2. (25 points) Consider the following characteristic equation: $4 +253 + (4 +K)s2 +95 + 25...
control systems
1) Using Routh Hurwitz Stability Criteria, determine whether the following system of equation is stable or not. a) S4+253+3S2+45+5=0 2) Using the Routh Hurwitz stability criterion, determine the range of K for stability of the following characteristic equation. a) s4+2s8+(4+K)s2+9s+25=0 3)Sketch the root-locus of the following systems a) G(s)H(s) = s(s+1)(s+2) b) G(s)H(s) = 52(8+3.6) K(5+1)
2. (8 pts) A system has a characteristic equation s3 Ks2 ( K)s6 0. Using the Routh- Hurwitz criterion, determine the range of K for a stable system.
6. Consider the following control system. s(s1)(s +3) (a) Derive the characteristic equation of the (closed-loop) system. (b) Determine the range of K for stability using Routh's stability criterion.
Q2 (a) List down THREE (3) important requirements to design a control system. (3 marks) State the possible consequence when a physical system becomes unstable. (2 marks) (6) (c) Consider the following characteristic Equation shown below: P(s) = 55 +683 + 582 +8s + 20 (1) Construct Routh table for the characteristic Equation. (6 marks) (ii) Using the Routh – Hurwitz criterion, determine the stability of the system. (2 marks) (ii) Determine the numbers of roots on the right half-plane,...
2. (30)Use Routh-Hurwitz criterion to determine the stability fo characteristic equations. a) (15) 2s6+4s5+2s4-s42s-2-0 b) (15) s3+2s2+s+2-0
2. (30)Use Routh-Hurwitz criterion to determine the stability fo characteristic equations. a) (15) 2s6+4s5+2s4-s42s-2-0 b) (15) s3+2s2+s+2-0
A. Consider the characteristic equations below, comment on their system stability? 1. D(s)=s4 +253 +852 + 4s + 3 2. D(s)=s5 +54 +353 +352 + 6s + 4 B. Find the range of values of K for the closed loop system to remain stable? R(s) C(s) K s(s? +5 +1)(8+3)(s+4)
Plot the root locus for a system with the following characteristic equation: s2 +8s 25 s2(s 4) Be sure to calculate (and clearly label) any asymptotes, break-in/break-away points, and arrival/departure angles. If there are any imaginary axis crossings, clearly identify the frequency () and gain (K) associated with such crossings.
2. Consider a unity feedback control system whose open-loop transfer function is K(s-2) G(s) (s+1)(s +6s +25) Using the R-H stability criterion, determine the range of K for stability. Assume that K > 0. (30pts)
For the following polynomial, 54 +253 +352 + 25 + 5 = 0 determine using the Routh Array if the poles are on the left hand side or the right hand side.
2. (30)Use Routh-Hurwitz criterion to determine the stability fo characteristic equations. a) (15) 2s6+4s5+2s4-s42s-2-0 b) (15) s3+2s2+s+2-0