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 functionality for system balancing, controllability and observability analysis, regulator and estimator design, and simulation of dynamic system responses.

These tools enable robust modeling, analysis, and control of linear dynamic systems for engineering and research applications.

Functions

• abcdchk - Verifies the dimensional compatibility of matrices A, B, C, and D.

• acker - Pole placement gain selection using Ackermann's formula.

• append - Appends the inputs and outputs of the two models.

• augstate - Append state vector to output vector.

• balreal - Gramian-based balancing of state-space realizations.

• bdschur - Block-diagonal Schur factorization.

• bode - Bode plot of frequency response, magnitude and phase data.

• c2d - Convert model from continuous to discrete time.

• care - Continuous-time algebraic Riccati equation solution.

• cloop - Feedback connection of multiple models.

• compreal - Companion realization of transfer functions.

• ctrb - Controllability of state-space model.

• ctrbf - Compute controllability staircase form.

• d2c - Convert model from discrete to continuous time.

• damp - Natural frequency and damping ratio.

• dare - Discret-time algebraic Riccati equation solution.

• dcgain - Low-frequency (DC) gain of LTI system.

• dlqr - Linear-quadratic (LQ) state-feedback regulator for discrete-time state-space system.

• dlyap - Discrete-time Lyapunov equations.

• dsort - Sort discrete-time poles by magnitude.

• esort - Sort continuous-time poles by real part.

• evalfr - Evaluate frequency response at given frequency.

• feedback - Feedback connection of multiple models.

• freqresp - Evaluate system response over a grid of frequencies.

• gensig - Create periodic signals for simulating system response.

• gram - Controllability and observability Gramians.

• hsvd - Hankel singular values of dynamic system.

• impulse - Impulse response plot of dynamic system.

• initial - System response to initial states of state-space model.

• isct - Checks if dynamic system model is in continuous time.

• isdt - Checks if dynamic system model is in discret 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.

• 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.

• lsim - Plot simulated time response of dynamic system to arbitrary inputs.

• lyap - Continuous Lyapunov equation solution.

• minreal - Minimal realization or pole-zero cancellation.

• nyquist - Nyquist plot of frequency response.

• obsv - Observability of state-space model.

• obsvf - Compute observability staircase form.

• ord2 - Generate continuous second-order systems.

• padecoef - Computes the Pade approximation of time delays.

• parallel - Parallel connection of two models.

• pole - Poles of dynamic system.

• series - Series connection of two models.

• ss - State-space model.

• ss2tf - Convert state-space representation to transfer function.

• ssdata - Access state-space model data.

• ssdelete - Remove inputs, outputs and states from state-space system.

• ssselect - Extract subsystem from larger system.

• step - Step response plot of dynamic system.

• tf - Constructs a transfer function model.

• tf2ss - Convert transfer function filter parameters to state-space form.

• tfdata - Access transfer function model data.

• tzero - Invariant zeros of linear system.

• zero - Zeros and gain of SISO dynamic system.