A discrete-time system is described by the following equations -1 0 x(k+1)= 1 -2 0 1 0 x(k)+ 0 -3 y(k)=[110]x(k) u(k) a) Find the transfer function Y(z)/U(z). b) Transform the system equations into the controllable canonical form. c) Using the pole placement design technique, find the state feedback gain matrix K so that the compensated system has poles at (0.5, j0.5, -j0.5}

A discrete-time system is described by the following equations -1 0 x(k+1)= 1 -2 0 1 0 x(k)+ 0 -3 y(k)=[110]x(k) u(k) a) Find the transfer function Y(z)/U(z). b) Transform the system equations into the controllable canonical form. c) Using the pole placement design technique, find the state feedback gain matrix K so that the compensated system has poles at (0.5, j0.5, -j0.5}

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

See similar textbooks

Related questions

Q: A unity negative feedback closed loop system has a plant with the transfer function G(s) = , set…

Q: An op amp has a dc gain of 100 dB and a unity-gain frequency of 10 MHz. (a) What is the bandwidth of…

A: Note: as per our honor code, we are authorized to answer up to 3 sub-parts, we’ll answer the first…

Q: QUESTION 4 Y(s) R(3) (a) With aided by an appropriate diagram, derive and obtain the transfer…

A: Consider a positive feedback control system having plant transfer function Gs and feedback gain…

Q: PROBLEM-4 transient analysis of this system; R(s) a. b. G₁ ): Consider the following unity feedback…

Q: G(s): = s²+2s+1 s³ +0.2s²+s+1

Q: Q-2 A unity feedback System has a forward Transfer Function G(s)=100(s+1)/(s^2+7s+10)] a) Draw the…

Q: For a plant with transfer function G_(s) = s+8 Calculate the proportional controller gain Kp that…

A: Controller: Controller is a device which minimize the difference between process value and desired…

Q: A unity Feedback system is characterized by open loop transfer function G(s) = K / S(S+40) %3D The…

A: we will find closed loop transfer function and we will compare with standard second order transfer…

Q: Q1) A closed loop system is shown below the input is W(s) and the output is Z(s) (s + 1) (s + 5) 1 1…

A: Control systems are represented by transfer function. This can be written in both time domain and…

Q: For the control system with unity feedback and forward transfer function: k(s + 12) G(s) = s(s² +…

A: Zeros of function = -12 Poles of function = -8+2i,-8-2i Following are the rules to plot the root…

Q: 2) A position control system uses the principle of velocity feedback, as shown in the following…

A: Please refer below pages.If you have any doubts feel free to ask.Explanation:Step 1: Step 2: Step 3:…

Q: B) Design a circuit using operational amplifiers, where the output voltage Yis given as, Y=…

A: Operational amplifier: An operational amplifier is an integrated circuit comprised of two input pins…

Q: The transfer function T(s) of a negative feedback control system is 2s/(s² + s + 2). If the…

A: Given: Closed loop transfer function, Ts=2ss2+s+2 Open loop transfer function, Gs=2s+1

Q: 7.For the unity feedback closed-loop system with forward transfer function K G(s) = 2 +5s +1) (a)…

A: In this question ,we will find range of K for system stable..And staady state error for different…

Q: Ex. 455. G (s)=k/(s(s+15)) is the forward transfer function of a unity-feedback closed- loop system.…

A: First find the break away points from given forward transfer function. Value of K at any value of S…

Q: a) The open loop transfer function of a unity feedback system is given by, K (1+0.25s)…

A: Given:Open loop transfer function of a unity feedback system, we need to sketch the root locus of…

Q: Consider a unitary feedback-controlled system with a direct chain transfer function given as. G(p)=-…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: A) 2.63

Q: For the open-loop pole-zero plot in the following figure (with unity feedback): R(S) G(s) with G(s)-…

A: Given, Gs=ks+1s+2s+3.

Q: 1 A control system has a plant G(s) feedback. = " a controller Gc(s) = K, and a unity s(s-4) a)…

Q: K (s+1) G(s)H(s) = s (s?+4s+8)

Q: An analog system with transfer function G(S) =is sampled through zero-order hold sampler with…

Q: Consider a unity feedback control system with open loop transfer function G(s) = K(s+1)/s(s+2)(s+3)…

Q: Ex. 460. G(s)=k(s+38)/(s(s+33)) is the forward transfer function of a unity- feedback closed-loop…

Q: Y(s) With aided by an appropriate diagram, derive and obtain the transfer function, for R(s)…

Q: Q.2. Consider the control system shown in figure (2), fined the final transfer function C(s)/R(s) By…

Q: fi. Aclosed-loop feedback system is shown in following figure R(s) K C(s) s(s–1)(s+5) 1+s (1) Find…

A: We will find close loop gain , and then we will find characteristics equation to find out range of k…

Q: Question 4. We have a biomedical measurement set-up that can be modeled as a second order system…

A: Disclaimer: Since you have asked multipart questions, we will solve the first three subpart for…

Q: D(s) R(s) + E(s) K PO C(s) s+1 H + Figure 220

Q: Ex. 440. G (s)=k/ ( (s+2)(s+ 8)) is the FTF of a unity-feedback closed-loop system. respect to k.…

Q: a) QUESTION 1 A control system has been identified to have the block diagram as shown in Figure Q1.…

Q: The root locus method consists of determining in the s-plane the desirable positions of the poles of…

Q: 7.For the unity feedback closed-loop system with forward transfer function K G(s) = 2 +5s +1) (a)…

Q: 10 For a plant with transfer function G,=Te L6YG IZ design a closed loop system with a proportional…

Q: Q.4. Consider a unity feedback control system with feed forward :transfer function is .Q.4 G(s)…

A: Step 1: Step 2:

Q: A unity feedback system is shown in Figure Q1. R(s) C(s) K G() Figure Q1 Given that K(s -4s +8) G(s)…

A: Since you have asked multiple questions in a single request, we will be answering only the first…

Q: Find the relation between error constants (Kp, Kv, Ka) and steady state error (e). Find error…

Q: Copy the control system shown in Figure Q2 into your answer book, labelling the actual output,…

Question

A discrete-time system is described by the following equations
11
0
0 x(k)+
-1 0
x(k+1)= 1 -2
0
0 -3
y(k)=[110]x(k)
u(k)
a) Find the transfer function Y(z)/U(z).
b) Transform the system equations into the controllable canonical form.
c) Using the pole placement design technique, find the state feedback gain matrix K so
that the compensated system has poles at {0.5, j0.5, -j0.5}

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Given:

VIEW

Step 2: Determination of transfer function

VIEW

Step 3: Determination of transfer function

VIEW

Step 4: Transformation to controllable canonical form

VIEW

Step 5: Determination of state-feedback gain matrix

VIEW

Step 6: Determination of state-feedback gain matrix

VIEW

Solution

VIEW

Step by step

Solved in 7 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Mathematical Modeling of Mechanical System

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.

Similar questions

Q6) For the open loop transfer function G, 100 s(s + 20) with a unity feedback Determine the step. ramp and parabolic error coefficients ( Kp. K, and Ka ). and draw the output response?
Consider a unity feedback system with the following open loop transfer function: G(s) = 5.7/[s(s+ 4) (s+20)] Using the second Ziegler-Nichols method design the PID controller G₂ (s) = K₂ (1+-+T₂5) The critical gain Kis a. 202.11 O b. 134.74 O c. 269.47 O d. 404.21 O e. 336.84
The maximum overshoot for a unity feedback control system having its forward path transfer function given below is to be reduced from 60% to 20%. The system input is a unity step function. Determine the factor by which K should be reduced to achieve the said reduction
Consider the following electrical system: R L C= Uc The equations describing the system dynamics are the following: di(t) и(t) — L- +(R, + R, )i(t)+u.(t) dt du (t) C- = i(t) dt Choose as state variables: x, (t) =u¸(t) and x,(t) = i(t). 2.
A closed loop feedback system has the following response specifications: a) Mp s 16% b) Settling time ts 5 6.9 sec c) Rise time tr 1.8 sec If the transfer function for the above closed loop system can be approximated by a simple second order system, sketch the region in the s-plane were the closed-loop transfer function poles can be placed.
please explain step by step
i need the answer quickly
For Wheatstone bridge circuit, the following values are given. Vsupply=120V; R₁ = 15 №; R₂ =3002; R3 = 30; R4 = 60; R5 = 300 • What is the voltage across R5? OV 45V 24 V 36 V Vsupply 2 m
6 - Forward path transfer function is applied to the input of a negative unit feedback system given as below, and the overrun rate at the output of the system is given as% OS = 5.4%. K G(s) = s(s +1) In this case, what is the damping rate of the system? A) 0.63 B) 0.57 C) 0.61 D) 0.68 E) 0.55
7) Which of the following is correct for the root locus that starts when the gain value is K-0 ends at K? a) It starts at finite and infinite zeros and ends at finite and infinite poles. b) It must be symmetrical with respect to the imaginary axis. c) The total number of branches is equal to the number of open-loop zeros. d) It must be symmetrical with respect to the real axis. e) It cannot intersect with the real axis.
A second-degree process is controlled using a closed-loop feedback control system and a Pl controller. Using the transfer functions given below: Gp (s) 2 (4s + 1)(s + 1) Ga(s) = (s + 1) G₂ (s) = G(s) = 1 a) Produce the transfer function of the closed loop system for setpoint change. b) Derive the transfer function of the closed loop system for the disruptive effect. c) Kc values that ensure the stable operation of the control system in the case when ti = 4 determine. Can setting K to very large values lead this closed loop control system to an unstable state? 3 b d) Determine the dynamic behavior of the control system in the case when Kc=2 and Ti= 4 (over- damped, critically damped, underdamped). If the control system is underdamped, calculate the damping coefficient.
Q4. For the unity feedback control system with forward transfer function K(s+5) G(s) = s(s+1)(s+2) (A) Draw bode diagram at k=20. (B) Find the values of G.M. and P.M., is the system stable?