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The closed-loop transfer function of a system is
Determine the range of K1 in order for the system to be stable. What is the relationship between K1and K2for stability? [Section: 6.4]
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Control Systems Engineering
- The Gilles & Retzbach model of a distillation column, the system model includes the dynamics of a boiler, is driven by the inputs of steam flow and the flow rate of the vapour side stream, and the measurements are the temperature changes at two different locations along the column. The state space model is given by: x = 0 00 -30.3 0.00012 -6.02 0 0 0 -3.77 00 0 -2.80 0 0 Is the system?: a. unstable b. C. not unstable x+ 6.15 0 0 0 0 3.04 0 0.052 not asymptotically stable d. asymptotically stable -1 u y = 0 0 0 0 -7.3 0 0 -25.0 Xarrow_forwardFor the system represented by the following block diagram, Find a) The Closed-loop Transfer function. b) Characteristic equation. c) Type and Order of the system. c) Time-domain Specifications ( Delay Time, Peak Time, Rise Time, Settling time, and Percentage overshoot). R(s) C(s) G(s) H(s) Where G(s) and H(s) are given as : 324 G(s) = s(s+6) H(S) : 1arrow_forwardöialg äbäi the open - loop transfer function of the system given as in figure below, what is error steady state * for an input r(t)=1+4t+3t^2 10 (s+1) G(s) s²(5s+6) 3.6 O 5.6 O 7.6 O 10.6 Oarrow_forward
- a) Suspension system of a car. Finding the transfer function F₁(s) = Y(s)/R(t) and F₂ (s) = Q(s)/R(t), consider the initial conditions equal to zero. car chassis www K₂ M₂ 1 Tire M₁ K₁ B₁ y(t)= output q(t) r(t)= input Where [r, q, y] are positions, [k1, k2] are spring constants. [B₁] coefficient of viscous friction, [M₁, M₂] masses. b) Find the answer in time q(t) of the previous system. With the following Ns values: M₁ = 1 kg, M₂ = 0 kg, k₁ = 4 N/m, k₂ = 0 N/m, B₁. = 1 Ns/m, considered m a unit step input, that is, U(s) = 1/sarrow_forwardQUESTION 1 Given a system model, d²x (t) dx (1) dt² dt x (0) = 1 dx (1) dt +2- +x(t) =f(t) t=0 What is the transfer function, X(s)/F(s)? O X(s) s² + s+1 F(s) 1 O X (s) F(s) O X (s) F(s) = 0. X (s) F(s) = 1 s²+2s+1 1 s²+1 S s²+2s+1arrow_forwardequations: QB: Obtain the transfer function of system defined by the following state space Hi 0 4 8 [x₁ 0 8 5 X2 + -10-30-20x330/u [123] [x1 Y=[1 2 0] X₂ X3 snp-you tvavearrow_forward
- For the given close-loop system transfer function, determine its stability using Routh-Hurwitz Test for Stability.1. What is the stability of the system? (Stable, Unstable, Marginally Stable)arrow_forwardFind the equivalent closed loop transfer function for the system R(s) E(s) Y(s) 3 K s+2 10 s+10 (Ctrl)arrow_forwardR(S) K D s+5 Find Open Loop Transfer function XIS s+2 s+3 Y(s)arrow_forward
- Part A: Find the steady-state solution of the mechanical system shown below: k mu E m G(s) F(t) F(t) = F sin wt Part B: Sketch the root locus for the transfer function: Ks (s+ 4) (s + 3)(s + 1)arrow_forwardConsider a system described by the following dynamic equation: 5x + 17* + 20x + 8x = 4f(t) -0.9g(t) Submit to Connect: What form is this dynamic model in? a. Draw the block diagram for this system if x(t) is the output and f(t) is the input to the system. b. Write out each of the Transfer Functions for this system, and describe the expected characteristic behavior of the system and the differences between the response x(t) to f(t) and g(t). c. Define the state equations for this system. Also define the A, and B matrices for the system.arrow_forward11. Consider a system that can be modeled as shown. The input x in (t) is a prescribed motion at the right end of spring k 2. Find X(s) the system transfer function Xeq(s)* m k₂ ww Xin The values of the parameters are m= 30 kg, k ₁=700 N/m, k 2= 1300 N/m, and b=200 N- s/m. Write a MATLAB script file that: (a) calculates the natural frequency, damping ratio, and damped natural frequency for the system; and (b) uses the impulse command to find and plot the response of the system to a unit impulse input.arrow_forward
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