三时间响应学时.pptVIP

Chapter 3 Time Response Analysis Control design methodology 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 poles of its transfer function are in the LHP (?pi, Re[pi]0). Performance SpecsStability Performance specifications Example Utilization control in a video server Periodic task Ti corresponding to each video stream i c[i]: processing time, p[i]: period Stream i’s requested CPU utilization: u[i]=c[i]/p[i] Total CPU utilization: U(t)=?{k}u[k], {k} is the set of active streams Completion rate: Rc(t)= (?{kc}u[m])/?t, where {m} is the set of terminated video streams during [t, t+?t] Unknown Admission rate: Ra(t)= (?{ka}u[j])/?t, where {j} is the set of admitted streams during [t, t+?t] Problem: design an admission controller to guarantee U(t)=Us regardless of Rc(t) Model Differential equation A Diverge to MathSystem representations Three ways of system modeling A Diverge to MathLaplace transform Laplace transform of a signal f(t) A Diverge to MathLaplace transform Basic translations Impulse function f(t)=?(t) ? F(s)=1 Step signal f(t)=a?1(t) ? F(s)=1/s Ramp signal f(t)=a?t ? F(s)=a/s2 Exp signal f(t)=eat ? F(s)=1/(s-a) Sinusoid signal f(t)=sin(at) ? F(s)=a/(s2+a2) Composition rules Linearity L[af(t)+bg(t)] = aL[f(t)]+bL[g(t)] Differentiation L[df(t)/dt] = sF(s) – f(0-) Integration L[?tf(?)d?] = F(s)/s A Diverge to MathTransfer function Modeling a linear time-invariant (LTI) system G(s) = Y(s)/U(s) ? Y(s) = G(s)U(s) A Diverge to MathPoles and Zeros The response of a linear time-invariant (LTI) system A Diverge to MathTime response vs. pole location A Diverge to MathBlock diagram A pictorial tool to represent a system based on transfer functions and signal flows Represent a feedback control system Back to Our utilization control example ModelTransfer