Problem 11. Consider a plant whose state-space description is i = Ax + B(u + v), y = Cx, where v is a disturbance input A = В - C = and the following state-feedback controller [k1 k2] x U = - where k1 and k2 are constants to be chosen (designed). 1. Compute the closed loop state-space model with input v and output y, leaving your answer as a function of ki and k2. 2. Compute the closed loop transfer function from input v to output y, leaving your answer as a function of kı and k2. 3. Determine values of k1 and k2 so that the closed loop transfer function from v to y becomes' 1 s +1 Designing a controller to achieve a specific closed loop transfer function is called model matching design.

Problem 11. Consider a plant whose state-space description is i = Ax + B(u + v), y = Cx, where v is a disturbance input A = В - C = and the following state-feedback controller [k1 k2] x U = - where k1 and k2 are constants to be chosen (designed). 1. Compute the closed loop state-space model with input v and output y, leaving your answer as a function of ki and k2. 2. Compute the closed loop transfer function from input v to output y, leaving your answer as a function of kı and k2. 3. Determine values of k1 and k2 so that the closed loop transfer function from v to y becomes' 1 s +1 Designing a controller to achieve a specific closed loop transfer function is called model matching design.

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

Similar questions

Consider the unit feedback control system shown in Fig. 4 for the control of a single- link rotational manipulator that includes a command shaping gain K as shown. The moment of inertia I = 5 kg m2 and the rotational viscous friction coefficient is br = 2 N m s/rad.a) Find the closed loop transfer function from the command angular velocity input ωr(t) to the angular response output ω(t) in terms of the system parameters I, br and K.b) For a unit step angular velocity reference input ωr(t) find the value of the gain K such that perfecttracking is achieved, i.e., the errore(t) = ωr(t) - ω(t) has steady-state value ess = 0 when t → ∞.c) Use Laplace Transform methods to find the closed-loop response ω(t) for the above values of the system parameters and gain K.
Consider the unity-feedback control system with the following feedforward transfer function: G(s) = K / s(s2+4s+5) (1) Plot the root locus. (2) Determine closed-loop poles that have the damping ratio of 0.5. Find the gain value K at this point. (3) For what value of K is the overshoot less than 10% and the maximum rise time less than 1.5s.
The control system G(s) = Kp / s (s+2) (s+6) has a unity feedback a. Kp is variable, discuss stability by using Routh Hurwitz method. Mark the poles ofthe system on root-locus curve below. b. When Kp = 26.7 , roots of the characteristic equation becomes s1= -0.6-1.89i, s2= -0.6+1.89i and s3= -6.8. Are you happy about this case? How do you evaluate,why ? c. How the root locus and step response would be effected by adding a controller Gc= Kp ( s + 0.5)2/ s . Give a comment about the addition of Gc on root locus andon step response.
When a unit step input is applied to the closed-loop control of a system with G(s) function and controlled by proportional control, the system operates at the point A= -2.5+j3.57. A) For the relevant operating point, Calculate the proportional gain K. Find the value of ζ. Find the percent (%OS) overshoot Find the natural frequency of the point of interest. B) For the PD controller to be added when the same system is wanted to be operated at the point B= -7.8+j8.77, Find the controller zero value. Find the new K value. Find the ζ value of the relevant point. Find the percent (%OS) overshoot Find the natural frequency of the point of interest.
below is the representation of a linear control system in the state space.a) examine the controllability and observability of this systemb) estimate the unit digit response by finding the current eigenvalues of this systemC) find the feedback Matrix K= (k1 k2) that must be applied so that the system can be a two - layer root in-2
Assume any finite duration discrete time signal x(n) following the necessary condition satisfying the property of energy signal of your own choice. Now consider a discrete time system whichperforms Amplitude scaling operation followed by time reversal operation based on y(n) = ax(n) + x(-n). Sketch the output of resultant signal. Now classify and justify your answer with necessary and sufficient conditions that whether the above system based on all types of system.
Consider unity negative feedback applied to the system: G(s) = k/s(s^2+4s+5) (a) Give a complete sketch of the root locus (0 ≤ k ≤ ∞) for this system assuming a unity feedback configuration. Make sure you show all the significant features on your sketch. Give particular attention to the angle of departure from the complex poles. (b) Indicate on your root locus diagram the point at which the damping ratio of the dominant poles is 0.5.
1-A unit feedback system has G(s) = 1/ 0.5s. Derive the time response (c(t)) of the system, when subjected to a step input signal. 2-A unit feedback system has G(s) = (5+3)/s(-2)(s+6). (a) Obtain the characteristic equation (b) Justify the stability of system.
the unity negative feedback controller shown below, in whichR(s) = thetades(s) is the desired pitch angle, H(s) is the transfer function computed in part (a), and C(s) =K(s+1)/s, a proportional-integral (PI) controller with a single control gain K. (a) Suppose that you want the pitch angle to increase at a constant acceleration of 1 deg/s2. Toachieve this, you set the desired pitch angle to a parabolic function, r(t) = 0.5t2 * us(t), where us(t) is the unit step function. What is the system type n? Calculate the steady-state error ess of the closed-loop system as a function of ?(b) Compute the closed-loop transfer function, Hcl(s) = Y(s)/R(s). Write the charateristic equation of the closed-loop system in the form 1 + KL(s) =0
The loop gain GH of a closed loop system is given by the following expression K/s(s+2)(s+4), The value of K for which the system just become unstable is ?
For a unity-feedback system with G(s) = K / s(s + 20)(s + 40) operating with a 20% overshoot, design a compensator to decrease the settling time by a factor of 2 without affecting the percent overshoot:i. Find the uncompensated system's dominant poles, gain, and settling time. ii. Find the compensated system's dominant poles and settling time. iii. Find the compensator's pole position and required gain. (Assume the compensator’s zero is at -20).
The block diagram of a control system is shown in Figure 4. The gain K is to be tuned to optimize the response of the system. To do so, the range of value for Kneed to be evaluated to make sure that the tuning will not go into instability. Root locus is the tool that can help in predicting the response of the system by plotting all the possible positions of poles as K is modified. (a) Develop the root locus sketch for the system. (b) Find the exact point and gain where the locus crosses the 0.45 damping ratio line. Conclude therefore the range of K within which the system is stable.