristic modes for this system? 1.5 1 0.5 0 -0.5 1 2 3 4 (1) 0.5 0 -0.5 -1 -1.5 (2) 4 01234 (3) 1.5 0.5 234 (4)4. Simplify the following expression using a 4-variable Karnaugh map: (a) in sum-of- products form, and (b) in product-of-sums form. g(q, r, s, t) Em(3, 6, 7, 8, 9, 11, 12, 13, 15) + D(4, 5, 10, 14)
- 4. Solve for the zero-input, zero-state responses, and the total response of the system shown below. The initial conditions are given as y(-1) = 1 and y(-2) = 1, and x(n) = 3u(n). x(n) (n)Q) By using the Z-N method for the model which given below calculate (Kd) * G1 G2 r(s) e(s) u(s) c(s) 10 PID (S+1)(S+2)(S+3)(S+4) Your answerQ1:b) Choose the correct answer among the following: 1- If there is no pole at the origin then the system is of type: b- three C-zero d- none of these a- two 2- For the system whose characteristic equation is s² + 2s +4= 0, the damping ratio : a- 0.5 b-0.25 c-0.3 -0.4 3- Transfer function of a control system depends on : a- nature of output b- nature of input c-initial conditions d- system parameters only 4-The output of a feedback control system must be a function of: a-reference I/P & O/P b- output c-reference I/P d- reference I/P& error signal 5-The system is represented by its transfer function has some poles lying on the imaginary axis, it is : a- stable b-marginally stable c-Unstable d- none of these 6-The condition for stability of the system who's characteristic equation aos³+a,s²+a₂s+a;=0 is: a-a₁aaa₂ b-a₁a2a0a3 с- aja₁a₂a3 d-aa₁For the control system whose block diagram is shown below with G(s) = (2s2+8s+6)/(s3+6s2+8s): (a) Draw the signal-flow graph for this system in the phase variable canonical form and then: %3D 1- Show the state variables on your graph. 2- Write the state differential equation and the output equation in matrix form. (b) Repeat (a) and its branches but this time using the input feed-forward canonical form. U(s) G(s) Y(s)A) B) Which of the following is not true of a stable system? Its output is bounded for any input eigenvalues have negative real parts all poles lie on the left-half of the s-plane a bounded input yields a bounded output Consider a series connection of R=2 Ohms, C-3F, a switch, and a voltage source, E=12 Volts. Assume that the capacitor is initially uncharged. If the switch is flipped on at t=0, what will be the charge on the capacitor immediately after the switched is closed? 1.5 C OC 6C 5C Which of the following is not a prtimary function of feedback in control systems. Make an unstable system stable O Improve system performance Allow the possibility of making the output follow the input Amplify the input.Example: consider the open-loop T.F GH(S) =1/S(S+2). Design PD- controller such that time constant =0.5 sec and damping ratio =0.707.2. Let y= fct) be as shown. ) 40 ) Express ft) in terms of the isuwitch" 6) Find 2d2y(z)/dz2 + 3(dy(z)/dz) + 2y(z) = 3(dx(z)/dz) +2x(z) The above is a linear differential equation. Let's assume x(z) and y(z) as the input and output of an RC sytem respectively. a.Suppose there is an application of an impulse x(z) = δ(z) determine the output y(z) of the system. b.Determine the frequency response & transfer function of the system Also plot the 0-pole locations of the system.$2+9s+20 Given the plant transfer function G(s)= s3+6s²+11s+6 1) Obtain a state space representation in Diagonal Canonical form. 2) Draw the simulation diagram. 3) Is the system stable, why?Recommended textbooks for youIntroductory Circuit Analysis (13th Edition)Electrical EngineeringISBN:9780133923605Author:Robert L. BoylestadPublisher:PEARSONDelmar's Standard Textbook Of ElectricityElectrical EngineeringISBN:9781337900348Author:Stephen L. HermanPublisher:Cengage LearningProgrammable Logic ControllersElectrical EngineeringISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill EducationFundamentals of Electric CircuitsElectrical EngineeringISBN:9780078028229Author:Charles K Alexander, Matthew SadikuPublisher:McGraw-Hill EducationElectric Circuits. (11th Edition)Electrical EngineeringISBN:9780134746968Author:James W. Nilsson, Susan RiedelPublisher:PEARSONEngineering ElectromagneticsElectrical EngineeringISBN:9780078028151Author:Hayt, William H. (william Hart), Jr, BUCK, John A.Publisher:Mcgraw-hill Education,Introductory Circuit Analysis (13th Edition)Electrical EngineeringISBN:9780133923605Author:Robert L. BoylestadPublisher:PEARSONDelmar's Standard Textbook Of ElectricityElectrical EngineeringISBN:9781337900348Author:Stephen L. HermanPublisher:Cengage LearningProgrammable Logic ControllersElectrical EngineeringISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill EducationFundamentals of Electric CircuitsElectrical EngineeringISBN:9780078028229Author:Charles K Alexander, Matthew SadikuPublisher:McGraw-Hill EducationElectric Circuits. (11th Edition)Electrical EngineeringISBN:9780134746968Author:James W. Nilsson, Susan RiedelPublisher:PEARSONEngineering ElectromagneticsElectrical EngineeringISBN:9780078028151Author:Hayt, William H. (william Hart), Jr, BUCK, John A.Publisher:Mcgraw-hill Education,