lecture_2

lecture_2 - Buildings; Machine suspension; 2. Electric...

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ME 421 Mechanical Dynamics and Control Fall 2006, Lecture 2 Today’s topics: 1. Generalization of analytical homogenous solution of ODE from 1 st -order to higher order; 2. Discussion of 2-order dynamics responses;
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Response from Lecture 1 ± Challenges: ± MATLAB; Math; Rmembering old materials; Labs; Getting up and Coming to the class; Abstract ideas… ± Expectation: ± Better understanding of dynamic systems and control technology; Getting a A… ± Examples: ± Hydraulic system; HVAC; Fly (drive) by wire vehicle…
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Dynamics Modeling 101: 1-Order System RC-Circuit Example
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Analytical Solution
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Analytical solution to 1-Order ODE
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Generalization to 2-Order ODE
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Extension: Higher-Order ODE?
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Examples of 2-order Dynamics 1. Spring-mass-damper model example of mechanical systems: • Car suspension;
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Unformatted text preview: Buildings; Machine suspension; 2. Electric circuit (resistor-capacitor-Inductance, RCI circuit) 3. Experimental pendulum (Lab. 2). Discussion of 2-order ODE Resoponse Discussion of 2-order ODE Resoponse 8/24/06 9:32 AM C:\Documents and Settings\Qingze Zou\M. ..\Resp.m 1 of 1 K_bar = omega_n = 1*2*pi xi = Phi = pi time = y_t = K_bar*sin(omega_n.*time + Phi) figure(1), plot(time, y_t) K_1 = K_2 = xi = y_t_2 = exp(-xi*omega_n*time).*. .. (K_1*exp(sqrt(xi^2 -1). .. .*omega_n*time)+K_2*exp(-sqrt(xi^2 -1). .. .*omega_n*time)) figure(2), plot(time, y_t_2) K_bar = xi = y_t_3 = exp(-xi*omega_n*time).*. .. K_bar.*sin(sqrt(1-xi^2)*omega_n.*time. .. + Phi) figure(3), plot(time, y_t_3) hold on, plot(time, K_bar.*exp(-xi*omega_n*time),'r--')...
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lecture_2 - Buildings; Machine suspension; 2. Electric...

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