1、Course ReviewYouqing WangCollege of Information Science & Technology2011.11.15Final ExamTotal 50 scores, 6 questions3 questions for linear continuous systems (29)2 questions for linear discrete systems (16)Linear continuous-time system theoryLinear discrete-time system theoryOverview: transfer funct

2、ion state space modelClassical control vs modern control“Transfer function” to “SS model” (multi-choice)Canonical formControl canonical formObserver canonical formModal canonical form5NamelyWe obtainDynamic response of SS modelConsider the following linear time-invariant systemzero-input response Fr

3、eedom motion zero-state response Forced motion6Its dynamic response is:Calculation of (1)(1) represents the power series of the matrix At(2) using typical matrix, such as Diagonal or Jordan matrix7Calculation of -2（3） taking the inverse Laplace transform of example：8Controllability : input - stateOb

4、servability : output - state Controllability and Observability9Their physical meanings?Criterion rank criterionPBH rank criterion System destruction according to controllability and observability1 Substituting the feedback law, yields then the characteristic equation of the CL system is (a)2 Assume

5、the desired location are known, then the corresponding desired characteristic equation: (b)3 the required elements of K are obtained by matching coefficients in Eq. (a) and Eq. (b)10Controller designCheck controllabilityFull-state feedback controlFull state feedback with reference input-K-K11How to

6、select pole positionDominant second-order poles-deals with pole selection without explicit regard for control effortNatural frequency + damping factoroptimal control (or symmetric root locus)- specifically address the issue of achieving a balance between good system response and control effort. corr

7、ection term , close-loop observer： weight matrix LReduced-order observerObserver equation：L13Observer (duality)First, introduce the integral of error eThe overall system state equations becomeState feedback control Output tracking for given systemState feedback for overall system14Integral Control a

8、nd Robust TrackingLinear continuous-time system theoryLinear discrete-time system theorySampling theorem (香農定理) f(t) can be represented uniquely by its sampled version fn if the sampling frequency s is chosen to be greater than 2 times the highest frequency contained in f(t)16ZOHZOH17Position of ZOH

9、?Table 8.1 Laplace Transforms and z-transformsF(s)f(kT)F(z)18F(s)(kT)F(z)19Note: ZOH exists in any practical engineeringZ-transform with ZOH（1eTs）For example20SS of continuous time-invariant linear systemAfter sampling, discrete SSheretime-invariant matrix, and is sampling period Discretization of S

10、SSS discrete SSWhy?21bilinear transformChange unit circle of Z to left half plane of W22stable criterionBilinear Transform + Louts CriterionBilinear Transform + Nyquist CriterionDesign by discrete equivalent (emulation):1.Design a continuous compensation;2.Digitize the continuous compensation;3.Using discrete analysis to verify the design. Discrete Analysis of Designs 1.Digitize the continuous system;2.Design discrete controller and verify.discrete system design23Tustins method24MPZMMPZDiscrete PID thenIncremental PID controlFi