Control systemsLesson 3 of 4 in the course Transfer functions and modelling

State-Space Models: Linear and Nonlinear Dynamics, Analysis, and Feedback

5 flashcards · 5 quiz questions · 5 match pairs · 5 fill-in sentences · English

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Summary

State-space representation describes a system through variables that summarize its internal condition and equations that show how that condition changes. It is useful for understanding dynamics over time, including systems with multiple inputs and outputs.

A state-space representation is a mathematical model that tracks the changing internal condition of a system. It expresses the evolution of the system using first-order differential equations for continuous time, or difference equations for discrete time.

All flashcards

What does matrix B represent in a linear state-space model?
How system inputs affect the rate of change of the state.
What does it mean for a system to be observable?
Its internal state can be inferred from its outputs over time.
What is controllable canonical form designed to emphasize?
A state-space realization arranged to be controllable.
How can a transfer function conceal internal dynamics?
Pole-zero cancellations can hide internal modes, including unstable ones.
What does the direct-feedthrough matrix D represent?
The direct contribution of the input to the output.

Quiz questions

  1. In the state-space output equation y=Cx+Duy=Cx+Du, what does DD represent?Answer: The direct contribution of the input to the output.
  2. For a continuous-time LTI system, what do eigenvalues of AA with negative real parts indicate about its natural modes?Answer: The modes decay over time.
  3. For an LTI system with nn states, what condition on the controllability matrix indicates controllability?Answer: Its rank is nn.
  4. What makes a transfer function strictly proper?Answer: Its numerator degree is lower than its denominator degree.
  5. What limitation can prevent state feedback from stabilizing a system?Answer: An unstable mode that cannot be controlled cannot generally be stabilized by state feedback.

Based on the Wikipedia article State-space representation, licensed CC BY-SA 4.0. Adapted into a summary, flashcards and quizzes.

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