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Ch 2 Solution of State space Equations






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Ch 2 Solution of State space Equations. Engineering/Scientific Theories. A model or framework for understanding A set of statements closed under certain rules of inference Validated & tested (not mere conjectures) Summarizes (infinitely) many practical situations Requires abstraction Types
Ch 2 Solution of State space Equations

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Ch 2 solution of state space equations l.jpgSlide 1

Ch 2 Solution of State space Equations

Engineering scientific theories l.jpgSlide 2

Engineering/Scientific Theories

  • A model or framework for understanding

  • A set of statements closed under certain rules of inference

  • Validated & tested (not mere conjectures)

  • Summarizes (infinitely) many practical situations

    • Requires abstraction

  • Types

    • Categorization (system of naming things)

    • Summarizes past experiences

    • Predicts future outcomes

    • Tool to design with

  • State space theory

    • super theory (physics, chemistry, etc hence abstract)

    • Helps understand engineering analysis and design techniques

Ct vs dt l.jpgSlide 3

CT vs DT

  • Discrete time state equations

  • Continuous time state equations

Discrete time state equations l.jpgSlide 4

Discrete time State Equations

Possibly nonlinear, most general, hardest to analyze

Linear, possibly time-varying

Linear & time-invariant, easiest to analyze, provides most convenient design techniques

Continuous time state equations l.jpgSlide 5

Continuous time State Equations

Possibly nonlinear, most general, hardest to analyze

Linear, possibly time-varying

Linear & time-invariant, easiest to analyze, provides most convenient design techniques

Solve lti dt state equations l.jpgSlide 6

Solve LTI DT state equations

  • Free response

  • Forced response

  • Weighting sequence (Markov parameters)

  • External equivalence

  • Impulse response

  • Convolution

Solve lti ct state equations l.jpgSlide 7

Solve LTI CT state equations

  • Scalar equation

  • Vector-matrix equation

    • Matrix exponential

  • Existence, uniqueness, Lipschitz condition

  • Free response, forced response

  • State transition matrix

  • Linearity

  • Complete response

  • Impulse response

  • convolution

Discretization l.jpgSlide 8

Discretization


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