15-02-2013, 09:33 AM
Mathematical Models of Systems
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Objectives
We use quantitative mathematical models of physical systems to design and analyze control systems. The dynamic behavior is generally described by ordinary differential equations. We will consider a wide range of systems, including mechanical, hydraulic, and electrical. Since most physical systems are nonlinear, we will discuss linearization approximations, which allow us to use Laplace transform methods.
We will then proceed to obtain the input–output relationship for components and subsystems in the form of transfer functions. The transfer function blocks can be organized into block diagrams or signal-flow graphs to graphically depict the interconnections. Block diagrams (and signal-flow graphs) are very convenient and natural tools for designing and analyzing complicated control systems
Introduction
Define the system and its components
Formulate the mathematical model and list the necessary assumptions
Write the differential equations describing the model
Solve the equations for the desired output variables
Examine the solutions and the assumptions
If necessary, reanalyze or redesign the system
[attachment=50974]
Objectives
We use quantitative mathematical models of physical systems to design and analyze control systems. The dynamic behavior is generally described by ordinary differential equations. We will consider a wide range of systems, including mechanical, hydraulic, and electrical. Since most physical systems are nonlinear, we will discuss linearization approximations, which allow us to use Laplace transform methods.
We will then proceed to obtain the input–output relationship for components and subsystems in the form of transfer functions. The transfer function blocks can be organized into block diagrams or signal-flow graphs to graphically depict the interconnections. Block diagrams (and signal-flow graphs) are very convenient and natural tools for designing and analyzing complicated control systems
Introduction
Define the system and its components
Formulate the mathematical model and list the necessary assumptions
Write the differential equations describing the model
Solve the equations for the desired output variables
Examine the solutions and the assumptions
If necessary, reanalyze or redesign the system