- Part I Matlab Is Very Useful For Modeling Systems An Excellent Example Is In The Area Of Feedback Controls In This Lab 1 (99.29 KiB) Viewed 35 times
- Part I Matlab Is Very Useful For Modeling Systems An Excellent Example Is In The Area Of Feedback Controls In This Lab 2 (152.14 KiB) Viewed 35 times
PART I Matlab is very useful for modeling systems. An excellent example is in the area of feedback controls. In this lab, we will look at some examples of modeling systems. Suppose you want to model a system (in this case the motion of a mass on a frictionless spring) governed by the following differential equations (neglect any motion in the y-direction due to gravity): у k M x 0 Frictionless mass-spring system (shown in steady state) Figure 1 F = Mein =M d²x dt2 F = -k.x
Problem I: (20 points) 1. (5 points) Plot the position of the mass as a function of time in Simulink for this system. 2. (5 points) Briefly explain (2-3 sentences) whether the system acts like a cosine wave or a sine wave, and why (in terms of what's actually happening in the mechanical system). 3. (5 points) Determine the cyclic frequency of the system from Simulink and clearly identify it on your plot from #1 above. 4. (5 points) Calculate the response of the system in the time domain by finding the impulse response of the system using your knowledge of inverse Laplace transforms. Scan your handwritten work and include it in your lab report. Problem II: (20 points) Suppose the initial position is at x=0, but at time zero an instantaneous push is provided such that X'(0) = 1 m/s. Repeat parts 1 through 4 of Problem I above. Problem III: (15 points) Suppose both the initial position is at x = 1 m, and the initial velocity is 1 m/s. Repeat parts 1, 3 and 4 of Problem I above.