A) Consider a mechanical translational system having mass M-2kg, damping coefficient B=24Nt per meter per second, and spring constant, K=18Nt per meter. The damping ratio is 02 01 Oo O 0.5
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- Consider the continuous-time model of the overhead crane proposed in Problem 7.10 with mc = 1000 kg, ml = 1500 kg, and l = 8 m. Design a discrete full-order observer state feedback control to provide motion of the load without sway. Problem 7.10 The following differential equations represent a simplified model of an overhead crane:3 where mC is the mass of the trolley, mL is the mass of the hook/load, l is the rope length, g is the gravity acceleration, u is the force applied to the trolley, x1 is the position of the trolley, and x3 is the rope angle. Consider the position of the load y = x1 1 + sinx3 as the output. (a) Determine a linearized statespace model of the system about the equilibrium point x = 0 with state variables x1, x3, the first derivative of x1, and the first derivative of x3. (b) Determine a second statespace model when the sum of the trolley position and of the rope angle is substituted for the rope angle as a third state variable.7.Differential equation for a simple wheelchair with a suspension system (bumper) can be written as: ?2???2+??????+????=1???. Fe is the gravitational force exerted by the sitting person, 800 N; “m” is mass of the wheelchair, 25 kg; “Ks” is the stiffness (inverse of compliance) of the spring, 2500 N/m; the damping coefficient of the dashpot “B” is 500N/(m/s). How much is the damping coefficient ?of the system? The original of the problem is attached.Consider two systems one is second order and the other is third order. The characteristic equations are: as2+bs+c for the second order and as3+bs2+cs+d for the third order, where a,b,c,d are positive real numbers. Then which of the following is correct with regard to the stability of these two systems? a. stability of either system cannot be confirmed with the given data b. third order is definitely stable but second order cannot be confirmed c. both systems are definitely stable d. second order is definitely stable but third order cannot be confirmed
- Which of the following is not true? a.Increasing system gain increases stability b.poles farther to the left of imaginary axisimprove speed c.steady-state errors are important in the studyof unstable systems d.multiple poles on the imaginary axis improvessystem stabilityA) Reduce the block diagram. B) G1(s)= 2/s, G2(s)= 1/4s+2, G3(s)=4, H(s)=0.5 according to the given values, find the system's time constant, natural frequency, and damping rate, and explain what dynamic behavior it will exhibit accordingly. C) G1(s)= 2/s, G2(s)= 1/4s+2, G3(s)=4, H(s)=0.5 Find the poles and zeros of the system according to the given values. Accordingly, specify whether the system is stable. Find the unit digit response (reverse laplace)A mass spring system is given by the ODE: 2x′′ +cx′ +8(π^2)x=0 a) What are the values of c ≥ 0 for which the system is: -Overdamped -Critically damped -Underdamped b) Pick a value of c > 0 (note you cannot use c = 0) which is underdamped, and write down a general solution of the system. c) Suppose c = 0, but there is an external force which is given by the periodic extension of F(t) = 4t, for −1 < t ≤ 1 That is the ODE is given by: 2x′′ +8(π^2)x=F(t), Does resonance occur? d) What is the Fourier series of F given in c)?
- The equation in Excel should be of the form: , where A and b are constants. In this case, x is the independent variable representing time, and y is your current measurements. A represents the initial value of the current from , and b represents the reciprocal of the time constant, RC. This means that b = 1/RC. Since RC = (100,000 Ω)(100x10-6 F) = 10 s, therefore the reciprocal should be: b = 0.1. It is this value that want to use to verify the theoretical equation in the Background. Please answer questions in image.Enter the value of the K coefficient required for the marginally stable/unstable system of a system whose characteristic equation is given as s3+6s2+3s+K=0.Find out following:i. Sketch the root locus.ii. The number of branches of the root locus.iii. The value of ? and gain ? where the locus crosses the ??-axis.iv. The breakaway and break-in point on the real axis.
- G(s)=((s+1)*(s+15))/((s+0.1)*(s+2.5)*(s+120)*(s+240)) 1-draw nyquist 2- Nyquist criterion, compute the number of unstable poles of the closed loop system as a function of K 3-determine for which values of K the closed system is stable.The translational mechanical system shown in Figure Q1 is at rest for t < 0. The force u(t) is the input to the system and the displacements x1(t) and x2(t), are measured from their respective equilibrium positions. Ifm1 is1kg,k1 =k2 =k3 is1N/mandb1 =b2=b3=is1N-s/m,determine the transfer function for the system (?(?) = ?1(?)) ?(?)The mathematical models of some continuous time systems are given above. x(t) is the input signal of the system, and y(t) is the output signal of the system. Which of the following systems is linear and which is nonlinear? For linear systems, write "linear" in the space next to the option. For non-linear systems, write "non-linear" in the space next to the option.