ME 360 Modeling, Analysis and Control of Dynamic Systems W 2010 Homework Set #9 (due Th 3/30/10) Please read sections 9.1 – 9.3 in your textbook (Palm, System Dynamics, 2 nd ed.), and please show your work in solving all the problems below. Problem 1: Problem 9.7 in your textbook. Problem 2: Problem 9.15 in your textbook. Problem 3: Problem 9.31 in your textbook. Problem 4: Consider a second-order system defined by the transfer function, ( ) 2 22 222 2 () 2 nd nn d Hs ss s ω σω ζω ω σω + = = ++ ++ 1) Let 2σ = . Use Matlab to plot the unit step response of ()Hs for { }0,1, 2, 4,6 d ω = . Put all of the curves on the same graph, and indicate the direction of increasing d ω . 2) Let 2 d ω = . Use Matlab to plot the unit step response of ()Hs for { }0,1, 2, 4,6σ = . Put all of the curves on the same graph, and indicate the direction of increasing, σ . Problem 5: Problem 9.36 in your textbook. Also, use Matlab (e.g., step and/or plot commands) to check your answers. Problem 6 (Project related problem): Determine the response of your system to appropriate initial conditions and appropriate test inputs (e.g., step, sinusoid, etc.) by multiple techniques (e.g., numerical integration of the nonlinear equations, Laplace transform of the linear equations) and discuss the results. UlsoyLab4