EEm  Winter  Control Engineering  Lecture   PID Control   or more of control loops in EEm  Winter  Control Engineering  Lecture   PID Control   or more of control loops in

EEm Winter Control Engineering Lecture PID Control or more of control loops in - PDF document

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EEm Winter Control Engineering Lecture PID Control or more of control loops in - PPT Presentation

01 01 10 20 15 10 5 02 04 06 08 y brPage 4br EE392m Winter 2003 Control Engineering 44 Example Servosystem command More stepper motor flow through a valve motor torque I control Introduce integrator into control Closedloop dynamics gk gk gk ID: 30216

page control 2003 winter control page winter 2003 engineering ee392m loop controller pid integrator dynamics performance model max plant




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EE392m - Winter 2003Control Engineering4-1•90% (or more) of control loops in industry are PID•Simple control design model EE392m - Winter 2003Control Engineering4-2 ExampleUtilization control in a video server •Integrator plant: •P controller: admission rate CPU completion rateserver utilizationVideo stream –processing time e i], period p[i]–CPU utilization: tUnew tUdone EE392m - Winter 2003Control Engineering4-3•Closed-loop dynamics •Steady-state (•Transient•Frequency-domain (bandwidth) SSPdSSdkyy1 TtSSPdTtkTedkyeyty/111)0()(//!!"#$$%& //)(ˆ)(ˆ)(ˆ2PPdkkidiyiy 0.01 0.1 -15 -10 -5 2 4 0 0.2 0.4 0.6 0.8 (t) i itiddeidtdeiyty )(ˆ)()(ˆ)( EE392m - Winter 2003Control Engineering4-4 Example:•Servosystem command•More:–stepper motor–flow through a valve–motor torque ...•Introduce integrator into control•Closed-loop dynamics dgkssygksgkyIdII y(t) u(t) EE392m - Winter 2003Control Engineering4-5•Step to step update:•Closed-loop dynamics•Deadbeat control: Iyyzkudugy1 dgkzzygkzgkyIdII111 sampled timeintegrator Igk zyzyd111 EE392m - Winter 2003Control Engineering4-6•Main APC (Advanced•Modification of a productrecipe between tool "runs" Tool Cell controller Process system parameters •Processes:–vapor phase epitaxy–lithography–chemical mechanicalplanarization (CMP)–plasma etch EE392m - Winter 2003Control Engineering4-7 •First-order system:•P control + integrator forcancelling steady state error •WDM laser-diode temperature control•Other applications•ATE•EDFA optical amplifiers•Fiber optic laser modules•Fiber optic network equipment heat loss to heat capacity = temperature - ambient temperature pumped heat produced heat TemperatureController Peltier Heatpump EE392m - Winter 2003Control Engineering4-8 •P Control + Integrator for•Velocity form of the controller ")(;vkekekvkuevyyePIkkiPPId! Inner loop Plant P e(t)u(t) i y-yd iIkkkekekuPI!!1()()()()1(tetektektutuPI EE392m - Winter 2003Control Engineering4-9•Closed-loop dynamics•Steady state (•Transient dynamics: look at thecharacteristic equation•Disturbance rejection (ˆ)()(ˆ idiHiyd dksksssyksksskskyIPdIPIP)1()1( 0.4 Frequency (rad/sec)DISTURBANCE REJECTIONMAGNITUDE (dB) 10 -30 -20 -10 ( iHd EE392m - Winter 2003Control Engineering4-10•Phase-locked loop is arguably a PLL VoltageOscillator LPF Loop Filter(controller) reference signalsignal phase-locked to reference uKttAKettAKvrKeoooodomoodmm    !)sin()cos()sin(LPF2LPF2eu EE392m - Winter 2003Control Engineering4-11•Small-signal model: PLL d (s) reference errorphaseouKKKeoddodd    #%!!)sin(eu1odott  odott  sKo'dtekekuKeuKdIPdo! d dkskKKssIPdo2 •Loop dynamics: EE392m - Winter 2003Control Engineering4-12•2-nd order dynamics•PD control•Closed-loop dynamics•Optimal gains (critical damping) •Disk read-write control DISTURBVCMTTJ  Coil ekekePD!!! dksksePD212;2 PDkk EE392m - Winter 2003Control Engineering4-13 eseesseDDDD1/111 •Derivative (rate of –speed sensor (tachometer)–low-level estimation logic•Signal differentiation–is noncausal–amplifies high-frequency noise•Causal (low-pass filtered) estimate of the derivative•Modified PD controller: ekesskuPDD1 EE392m - Winter 2003Control Engineering4-14•The performance seems to be infinitely improving for•This was a simple design model, remember?•Performance is limited by–system being different from the model•flexible modes, friction, VCM inductance–sampling in a digital controller–rate estimation would amplify noise if too aggressive–actuator saturation–you might really find you have tried to push the performance•If high performance is really that important, careful EE392m - Winter 2003Control Engineering4-15•Constant gain - I control•Integrator - P control•Double integrator - PD control•Generic second order dynamics - PID control EE392m - Winter 2003Control Engineering4-16•Generalization of P, PI, PD•Early motivation: control of firstorder processes with deadtime Example: usgeysTD1 machine T EE392m - Winter 2003Control Engineering4-17•PID: three-term control•Sampled-time PID•Velocity form–bumpless transfer betweenmanual and automatic zkekezkuIPD11111 future 2()1(2)()1()()()()1(tetetektetektektutuDPI independent sensor or an estimate121zekekekuIPD EE392m - Winter 2003Control Engineering4-18 •Model-based tuning•Look at the closed-loop poles•Numerical optimization–For given parameters run a sim,compute performance parametersand a performance index–Optimize the performance indexover the three PID gains usinggrid search or Nelder method. eskkskuIPD!"#$%& Plant model Optimizer PDkkk,, EE392m - Winter 2003Control Engineering4-19•Explore the plant:–set the plant under P control and start increasing the gain till the–note the critical gain and oscillation period •Tune the controller:•Z and N used a Monte Carlo method to develop the rule•Z-N rule enables tuning if a model and a computer are both 0.5____________ 0.451.2______ PID0.5 EE392m - Winter 2003Control Engineering4-20•In practice, control authority isalways limited:MAX•Wind up of the integrator:–if the integral will keep growing while the controlovershoot later•Anti wind-up:–switch the integrator off if thecontrol has saturated MAXcuu)*+MINcMAXcMAXcMINuuuuuuuevor if0,for ,! EE392m - Winter 2003Control Engineering4-21•A box, not an algorithm•Auto-tuning functionality:–pre-tune–self-tune•Manual/cascade mode switch•Bumpless transfer betweendifferent modes, setpoint ramp•Loop alarms•Networked or serial port