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Robotics Control System Consider a closed-loop system with an open-loop transfer function G(s)H(s) = \frac{10(s + 0.5)}{s^2(s + 2)(s + 10)} Apply the Nyquist stability criterion to determine the closed-loop stability of the system.202414m Robotics Control System Draw the root locus for G(s)H(s) = \frac{k}{s(s^2 + 2s + 5)} and find the range of 'k' for stability.20247m Robotics Control System The open-loop transfer function of a unity feedback system is given by G(s) = \frac{k}{s(1 + sT)} where k and T are positive constants. By what factor should the amplifier gain be reduced so that the peak overshoot of the unit-step response of the system is reduced from 75\% to 25\%.20247m Robotics Control System Find the number of poles in the left half-plane, the right half-plane, and on the j\omega-axis for the characteristic equation p(s) = 2s^5 + 3s^4 + 2s^3 + 3s^2 + 2s + 1 = 020247m
PreviousFor system A = \begin{bmatrix} 0 & 1 \\ -1 & -3 \end{bmatrix}, B = \begin{bmatrix} 0 \\ 1 \end{bmatrix}, check controllability using rank. (i) Rank = 2, controllable (ii) Rank = 1, uncontrollable (iii) Rank = 2, not observable (iv) Rank = 1, observableNextDraw the root locus for G(s)H(s) = \frac{k}{s(s^2 + 2s + 5)} and find the range of 'k' for stability.