Topic 8 16.31 Feedback Control State-Space Systems What are state-space models? Why should we use them? How are they related to the transfer functions used in classical control design and how do we develop a state- space model?

16.31 Feedback Control State-Space Systems What are state-space models? Why should we use them? and how do we develop a state-space mode( &ased in classical control design How are they related to the transfer functions What are the basic properties of a state-space model, and how do we analyze these?

Goal: Design a controller K(s so that the system has some desired characteristics. Typical objectives Stabilize the system( Stabilization) Regulate the system about some design point(Regulation Follow a given class of command signals(Tracking) Reduce the response to disturbances(Disturbance Rejection Typically think of closed-loop control > so we would analyze the

Fall 2001 16.313-1 Introduction Root locus methods have Advantages k Good indicator if transient response k Explicity shows location of all closed-loop poles Trade-offs in the design are fairly clear Disadvantages k Requires a transfer function model(poles and zeros) k Difficult to infer all performance metrics k Hard to determine response to steady-state(sinusoids

MG!∈R- ORDER5)sT6As RREL丹T(0sHP5 BETWEEN1MER6soN5毛 TAST∈P兵 ND THE POLE LOCAT(0NS心EK ALCULATE0 FoR A SECOND-ORDER SYSTEM GuES60工 NSIGHTS AcTuALLy Gooo APPRoXIMATIONS foR MAwy HIGHER- ORDER SYSTEMS BECAUSE THEIR

properties of finite dement soltions Noded point equilibrio At a node, the sow of he elemeat nodal forces s in equilibriun with Hhe externed loads

How many quadrature points do you need to integrate a polynomial of order p= 3 exactly using Gauss'method

Concept Question How many quadrature points do you need to integrate exactly the stiffness matrix of a lD finite element with quadratic interpolation for the displacements? gauss

The finite element method(I for three-diwnensional robles Potential enery applied to one eleet

cmaulenon o isoparametRic elemets (Bathes book Consider the uadriltersd denat shown in the 8oc nodd coordinates