## Analysis of Chatter in Contactor Control Systems, with Applications to Dual-input Plants |

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Alzac analog computer analysis angle average motion bang-bang becomes buckling coefficient characteristic equation chatter motion chatter region chatter to occur chattering system Contactor Control Systems continuous switching function controlling chatter damping deflection differential equation disc DISCONTINUOUS SWITCHING FUNCTION DISTRIBUTION AT BUCKLING Doctor of Philosophy Engineering error state variables EXAMPLE 3-2 Example 4-1 fixed edge Flugge-Lotz focusing plate Free Edge Condition fringe movement Fringe Pattern galvanometer Graduate Division H H H heat energy IA OJ inch initial conditions inner edge input kjkj Laplace transform large disturbances limit cycle linear plant linear switching functions logarithmic spiral Lyapunov Maximum Principle milk glass non-controlling chatter normal obtain optical optimal control origin Oscillograph parallel lines parameters plane problem radius Reference satellite set of lines shown in figure slope sn+1 Stanford University switching surface temperature distribution test plate test specimens Thermal Stress Equations thermocouples time-optimal trajectory Trdr