ME3401 HOMEWORK SET 6 Prof. Tsuchiya Cal Poly Pomona Due: Wednesday, 4/15/2020, 5:00PM Background Review the video lecture describing the Quarter-Car Suspension model for automobiles, then complete the following assignment. Below is a simplified schematic for a quarter-car suspension model. The sprung mass mã is the mass supported by the vehicle suspension and includes the driver and passengers. The unsprung mass m₁ represents the mass not supported by the vehicle suspension and includes the wheel, tire, shock, spring, hub, brakes, etc.. mc and mt are linked by the actual vehicle suspension strut/spring combo, which is modeled as a spring kc and damper c. The tire itself is also modeled as a spring connecting the unsprung mass to the ground and has constant kt Me + M kt fr Activity For this assignment, you should recall the many concepts for modeling and simulation you have learned so far to produce a simulation of this system. Complete the following steps below to guide you to a functioning simulation: a) Derive the governing ODEs for the quarter-car system (hint: you will need 2 equations). b) Develop the transfer functions: P(s) = Y₁(s) R(s) and Q(s) = Y2(s) R(s) c) Build a single Simulink Block Diagram that expresses the ODEs and the transfer functions for this system. 1 d) Write a MATLAB script that calls your Simulink block diagram and plots the simulated re- sponses to a step input with a step time of 1 sec and a step value of 0.1 (use the 'step' block from the sources menu). e) Your MATLAB script should produce 2 figures when executed: Figure 1 should demonstrate that the outputs y₁(t) and y2(t) for the ODEs and the transfer function blocks are equivalent. Figure 2 should plot the acceleration of the sprung mass ÿ2(t) and the reference (ground) input r(t). You may use the following parameters as a starting point in your simulations: % Define Vehicle Parameters 응 mc = 130; mt = 50; kc = 200; kt = 500; C = 100; % 1/4 sprung mass of car chassis (kg) % 1/4 unsprung mass of tire/wheel (kg) % spring constant (N/m) % tire stiffness (N/m) % damping coefficient (N-s/m^2) % Define Simulation Parameters ... ts = t_f = .01; 20; % Sample time % Simulation time The sample time and the simulation time are adjusted in the Simulink block diagram in the 'con- figuration parameters' menu. You may also find the Simulink Video tutorial series available at nolantsuchiya.com to be helpful when setting up your simulation (scroll down on homepage for video links). What to Submit: Submit 1 PDF file that includes: • your hand calculations for part (a) and (b) • screenshots of your Simulink block diagram ⚫ your MATLAB code as text (do not submit .m file) • output plots according to part (e) ● a brief discussion of your simulation results 2