Consider the system defined by x1 x2 0 1 25 4 x1 x2 1 1 0

Consider the system defined by [x_1 x_2] = [0 1 -25 -4] [x_1 x_2] + [1 1 0 1] [u_1 u_2] and [y_1 y_2] =[1 0 0 1] [x_1 x_2] + [1 0 0 1] [u_1 u_2]. This system has two inputs (u_1 and u_2) and two outputs (y_1 and y_2). There are thus four transfer functions: Y_1/U_1, Y_2/U_1, Y_1/U_2, and Y_2/U_2. Using Matlab (or other software of your choice) obtain all four transfer functions (the four elements of the 2 times 2 transfer matrix Consider the system described by the following state and output equations, corresponding to the quarter-car model with specific values for suspension stillness and damping and tire stillness (the outputs y_1 and y_2 are the displacements of the car body and wheel, respectively): [x_1 x_2 x_3 x_4] = [0 1 0 0 -10 -2 10 2 0 0 0 1 10 2 -410 -2] [x_1 x_2 x_3 x_4] + [0 0 0 400] [u] [y_1 y_2] = [1 0 0 0 0 0 1 0] [x_1 x_2 x_3 x_4] (D is zero) Obtain (using Matlab or other software of your choice) the unit step response (the input u(t) is a unit step function occurring at t = 0). and the unit impulse response (the input u(t) is a Dirac delta function occurring at t = 0). For both cases, generate a plot of both outputs (y_1 and y_2) vs. t for the first 5 seconds. For the same system descried in problem #5. obtain the response to initial conditions x_1 =1, x_2 = 0 x_3 = 1, x_4 = 0(without any input). the response to an input u(t) that is I for the first second (0 lessthanorequalto t lessthanorequalto1) and zero after that (when t > 1), w hen there are no initial conditions, and the response to the same input (u(t) = 1 for the first second and zero after that) when the initial conditions are x_1 = 1, x_2 = 0, x_3 =1, x_4 = 0. For all three cases, generate a plot of both outputs (y_1 and y_2) vs. t for the first 5 seconds.

Solution

Before going on to discuss the five steps of creating a program it is important to determine what exactly a program is. A program is a list of instructions that contain data for a computer to follow. Different programs are written with different languages. An editing program is made with a different programming \"language\" than one that uses graphics. Some well known programming languages are COBOL -business, BASIC -language, and - C which is used in science. Programming is complicated process,