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

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