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This assignment will help you understand the concepts of feedback and control systems, as well as...
' 1. Review Question a) Name three applications for feedback control systems. b) Functionally, ho...
' 1. Review Question a) Name three applications for feedback control systems. b) Functionally, how do closed-loop systems differ from open-loop systems? c) Name the three major design criteria for control systems. d) Name the performance specification for first-order systems. e) Briefly describe how the zeros of the open-loop system affect the root locus and the transient response. What does the Routh-Hurwitz criterion tell us? f) 2. Given the electric network shown in Figure. a) Write the differential equation for...
#I want you only to answer (b) Problem 1. Optimal Control. (30 pts.) a) Write 1-2...
#I want you only to answer (b)
Problem 1. Optimal Control. (30 pts.) a) Write 1-2 pages, in your own words, about basic concepts on optimal control. - What is a two-point boundary value problem? - What is the linear quadratic regulator? b) Consider the continuous time system 0 1 0 . + u (1) 0 0 1 and consider the cost J = So*(x+Qx + u?)dt (2) where 91 0 for qı > 0, 92 > 0 (3) 0...
Please be as descriptive as you can In Chapter 3, we have studied techniques for solving...
Please be as descriptive as you can
In Chapter 3, we have studied techniques for solving linear systems. Given the coeffi- cient matrix for the system, we can use these techniques to classify the system, describe the qualitative behavior of solutions, and give a formula for the general solution. In this lab we consider a two-parameter family of linear systems. The goal is to better under- stand how different linear systems are related to each other, or in other words,...
Please help me complete this problem!!! Thank you and please write neatly!!! (c) Consider the following general second order linear initial value problem with linear variable coefficient:s (at +bi)y&...
Please help me complete this problem!!! Thank you and please
write neatly!!!
(c) Consider the following general second order linear initial value problem with linear variable coefficient:s (at +bi)y"+(at +b'+(ast+bs)y 0, y(0) (00 Use the Laplace Transform to find the ODE that is satisfied by Y(s) y(t)s). What is the order of the new equation? What can you say about the solution to this equation? What can you say about the solution to the original equation?
(c) Consider the following...
I need help with the matlab code, thank you. The purpose of this assignment is to...
I need help with the matlab
code, thank you.
The purpose of this assignment is to illustrate one important difference between linear and nonlinear models of oscillating systems. In an undamped, unforced linear system, the period of a periodic solution depends only on system parameters and not on the initial conditions, but in a nonlinear system the period can depend on the initial conditions Consider the following nonlinear differential equation, which models the free, undamped motion of a block attached...
Could you please try to explain to me how we get the solution because I want...
Could you please try to explain to me how we get the
solution because I want to understand the solution so that to be
solved step by step including all of the details
If the conditions for a time-invariant optimal control law are satisfied by a linear regulator problem, the constant K matrix must be a solution of the nonlinear algebraic equations Using this result, determine the optimal control laws for: a) The first-order system x(t)-ax(t) + u (t) with...
1. The Duffing equation is a non-linear second-order differential equation used to model certain damped and...
1. The Duffing equation is a non-linear second-order differential equation used to model certain damped and driven oscillators. The equation is given by -ax+3x3 = cos(wt) at medt dr. where function r = r(t) is the displacement at timet, is the velocity, and is the acceleration. The parameter 8 controls the amount of damping, a controls the linear stiffness, B controls the amount of non-linearity in the restoring force, and 7 and w are the amplitude and angular frequency of...
(2) Why First-Order Systems (of a Specific Form) Are Sufficient: In class I stated that all syste...
Please be specific, thanks！
(2) Why First-Order Systems (of a Specific Form) Are Sufficient: In class I stated that all systems of differential equations can be turned into first-order systems. And I wrote that first-order systems can be written in the form: For 3-by-3 system, the form is: r-f(r, y,z,t) y- g(x, y, z, t) , = h(z,y,z, This can be generalized to any number of unknown functions. a) Notice that r', y', and z are not included in the...
Week W8 Written Assignment: Due on Wednesday, October 16. 1. When we discussed the method of...
Week W8 Written Assignment: Due on Wednesday, October 16. 1. When we discussed the method of undetermined coefficients for finding a solution to ay" + by' + cy=9(1), we had three rules. "Rule 1" directed you to start with a guess of an linear combination (with undetermined coefficients) of all the terms that appear in g(t) and it's derivatives. "Rule 2" said that if your first guess is a solution to the corresponding homogeneous equation, you should multiply your initial...
PLEASE DO IN MATLAB Problem 8 (PID feedback control). This problem is about Proportional-Integral-Derivative feedback control...
PLEASE DO IN MATLAB
Problem 8 (PID feedback control). This problem is about Proportional-Integral-Derivative feedback control systems. The general setup of the system we are going to look at is given below: e(t) u(t) |C(s) y(t) P(s) r(t) Here the various signals are: signal/system r(t) y(t) e(t) P(s) C(s) и(t) meaning desired output signal actual output signal error signal r(t) y(t) Laplace transform of the (unstable) plant controller to be designed control signal Our goal is to design a controller...
' 1. Review Question a) Name three applications for feedback control systems. b) Functionally, how do closed-loop systems differ from open-loop systems? c) Name the three major design criteria for control systems. d) Name the performance specification for first-order systems. e) Briefly describe how the zeros of the open-loop system affect the root locus and the transient response. What does the Routh-Hurwitz criterion tell us? f) 2. Given the electric network shown in Figure. a) Write the differential equation for...
#I want you only to answer (b)
Problem 1. Optimal Control. (30 pts.) a) Write 1-2 pages, in your own words, about basic concepts on optimal control. - What is a two-point boundary value problem? - What is the linear quadratic regulator? b) Consider the continuous time system 0 1 0 . + u (1) 0 0 1 and consider the cost J = So*(x+Qx + u?)dt (2) where 91 0 for qı > 0, 92 > 0 (3) 0...
Please be as descriptive as you can
In Chapter 3, we have studied techniques for solving linear systems. Given the coeffi- cient matrix for the system, we can use these techniques to classify the system, describe the qualitative behavior of solutions, and give a formula for the general solution. In this lab we consider a two-parameter family of linear systems. The goal is to better under- stand how different linear systems are related to each other, or in other words,...
Please help me complete this problem!!! Thank you and please
write neatly!!!
(c) Consider the following general second order linear initial value problem with linear variable coefficient:s (at +bi)y"+(at +b'+(ast+bs)y 0, y(0) (00 Use the Laplace Transform to find the ODE that is satisfied by Y(s) y(t)s). What is the order of the new equation? What can you say about the solution to this equation? What can you say about the solution to the original equation?
(c) Consider the following...
I need help with the matlab
code, thank you.
The purpose of this assignment is to illustrate one important difference between linear and nonlinear models of oscillating systems. In an undamped, unforced linear system, the period of a periodic solution depends only on system parameters and not on the initial conditions, but in a nonlinear system the period can depend on the initial conditions Consider the following nonlinear differential equation, which models the free, undamped motion of a block attached...
Could you please try to explain to me how we get the
solution because I want to understand the solution so that to be
solved step by step including all of the details
If the conditions for a time-invariant optimal control law are satisfied by a linear regulator problem, the constant K matrix must be a solution of the nonlinear algebraic equations Using this result, determine the optimal control laws for: a) The first-order system x(t)-ax(t) + u (t) with...
1. The Duffing equation is a non-linear second-order differential equation used to model certain damped and driven oscillators. The equation is given by -ax+3x3 = cos(wt) at medt dr. where function r = r(t) is the displacement at timet, is the velocity, and is the acceleration. The parameter 8 controls the amount of damping, a controls the linear stiffness, B controls the amount of non-linearity in the restoring force, and 7 and w are the amplitude and angular frequency of...
Please be specific, thanks！
(2) Why First-Order Systems (of a Specific Form) Are Sufficient: In class I stated that all systems of differential equations can be turned into first-order systems. And I wrote that first-order systems can be written in the form: For 3-by-3 system, the form is: r-f(r, y,z,t) y- g(x, y, z, t) , = h(z,y,z, This can be generalized to any number of unknown functions. a) Notice that r', y', and z are not included in the...
Week W8 Written Assignment: Due on Wednesday, October 16. 1. When we discussed the method of undetermined coefficients for finding a solution to ay" + by' + cy=9(1), we had three rules. "Rule 1" directed you to start with a guess of an linear combination (with undetermined coefficients) of all the terms that appear in g(t) and it's derivatives. "Rule 2" said that if your first guess is a solution to the corresponding homogeneous equation, you should multiply your initial...
PLEASE DO IN MATLAB
Problem 8 (PID feedback control). This problem is about Proportional-Integral-Derivative feedback control systems. The general setup of the system we are going to look at is given below: e(t) u(t) |C(s) y(t) P(s) r(t) Here the various signals are: signal/system r(t) y(t) e(t) P(s) C(s) и(t) meaning desired output signal actual output signal error signal r(t) y(t) Laplace transform of the (unstable) plant controller to be designed control signal Our goal is to design a controller...
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