State Representation and Stability Analysis of Control Systems
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Control System, State Representation, Stability Analysis, Transfer Function, Laplace Representation, MIMO Control, System Stability, Closed-loop Transfer Function
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Abstract
This document provides a detailed analysis of state representation and stability of control systems, including simulation schemes, transfer functions, and state equations.
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Problem n1
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Problem n1
Problem n2
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[...] On replace, in , by the expression obtained: so , from where . On finally got the two equations: et . This gives us the following state representation: [...]
[...] System stability: The system has a double pole in the positive real part. The system is therefore unstable. Transition matrix: We use the inverse Laplace transform as follows: et . On a donc : . Return status: On pose with , then we have the system and On writes . On identifie avec : . Closed-loop transfer function: Donc . Static gain: To get a unit profit, one therefore needs a profit of to pre-filter the assignment. [...]
