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Control System functions

The Control System module provides algorithms and tools for designing, analyzing, and tuning linear control systems in Nelson.

It supports state-space and transfer function models, system transformations between continuous and discrete time, and computation of poles, zeros, and frequency responses.

The module also includes system balancing, controllability and observability analysis, regulator and estimator design, and simulation of dynamic responses.

These tools are used to model, analyze, and control linear dynamic systems in engineering and research code.

Dynamic System Models

Functions for creating, inspecting, and reducing dynamic system models.

  • balreal
    Gramian-based balancing of state-space realizations.
  • isct
    Checks if dynamic system model is in continuous time.
  • isdt
    Checks if dynamic system model is in discrete time.
  • islti
    Checks if variable is an linear model tf, ss or zpk.
  • issiso
    Checks if dynamic system model is single input and single output.
  • isstatic
    Checks if model is static or dynamic.
  • minreal
    Minimal realization or pole-zero cancellation.
  • pole
    Poles of dynamic system.
  • ss
    State-space model.
  • ssdata
    Access state-space model data.
  • tf
    Constructs a transfer function model.
  • tfdata
    Access transfer function model data.
  • tzero
    Invariant zeros of linear system.
  • zero
    Zeros and gain of SISO dynamic system.
Model Conversion and Interconnection

Functions for model conversion, composition, selection, and interconnection.

  • abcdchk
    Verifies the dimensional compatibility of matrices A, B, C, and D.
  • append
    Appends the inputs and outputs of the two models.
  • augstate
    Append state vector to output vector.
  • c2d
    Convert model from continuous to discrete time.
  • d2c
    Convert model from discrete to continuous time.
  • feedback
    Feedback connection of multiple models.
  • gensig
    Create periodic signals for simulating system response.
  • padecoef
    Computes the Pade approximation of time delays.
  • parallel
    Parallel connection of two models.
  • series
    Series connection of two models.
  • ss2tf
    Convert state-space representation to transfer function.
  • ssdelete
    Remove inputs, outputs and states from state-space system.
  • ssselect
    Extract subsystem from larger system.
  • tf2ss
    Convert transfer function filter parameters to state-space form.
Linear Analysis

Functions for time-domain, frequency-domain, and model-response analysis.

  • bode
    Bode plot of frequency response, magnitude and phase data.
  • damp
    Natural frequency and damping ratio.
  • dcgain
    Low-frequency (DC) gain of LTI system.
  • evalfr
    Evaluate frequency response at given frequency.
  • freqresp
    Evaluate system response over a grid of frequencies.
  • hsvd
    Hankel singular values of dynamic system.
  • nyquist
    Nyquist plot of frequency response.
  • sigma
    Singular value response of an LTI model.
Time and Frequency Responses

Simulation and response functions for dynamic systems.

  • impulse
    Impulse response plot of dynamic system.
  • initial
    System response to initial states of state-space model.
  • lsim
    Plot simulated time response of dynamic system to arbitrary inputs.
  • step
    Step response plot of dynamic system.
Control Design and Tuning

Functions for controller design, estimators, and regulator computations.

  • acker
    Pole placement gain selection using Ackermann's formula.
  • are
    Algebraic Riccati equation solution.
  • care
    Continuous-time algebraic Riccati equation solution.
  • dare
    Discrete-time algebraic Riccati equation solution.
  • dlqr
    Linear-quadratic (LQ) state-feedback regulator for discrete-time state-space system.
  • kalman
    Design Kalman filter for state estimation.
  • lqe
    Kalman estimator design for continuous-time systems.
  • lqed
    Calculates the discrete Kalman estimator configuration based on a continuous cost function.
  • lqr
    Linear-Quadratic Regulator (LQR) design.
  • lqry
    Form linear-quadratic (LQ) state-feedback regulator with output weighting.
  • ord2
    Generate continuous second-order systems.
Matrix Computations

Control-oriented matrix computations for state-space analysis.

  • bdschur
    Block-diagonal Schur factorization.
  • cloop
    Feedback connection of multiple models.
  • compreal
    Companion realization of transfer functions.
  • ctrb
    Controllability of state-space model.
  • ctrbf
    Compute controllability staircase form.
  • dlyap
    Discrete-time Lyapunov equations.
  • dsort
    Sort discrete-time poles by magnitude.
  • esort
    Sort continuous-time poles by real part.
  • gram
    Controllability and observability Gramians.
  • lyap
    Continuous Lyapunov equation solution.
  • obsv
    Observability of state-space model.
  • obsvf
    Compute observability staircase form.
  • schord
    Order a Schur decomposition.