## 5. Dynamic System Modeling and Control

• A mathematical model allows us to examine a system, and refine good solutions to design problems.

• Some engineered systems are intended to be fixed, or static.

• Many other systems are designed to be dynamic in behavior or response. These include,

internal combustion engines

loudspeakers

vibration isolators

car shock absorbers

missile guidance systems

tall buildings

• We know many relationships for modeling individual properties of mechanism pieces (eg, friction). These can be combined (lumped) to model more complex systems.

• when we develop a lumped model of a system, we can then calculate with a high level of precision, the effects various inputs (forces, motions, torques, etc) will have on the overall system.

• As an engineer attempts to design high quality systems, one of the most powerful weapons is a good analytical understanding of the phenomena.

5.1 Modeling

• We must first look at the equations for different phenomenon, and we can then look at how we can combine these into a more complex system.

• In this section we will focus on developing equations that model systems. These equations will tend to be complex, and we will save their solution for later.

• By developing the system model we are able to describe the system mathematically. We can then use various mathematical techniques to analyze the systems behavior.