530_343lecture19

530_343lecture19 - ME 530.343 Design and Analysis of...

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ME 530.343: Design and Analysis of Dynamic Systems Spring 2009 Lecture 19 - Controller Design Tuesday, April 8, 2009 Today’s Objectives Metrics for system behavior (and thus, controller performance) PID Controller design Mass-spring-damper example Metrics for System Behavior The maximum overshoot and settling time are quantities that are useful in the design and analysis of inhomogeneous systems. Since they require knowledge of a single steady-state value, they are usually related to the response of a system to a step input. The maximum overshoot M p is the ratio of overshoot of y ( t ) of its steady-state value to the steady- state value of y ( t ). For an underdamped second order ODE, the maximum overshoot and damping ratio ζ are related by M p = e ζπ 1 - ζ 2 ζ = s (ln ( M p )) 2 (ln ( M p )) 2 + π 2 The settling time t s is the amount of time required for the transient’s damped oscillations to remain within ± 1% of the steady-state value. (There can be different definitions, but this is the one we will use.) For an underdamped, second order ODE, the settling time, damping ratio, and natural frequency are related by t s = - ln (0 . 01) ζω n The rise time t r is the time is takes to go from 10% to 90% of the steady state value. (There can be different definitions, but this is the one we will use.) Something good for practice: derive these quantities from first principles. 1
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Servo Control System In yesterday’s example, we developed a controller that effectively changed the dynamic behavior of the system. However, it did not allow us to make the system move to a particular position (or velocity). However, if we set up a servo system as shown below, we can move the output
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This note was uploaded on 03/02/2010 for the course MECH 530.343 taught by Professor Sun during the Spring '08 term at Johns Hopkins.

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530_343lecture19 - ME 530.343 Design and Analysis of...

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