自动控制原理-control_tutorial.ppt

1、Feedback Control Theory a Computer Systems Perspective,Chenyang Lu Department of Computer Science University of Virginia /cl7v,Outline,Introduction What is feedback control? Why do computer systems need feedback control? Control design methodology Sys

2、tem modeling Performance specs/metrics Controller design Summary,Control,Applying input to cause system variables to conform to desired values called the reference. Cruise-control car: f_engine(t)=? speed=60 mph E-commerce server: Resource allocation? T_response=5 sec Embedded networks: Flow rate? D

3、elay = 1 sec Computer systems: QoS guarantees,Open-loop control,Compute control input without continuous variable measurement Simple Need to know EVERYTHING ACCURATELY to work right Cruise-control car: friction(t), ramp_angle(t) E-commerce server: Workload (request arrival rate? resource consumption

4、?); system (service time? failures?) Open-loop control fails when We dont know everything We make errors in estimation/modeling Things change,Feedback (close-loop) Control,Actuator,Monitor,reference,control input,controlled variable,manipulated variable,Controlled System,+,-,error,control function,C

5、ontroller,sample,Feedback (close-loop) Control,Measure variables and use it to compute control input More complicated (so we need control theory) Continuously measure differential equations.,s (frequency) domain: multiplication,s-domain is a simple completion rate Rc(s) Close-loop system transfer fu

6、nctions Us(s) as input:G1(s) = C(s)Go(s)/(1+C(s)Go(s) Rc(s) as input:G2(s) = Go(s)/(1+C(s)Go(s) Output: U(s)=G1(s)Us/s+G2(s)Rc(s),CPU is modeled as an integrator,Control design methodology,Controller Design Root-Locus PI Control,Requirement Analysis,Modeling analytical system IDs,Dynamic model,Contr

7、ol algorithm,Performance Specifications,Satisfy,Design GoalsPerformance Specifications,Stability Transient response Steady-state error Robustness Disturbance rejection Sensitivity,Performance SpecsStability,BIBO stability: bounded input results in bounded output. A LTI system is BIBO stable if all p

8、oles of its transfer function are in the LHP (pi, Repi0).,Performance SpecsStability,Unstable,Stable,Performance specifications,Settling time,Overshoot,Controlled variable,Time,Reference,%,Steady State,Transient State,Steady state error,Example: Control task completion Rc(s) Close-loop system transf

9、er functions Us(s) as input:G1(s) = C(s)Go(s)/(1+C(s)Go(s) Rc(s) as input:G2(s) = Go(s)/(1+C(s)Go(s) C(s)=? to achieve zero steady-state error: U(t) Us,CPU is modeled as an integrator,Proportional ControlStability,Proportional Controller ra(t)=Ke(t); C(s) = K Transfer functions Us/s as input: G1(s)

10、= K/(s+K) Rc(s) as input: G2(s) = 1/(s+K) Stability Pole p0 = -K0 Note: System may shoot to 100% if K0!,Proportional ControlSteady-state error,Assume completion rate Rc(t) keeps constant for a time period longer than the settling time: Rc(s)=Rc/s System response is,Compute steady-state err using fin

11、al value theorem,P-control cannot achieve the desired CPU utilization Us; instead it will end up lower by Rc/KOops! The larger the proportional gain K is, the closer will CPU utilization approach to Us,CPU UtilizationProportional Control,U(t),ess=-20%,Us,Proportional-Integral ControlStability,Propor

12、tional Controller ra(t)=K(e(t)+Kite()d)C(s) = K(1+Ki/s) Transfer functions Us/s as input: G1(s) = (Ks+KKi)/(s2+Ks+KKi) Rc(s) as input: G2(s) = s/(s2+Ks+KKi) Stability Poles Rep00 sampled system denoted k instead of t Main tool is z-transform f(k) F(z) , where z is complex Analogous to Laplace transf

13、orm for s-domain,Discrete Modeling,Difference equation V(m) = a1V(m-1) + a2V(m-2) + b1U(m-1) + b2U(m-2) z domain: V(z) = a1z-1V(z) + a2z-2V(z) + b1z-1U(z) + b2z-2U(z) Transfer function G(z) = (b1z + b2)/(z2-a1z - a2) V(m): output in mth sampling window U(m): input in mth sampling window Order n: #sa

14、mpling-periods in history affects current performance SP = 30 sec, and n = 2 Current system performance depends on previous 60 sec,Root Locus analysis of Discrete Systems,Stability boundary: |z|=1 (Unit circle) Settling time = distance from Origin Speed = location relative to Im axis Right half = sl

15、ower Left half = faster,Effect of discrete poles,|z|=1,Longer settling time,Re(s),Im(s),Unstable,Stable,Higher-frequency response,Feedback control works in CS,U.Mass: network flow controllers (TCP/IP RED) IBM: Lotus Notes admission control UIUC: Distributed visual tracking UVA Web Caching QoS Apache

16、 Web Server QoS differentiation Active queue management in networks Processor thermal control Online data migration in network storage (with HP) Real-time embedded networking Control middleware Feedback control real-time scheduling,Advanced Control Topics,Robust Control Can the system tolerate noise

17、? Adaptive Control Controller changes over time (adapts) MIMO Control Multiple inputs and/or outputs Stochastic Control Controller minimizes variance Optimal Control Controller minimizes a cost function of error and control energy Nonlinear systems Neuro-fuzzy control Challenging to derive analytic results,Issues for Computer Science,Most systems are non-linear But linear approximations may do eg, fluid approximations First-principles modeling is difficult Use empirical techniques Mapping control objectives to fe