1- Using the Routh theorem, find the interval of K for stability of the system with...

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1- Using the Routh theorem, find the interval of K for stability of the system with following characteristics equation. s+3s3+Ks+6s+1=0 2- For the following systems: G(s) = K(s + 4) (s + 1) H(s) = 1 K G(s) == H(s) = 1 s(s+1)(s + 4s + 5) R(s) s+1 K 2 C(s) 5+5 s (s+2) a) Plot the root locus on the paper. b) Plot the root locus by using Matlab. c) Design the magnitude of K to have the desired damping ratio of 0.7 in all cases. Do this step on the paper and by using the Matlab. d) Plot the step response of the system for all cases using Matlab for three different values of K (K for damping ratio of 0.2, 0.5, 0.7). 1- Using the Routh theorem, find the interval of K for stability of the system with following characteristics equation. s+3s3+Ks + 6s+1=0 2- For the following systems: G(s) = K(s + 4) G(s) = (s+1)2' H(s) = = 1 K s(s+1)(s+4s + 5)' H(s) = 1 == R(s) s+1 2 C(s) K 5+5 s (s+2) a) Plot the root locus on the paper. b) Plot the root locus by using Matlab. c) Design the magnitude of K to have the desired damping ratio of 0.7 in all cases. Do this step on the paper and by using the Matlab. d) Plot the step response of the system for all cases using Matlab for three different values of K (K for damping ratio of 0.2, 0.5, 0.7). 1- Using the Routh theorem, find the interval of K for stability of the system with following characteristics equation. s+3s3+Ks+6s+1=0 2- For the following systems: G(s) = K(s + 4) (s + 1) H(s) = 1 K G(s) == H(s) = 1 s(s+1)(s + 4s + 5) R(s) s+1 K 2 C(s) 5+5 s (s+2) a) Plot the root locus on the paper. b) Plot the root locus by using Matlab. c) Design the magnitude of K to have the desired damping ratio of 0.7 in all cases. Do this step on the paper and by using the Matlab. d) Plot the step response of the system for all cases using Matlab for three different values of K (K for damping ratio of 0.2, 0.5, 0.7). 1- Using the Routh theorem, find the interval of K for stability of the system with following characteristics equation. s+3s3+Ks + 6s+1=0 2- For the following systems: G(s) = K(s + 4) G(s) = (s+1)2' H(s) = = 1 K s(s+1)(s+4s + 5)' H(s) = 1 == R(s) s+1 2 C(s) K 5+5 s (s+2) a) Plot the root locus on the paper. b) Plot the root locus by using Matlab. c) Design the magnitude of K to have the desired damping ratio of 0.7 in all cases. Do this step on the paper and by using the Matlab. d) Plot the step response of the system for all cases using Matlab for three different values of K (K for damping ratio of 0.2, 0.5, 0.7).