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Unformatted text preview: EE4580 CONTROL DESIGNPROJECT 1 INVERTED PENDULUMJASON MCALLISTER438494726101804Introduction:In this project we have analyzed an inverted pendulum. This is a system which has both an angle and distance considerations. The control of such a system is given with specific specifications of a Wn=1.83 and a damping ratio equal to 0.83. We first derive the linear model of the inverted pendulum to have controllable transfer function. After this, we take the root locus to decide what we have to do to improve the response to meet within the specification. These situations where both an improvement in the transient response and a significant reduction in steadystate error are needed, neither a lag nor a lead compensator will suffice. We need a compensator, which includes a lead as well as a lag section known as a laglead compensator. Thus, we are able to improve both the transient and steadystate response using a laglead compensator. We compute these values as follows. System Modeling:We modeled the picture below using Lagrange Mechanics. By using relationships between kinetic and potential energy for the picture above, we derived a nonlinear and time invariant model for the inverted pendulum. By setting the model at equilibrium for we produced the dynamic model that follows:By using masons formula and plugging in the given parameters we produced the two plants with respect to y(t) and (t):Now we designed controllers with respect to the following flow diagram below. These controllers were of the form:...
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 Fall '10
 GU

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