AME 455 Sample eXam#l/Hwk 5 Due2/22/02 Problem 1. For the system shown below (a) Show the system has a zero on the right half plane (i.e. the system is non-minimum (b)Obtain the time response of the system c(t)due to a unit step input (20pts) (c)Sketch c(t) from part(b)versus the time t. (10pts) Problem 2. For the following second order system C(s) s+b R(s)s2+4s+4 (a) Find the value of b that gives the following system a 5% overshoot to a unit step inpu (5pts) (b) What is the maximum value of the system output for the unit step input?(10pts) Problem 3 (a)Determine the transfer function Y(s)/F(s) between the input force F(t) and the output y(t) of the following mass-spring system(20pts) k k y(1) F(1) (b)What is the order of this systems(how many poles does the Y(s)/F(s)have)? (pts) (c)What are the energy storage elements corresponding to these orders"(5pts) Problem 4. You are asked to design a controller for the water level in a water tower of a small city. Formulate at least one question you would ask from the city engineer, which will give you a starting point in the design of the controller (5pts)
AME 455 Sample EXAM #1/Hwk 5 Due 2/22/02 Problem 1. For the system shown below (a) Show the system has a zero on the right half plane (i.e. the system is non-minimum phase) (10pts) (b) Obtain the time response of the system c(t) due to a unit step input. (20pts) (c) Sketch c(t) from part (b) versus the time t. (10pts) Problem 2. For the following second order system ( ) 4 4 ( ) 2 + + + = s s s b R s C s (a) Find the value of b that gives the following system a 5% overshoot to a unit step input. (15pts) (b) What is the maximum value of the system output for the unit step input? (10pts) Problem 3. (a) Determine the transfer function Y(s)/F(s) between the input force F(t) and the output y(t) of the following mass-spring system. (20pts) (b) What is the order of this systems (how many poles does the Y(s)/F(s) have)? (5pts) (c) What are the energy storage elements corresponding to these orders “(5pts) Problem 4. You are asked to design a controller for the water level in a water tower of a small city. Formulate at least one question you would ask from the city engineer, which will give you a starting point in the design of the controller. (5pts) 2 6 s + 1 4 s + + _ R(s) C(s) m1 m2 2 k 1 k 1 c 2 c F(t) y(t)
