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PROJECT 1 ANALYSIS

# PROJECT 1 ANALYSIS - EE-4580 CONTROL DESIGN PROJECT 1...

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EE-4580 CONTROL DESIGN PROJECT 1- INVERTED PENDULUM JASON MCALLISTER 438-49-4726 10-18-04

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Introduction: 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 steady-state 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 lag-lead compensator. Thus, we are able to improve both the transient and steady-state response using a lag-lead 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 non-linear and time invariant model for the inverted pendulum. By setting the model at equilibrium for we produced the dynamic model that follows:
By using mason’s formula and plugging in the given parameters we produced the two plants with respect to y( t ) and ө ( t ): Now we designed controllers with respect to the following flow diagram below.

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