IP | Assumptions

In general, an accurate model of the system is desired. Unfortunately, modeling a system accurately may make it very difficult to design a controller.

Referring to figure (25), in IP modeling section, the following assumption will be used in the derivation of the system model:

A frictionless system will be assumed because modeling the friction is difficult and in most of the cases is nonlinear. However, friction will be minimized in the mechanical design by using good bearing system.
The pole mass will be assumed as lumped mass (point mass) in contrast to a distributed mass through the pole. Hence, the inertia effect will be based on this assumption.
The inverted pendulum is adherently a nonlinear system due to the cosine and sine terms generated while modeling the pendulum. Assuming that the pendulum’s angle will remain small, since there should be sufficient control to keep it balanced, it may be possible to approximate sin θ = θ and cos θ = 1. Thus this will linearize the system, which will allow for controller design methods to use linear system techniques. Designing for a non-linear system may be quite difficult and will not be addressed in this project.


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Assumptions IP Modeling MATLAB Simulation	Assumptions [11] In general, an accurate model of the system is desired. Unfortunately, modeling a system accurately may make it very difficult to design a controller. Referring to figure (25), in IP modeling section, the following assumption will be used in the derivation of the system model: A frictionless system will be assumed because modeling the friction is difficult and in most of the cases is nonlinear. However, friction will be minimized in the mechanical design by using good bearing system. The pole mass will be assumed as lumped mass (point mass) in contrast to a distributed mass through the pole. Hence, the inertia effect will be based on this assumption. The inverted pendulum is adherently a nonlinear system due to the cosine and sine terms generated while modeling the pendulum. Assuming that the pendulum’s angle will remain small, since there should be sufficient control to keep it balanced, it may be possible to approximate sin θ = θ and cos θ = 1. Thus this will linearize the system, which will allow for controller design methods to use linear system techniques. Designing for a non-linear system may be quite difficult and will not be addressed in this project.
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