A DISCRETE-TIME system has the poles p1 = -0.1, p2 = 0.4, p3 = 1. Describe the stability of the system. Stable Marginally stable Unstable Unknown
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- State the equation that mathematically represents the system. All in domain X(s) hint: there are 2 equations k₁ oooo m₁ B₁ X1 (1) B3 k₂ 0000 M2 B₂ x₂ (1) k3 0000Characteristic equation of a system is given by: C = s³ + 4s² + 25s + K = 0 %3D determine the range of values of K for which the system is stable. Use Roth Hurwitz stability criteria.Using similarity transform we transform a system into a different system. Select one: True False
- The Routh-Hurwitz criterion to be used to determine the stability of a system with a characteristic equation given by 85 + 2s4 + 2s3 + 4s² + 11s + 10 Comment on the stability of the system. Neutral Stable Unstablexa 0- 1 point) Which of the systems presented on Fig. 2 is stable and which unstable? (a) t Fig. 2. System response (b) AA velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): A. Use Laplace transform of the differential equation to determine the transfer function of the system.
- A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): 1. What is the order of this system?A system has the following characteristic equation: s+ s+ 3s+ 2s + 2 = 0 Using the Routh-Hurwitz method, checka. How many roots are to the right of the imaginary axis?b. Is the system stable?.A linear, time-invariant system is marginally stable if the natural response: oscillates as time approaches infinity grows without bound as time approaches infinity approaches zero as time approach infinity approaches infinity as time approach infinity
- 4.A system has the characteristic equation D(s) = s' + 2s² + (k+1)s+ 6 = 0 2. Find the range of K for a stable system:) Determine the equivalent mass of the system shown in Figure Q.A3c. X m 2r m Figure Q.A3c. m WE For the system shown in Figure QA1a write appropriate response variables and find the degrees of freedom. r= 10 cm /= 1.5 kg-m² m = 10 kg nollos 2k1. Linearized the dynamic model of the system shown below: - cô – mgL sin 0 + u. daor at| L sine mg