上交自控讲义第三讲.ppt

Module 3 First-order systems Contents and Requirements on the Modules Concept and examples of First-order systems Concept of first-order systems A first-order mechanical system A first-order electrical system A first-order hydraulic system First-order response analysis for typical inputs Impulse response Step response Ramp response Harmonic response Complex-plane representation First-order feedback systems Concepts of poles and zeros Poles and zeros of first-order systems Dominant poles Mechanical first-order system Equate the forces at A, Take Laplace transforms, assuming initial conditions to be zero, Lead to the transfer function, where, T is called Time Constant, having units of seconds Electrical first-order system Apply Kirchhoff’s law to the circuit directly in Laplace transforms, Lead to the transfer function, Hydraulic first-order system According to the property of a laminar restrictor: pressure drop between both sides is proportional to the flow, with K as flow-pressure constant, we get, Apply the law of mass conservation in addition, Take Laplace transforms, leading to the transfer function, Hydraulic first-order system The previous modeling result is insufficient, because the impression of flow q on h1 has not been taken into account, Apply block diagram algebra, Apply final-value theorem, Contents and Requirements on the Modules Concept and examples of First-order systems Concept of first-order systems A first-order mechanical system A first-order electrical system A first-order hydraulic system First-order response analysis for typical inputs Impulse response Step response Ramp response Harmonic response Complex-plane representation First-order feedback systems Concepts of poles and zeros Poles and zeros of first-order systems Dominant poles Typical inputs for control system Unit-step function Step response of first-order system First-order system output under step input becomes, Take inverse Laplace transforms, T r