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Unformatted text preview: ME375 Handouts 1 PID Controller PID Controller • Controller Structure Controller Structure • Effects of Proportional, Integral and Derivative Effects of Proportional, Integral and Derivative Actions Actions D i f P I D C t l l D i f P I D C t l l • Design of PID Controllers Design of PID Controllers School of Mechanical Engineering Purdue University ME375 PID Control  1 ME375 Handouts 2 PID Controller PID Controller Disturbance D (s Output Y (s) D (s) Plant G P ( s ) Control Input U ( s ) G C ( s ) H ( s ) + − Reference Input R ( s ) Error E ( s ) + + Controller Proportional plus Integral plus Derivative (PID) Control Proportional plus Integral plus Derivative (PID) Control In time domain: In time domain: In s In sdomain: domain: ( ) ( ) ( ) ( ) , w h ere ( ) ( ) ( ) t P I D u t K e t K e t d K e t e t r t y t τ = ⋅ + ⋅ + ⋅ = − ∫ & 1 ( ) ( ) P I D U s K K K s E s ⎛ ⎞ = + + ⎜ ⎟ School of Mechanical Engineering Purdue University ME375 PID Control  2 2 1 2 ( ) ( ) ( ) ( ) ( ) ( ) P I D C D P I D C C C C G s s N s K s K s K K s z s z G s K D s s s ⎜ ⎟ ⎝ ⎠ + + + + ⇒ = = = 144424443 1 2 1 2 ( ) D C P C I C K K K K z z K K z z = ⎧ ⎪ = + ⎨ ⎪ = ⎩ ME375 Handouts 3 Effect of PID Actions Effect of PID Actions • Derivative Action Derivative Action ( ( K D D s s ) Step Response 1 2 1.4 Provides Provides added added damping damping effect effect to to the the closed closedloop loop system system; reduces reduces overshoot overshoot and and oscillation oscillation in in step step responses responses; tends tends to to slow slow down down the the closed closedloop loop system system response response. Dominant Dominant during during initial initial transient, transient, due due to to the the effect effect of of the the differentiation differentiation. Amplitude Time (sec.) 5 10 15 0.2 0.4 0.6 0.8 1 1.2 • Integral Action Integral Action ( ( K I / s s ) I Eliminates Eliminates steady steadystate state error error to to step step inputs inputs; tends tends to to destabilize destabilize the the closed closedloop loop system system. Dominant Dominant during during steady steadystate state by by producing producing an an accumulation accumulation of of steady steadystate state error error to to increase increase control control effort effort. t t ⇒ = − + − → = + + + → ⇐ z e t d A A A A e d A A A A t t ( ) τ τ 1 2 3 4 small large School of Mechanical Engineering Purdue University ME375 PID Control  3 • Proportional Action Proportional Action ( ( K P ) Introduces Introduces immediate immediate action action due due to to error error; improves improves system system response response time...
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This note was uploaded on 12/23/2011 for the course ME 375 taught by Professor Meckle during the Fall '10 term at Purdue University.
 Fall '10
 Meckle
 Mechanical Engineering

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