MECH 466 - Lecture7-Routh-HurwitzCriterion-2009W

Stability controller pi controller gain range for

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Unformatted text preview: t Next Time responses Time If K=35, oscillation frequency is obtained by the If auxiliary equation 2008/09 MECH466 : Automatic Control Exercises Exercises Read Sections 6.1-6.4. Read 6.1Solve Problems 6.12,13,14,20,21,22. Solve 23 2008/09 MECH466 : Automatic Control 24 6 Announcements How to write a lab report Lab #2 starts next week. If you miss the regular Lab session of Lab 2 exercise, please finish it by February 13 (one day after the midterm). (We need to remove the water column setup soon after that.) Lab #1 reports (per group) must be handed in to Lab TAs at the beginning of your Lab #2 session. Late hand-in will NOT be accepted! (Without Late hand- As part of your formal write-up, for each As writeexperiment, include Brief background Brief Objective Objective Tables and graphs Tables Answers to the questions Answers Analysis of your results Analysis Conclusions Conclusions handing in the report in time, you lose 2.5 % automatically.) 2008/09 MECH466 : Automatic Control 25 2008/09 Inlet Valve A Inlet Valve B Requirement: Tank A Tank B Proportiona l Control Valve Control Unit Valve AB Pressure Transducer A Pressure Transducer B Process Valve A Disturbance Valve Maintain the level of Tank B at a desired level by controlling the flow through control valve. Desired level (inch) Model-free Modeldesign (Actuator) Controller (Lab #2) Control valve Flow (Plant) Tank level (inch) Tank B Sensor (Lab #1) Process Valve B Sensed level Pump MECH466 : Automatic Control Voltage Pressure Actual level Calibration! Figure 1. Schematic of the Tank Level Control Setup. 2008/09 26 Water tank level control Block diagram Water tank level control (Lab 2) Control valve MECH466 : Automatic Control 27 2008/09 MECH466 : Automatic Control 28 7 On-off (bang-bang) control “Off” “On” Off” On” (Valve fully open) (Valve fully closed) On-off control (cont’d) “On” On” Simplest control Simplest No parameters to be chosen No Oscillatory behavior Oscillatory Difficult to maintain the level at the desired level. Difficult Small difference between high and low limits Small causes the chattering (rapid switching) problem. Over-reaction (Small change of water level may Overcause full action of valve.) This can be avoided by a proportional control. High limit desired Low limit High limit desired Low limit 2008/09 MECH466 : Automatic Control 29 2008/09 Proportional control (P-control) MECH466 : Automatic Control 30 Prelab for Lab 2 Before going to Lab 2, think about how to complete the blank part for both on-off and P-control! onP- Set value (desired level) Set Controller gain KP (design parameter) (design Controller Command voltage (See Slide 26 for notation) Command Note that there is a steady state error. Note error. Set value 2008/09 MECH466 : Automatic Control 31 2008/09 MECH466 : Automatic Control 32 8 Some useful LabVIEW blocks coerced(x) coerced(x) x (TRUE or FALSE) If “s”=TRUE, then the output is “t”. If “s”=FALSE, then the output is “f”. 2008/09 MECH466 : Automatic Control 33 9...
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