DiscreteTimeControlSystems - ETH Z

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Discrete Time Control SystemsLino GuzzellaSpring 20130-01 Lecture IntroductionInherently Discrete-Time Systems, example bank accountBank account, interest ratesr+>0 for positive,r >0 for negativebalancesx(k+ 1) = (1 +r+)x(k) +u(k), x(k)>0(1 +r )x(k) +u(k), x(k)<0(1)wherex(k) is the account s balance at timekandu(k) is theamount of money that is deposited to (u(k)>0) or withdrawn from(u(k)<0) the general such systems are described by a difference equation of theformx(k+ 1) =f(x(k), u(k)), x(k) n, u(k) m, f: n m n(2)with which an output equation of the formy(k) =g(x(k), u(k)), y(k) p, g: n m p(3)is often will learn how continuous-time systems can be transformed to aform similar to that that there is a fundamental difference between inherentlydiscrete time systems and such approximations: for the former thereis no meaningful interpretation of the system behavior in between thediscrete time instancesk={1,2.}

Chapter 2: “emulation techniques” (following the path “B”), works well when the sampling times are much smaller than the relevant time constants of the system. No guarantee that stability or robustness properties are invariant to the transformation B. Chapter 3: main properties of the sample-and-hold procedure, i.e.,

  Chapter, Chapter 2