msim

Method of mdss.

Simulate the time response of a discrete- or continuous-time implicit MTI (mdss) model to arbitrary inputs.

Source: src/model/@mdss/msim.m

Syntax

y                          = msim(sys, u, t, x0)
[y, tsim]                  = msim(sys, u, t, x0)
[y, tsim, x]               = msim(sys, u, t, x0)
[y, tsim, x, z]            = msim(sys, u, t, x0)
[y, tsim, x, z, tEvents]   = msim(sys, u, t, x0)
[y, tsim, x, z, tEvents]   = msim(sys, u, t, x0, y0, z0)        % with initial guesses
[y, tsim, x, z, tEvents]   = msim(sys, u, t, x0, [], [], opt)   % with solver options

Request only the outputs you need — any of the left-hand sides above works. The argument order is the same as for mss and lsim: inputs, time, initial state. The initial guesses y0 and z0 are optional and default to []; opt (continuous-time solver options) follows them, so pass [], [] when you want solver options but no guesses.

Description

msim simulates the model sys. The solver is selected automatically from sys.timeStepSize: 0 runs a continuous-time solve (MATLAB ode15i), a positive value runs the discrete-time solver.

The initial guesses for the algebraic (y0) and binary (z0) signals may be left empty:

y0 = [] → the solver tries both zeros and ones for the algebraic signals.
z0 = [] → the solver starts from zeros and searches for a consistent binary combination.

Otherwise y0 / z0 must have one entry per algebraic / binary signal.

Input arguments

Argument	Description
`sys`	The `mdss` model to simulate.
`u`	Input trajectory: one row per time sample, one column per input (`sys.nInput`). Use `[]` for an autonomous model.
`t`	Time samples of the input trajectory. For discrete-time models the step `dT` must equal `sys.timeStepSize`.
`x0`	Initial state values — one entry per state (`sys.nState`).
`y0`	(optional) Initial algebraic guess; `[]` (default) lets the solver search.
`z0`	(optional) Initial binary guess; `[]` (default) lets the solver search.
`opt`	(optional) solver options from `odeset`. Continuous-time only.

Output arguments

The order matches lsim and mss/msim: the non-state signals first, then time, then the states.

Output	Description
`y`	Simulated algebraic-signal trajectory.
`tsim`	Simulated time samples.
`x`	Simulated state trajectory.
`z`	Simulated binary-signal trajectory.
`tEvents`	Event times where binary signals switched.

Example

% Continuous-time model with one input
sys = stringParser.symbolicToMdss(["xp1 = -2*x1 + u1"; ...
                                    "xp2 = x1 - x2"], 0);

t  = (0:0.1:10).';
u  = ones(numel(t), 1);            % one column: sys.nInput == 1
x0 = [0 0];

opt = odeset('RelTol', 1e-5, 'AbsTol', 1e-7);
[~, tsim, x] = msim(sys, u, t, x0, [], [], opt);

plot(tsim, x); grid on

For fast-varying inputs, cap the solver step, e.g. odeset('MaxStep', dt/2) where dt is the smallest spacing between input samples.

Solver options

opt is applied on top of the scheme defaults (for a continuous-time mdss the default solver is ode15i). It accepts two styles, and later sources win in the order built-in standards → scheme default → your opt:

a legacy odeset struct (AbsTol, RelTol, MaxStep, …), and
a new ode()-style struct, which additionally lets you pick the solver and set integrator-specific options.

Passing a struct that selects the solver and non-standard integrator options:

opt = struct( ...
    'Solver',            "ode15i", ...   % DAE solver (default for mdss)
    'RelativeTolerance', 1e-6, ...
    'AbsoluteTolerance', 1e-8, ...
    'MaxStep',           0.05, ...
    'MaxOrder',          2);              % integrator-specific option

[~, tsim, x] = msim(sys, u, t, x0, [], [], opt);

Recognised fields include Solver, AbsoluteTolerance / AbsTol, RelativeTolerance / RelTol, InitialStep, MaxStep, MinStep, MaxOrder, NormControl, OutputFcn, OutputSelection and Vectorization. Unknown field names are ignored.