Suppose that the characteristic equation for a closed-loop discrete time system is given by the expression F(z) = 2z³+z²+z+1=0 Test the stability of the system using Routh-Hurwitz criterion.
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- Assume that the system recorded by the block diagram is reliable. a) Determine the position constant, kp, of velocity, kv, and of acceleration, ka, of the system. b) Determine the steady-state errors for a magnitude 5 input in step, ramp, and parabola, respectively.The following closed loop system damping ratio, natural frequency, system poles,% Overrun value and Calculate the relaxation time. A=16 B=90 X=32 Y=45Which of the following is not considered for the formation of Lagrangian function solution? a. Equality Constraint b. Cost function c. Objective Function d. Inequality Constraint
- H6. You are planning a trip to a new high altitude space station. Your spacecraft is in an initial 200 km altitude circular earth orbit. Performing a Hohmann transfer compute: (a) the TOTAL delta-v required for a Hohmann transfer to a 1000 km altitude coplanar circular earth orbit. answer choices a. Dv = 445.38 m/sec b.Dv = 421.309 m/sec c.433.778 m/sec d. 220.00 m/secQ1. Consider the following characteristic equations. Determine the values of K that corresponds to a stable system. Use the Routh-Hurwitz criterion.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.
- 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)?Determine the systems stability using the Routh Hurwitz Criterion for Stability. 1. Number of Poles in the Left-Half Plane?2. Number of Poles in the jw-axis? 3. Number of Poles in the Right-Half Plane? 4. What is the stability condition of the given system? (stable, unstable, or maginally stable)In order for the closed loop system, whose block diagram is given below, to be stable, the parameters K1 and K2 must be determined. Calculate the values it will take. Draw the graph of the stable region in the K1-K2 plane. (Hint: Routh-Hurwitz use the method)
- III. Find the stability of the system using the Routh-Hurwitz criterion.Which row represent the most stable system and why? nyquist and root locus plot attached.A) Sketch the complex plane and locate poles for 2 cases: 2 Second Order underdamped systems where both systems have the same settling time, but system #1 has a larger overshoot. B) Sketch the time response for each system in part A to a unit step input. Show clearly which system is 1 and 2. Show the relative values of the overshoot for both systems, the overshoot time, damped natural frequency and time to steady state .