Consider a linear system of the form dx dt where u is a scalar and d...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Consider a linear system of the form dx dt where u is a scalar and d is a disturbance that enters the system through a disturbance vector FER". In this problem, we will explore how integral feedback compensates for a constant disturbance by giving zero steady- state output error even when d 0. = Ar + Bu + Fd, y = Cx, (a) First, apply basic state feedback u = - Kafr to the system. With an appropriate choice of Ksf, the closed loop system will stabilize and approach a steady state equilibrium, xe,sf. Je, sf- Solve for this equilibrium point to show that, for a nonzero disturbance d, this system will have a nonzero steady state error. (b) Next, we will set up the system to do integral control: Augment the state space description of this system to include a state z that inte- grates the output of the system. In other words, let the augmented system be: 40-40 + Bu + Fd, and find A, B, and F. You are welcome to write these as block matrices. d dt (c) Apply integral control (with r = 0, since our aim is to reject dis- turbances): u = -Kic-kiz to the augmented system from part b. With an appropriate choice of gains Kic and k, the system will again stabilize and approach a stable equilibrium point Te,ic, Zeic Ye,ic. Solve for this equilibrium point. Under what conditions on F does this controller enable the system to reach zero steady-state error on the state, Te,ic = 0? Consider a linear system of the form dx dt where u is a scalar and d is a disturbance that enters the system through a disturbance vector FER". In this problem, we will explore how integral feedback compensates for a constant disturbance by giving zero steady- state output error even when d 0. = Ar + Bu + Fd, y = Cx, (a) First, apply basic state feedback u = - Kafr to the system. With an appropriate choice of Ksf, the closed loop system will stabilize and approach a steady state equilibrium, xe,sf. Je, sf- Solve for this equilibrium point to show that, for a nonzero disturbance d, this system will have a nonzero steady state error. (b) Next, we will set up the system to do integral control: Augment the state space description of this system to include a state z that inte- grates the output of the system. In other words, let the augmented system be: 40-40 + Bu + Fd, and find A, B, and F. You are welcome to write these as block matrices. d dt (c) Apply integral control (with r = 0, since our aim is to reject dis- turbances): u = -Kic-kiz to the augmented system from part b. With an appropriate choice of gains Kic and k, the system will again stabilize and approach a stable equilibrium point Te,ic, Zeic Ye,ic. Solve for this equilibrium point. Under what conditions on F does this controller enable the system to reach zero steady-state error on the state, Te,ic = 0?
Expert Answer:
Related Book For
Applied Regression Analysis and Other Multivariable Methods
ISBN: 978-1285051086
5th edition
Authors: David G. Kleinbaum, Lawrence L. Kupper, Azhar Nizam, Eli S. Rosenberg
Posted Date:
Students also viewed these mechanical engineering questions
-
QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...
-
Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...
-
Determine the degrees of freedom under the following conditions: (a) Tl-20 wt% Pb at 325 C and 400 C; (b) Tl-40 wt% Pb at 325 C and 400 C; (c) Tl-90 wt% Pb at 325 C and 400 C. Refer to the phase...
-
Use following info for Middle company: VII. Use following info for Middle company: - sales account included an $800,000 (net of tax) loss due to flood destroying a facility, never happened before. -...
-
The pendulum consists of the slender rod OA, which has a mass per unit length of 3 kg/m. The thin disk has a mass per unit area of 12 kg/m2. Determine the distance y to the center of mass G of the...
-
In a study to develop the growth behavior for protozoa colonization in a particular lake, an experiment was conducted in which 15 sponges were placed in a lake and 3 sponges at a time were gathered....
-
Arrington Company manufactures T- shirts printed with tourist destination logos. The following table shows sales prices and projected sales volume for the summer months: Prepare a sales budget for...
-
A $1,000 par value bond that pays interest annually just paid $106 in interest. What is the coupon rate? Q2) A 09.60% coupon, 21-year annual bond is priced at $986. What is the current yield for...
-
The worm shaft shown in part a of the figure transmits 1.2 hp at 500 rev/min. A static force analysis gave the results shown in part b of the figure. Bearing A is to be an angular-contact ball...
-
it's a case study Recommendation: In one paragraph of at least five or six sentences in length,write your final recommendation of a solution or solutions to solvethe problem(s) from your case study,...
-
Why is it so important for a healthcare organization to develop a five-year strategic financial plan,? explain
-
The decedent was married at the time of death. He was survived by his wife and children. The following were presented to you and you were asked to compute the 1) exclusive and conjugal properties...
-
Describe four approaches to quality management. Which approach do you believe is most effective? Why?
-
Consider the improper integral (a) Find the value of the constant C for which the integral converges. C = Answer: -7x 1 = [ (-=-= 7+ 1 - 380 + ) dr. I x +1 3x 4 0 (b) Evaluate the integral for the...
-
Find the indefinite integral. Check your answer by differentiation. [2x(x +3) dx = +C
-
Define the Wiener-Hopf approximation, apply it to a Neumann problem.
-
Do public and private companies follow the same set of accounting rules? Explain.
-
Assume that the following table came from an analysis of a randomized-blocks study. a.-f. Complete the ANOVA table by determining the numerical values for the entries a through f. Show your work. g....
-
In Section 13.6, adjusted mean BMI values were obtained for the two nominal variables exercise and tobacco_now. A drawback of the approach used is that these four adjusted means were estimated for...
-
Refer to the residential sales data in Problem 19 in Chapter 12. Use the computer output given below to answer the following questions. a. State an ANACOVA regression model that can be used to...
-
Which of the following is not a reason that the prevention and detection of fraud resulting from management override and collusion presents a significant challenge for the antifraud community? 1....
-
Which of the following statements best describes corporate governance with respect to fraud? 1. Auditors are primarily responsible for the detection of fraud, the Board of Directors for the...
-
Which of the following is not an inherent part of Statement on Auditing Standards, No. 99/113? 1. Greater scrutiny of the chief executive and chief financial officers personal financial condition 2....
Study smarter with the SolutionInn App