LPV System — Control Systems/Linear Parameter Varying

LPV System

Control Systems / Linear Parameter Varying

Simulates a linear parameter-varying state-space model given on a grid over one to three scheduling parameters: a set of matrices A, B, C and D at every grid point, interpolated at the parameter values arriving on port p, with operating-point offsets:

y = C(p)·(x − x0) + D(p)·(u − u0) + y0
dx = A(p)·(x − x0) + B(p)·(u − u0) + dx0

For a discrete model the next state is dx; for a continuous one the state is integrated by forward Euler at the block's sampling time. Gain-scheduled plants – a model linearized at several operating points – are the usual use.

It is Control System Toolbox's LPV System block, with the model array given as stacked matrices instead of an ss array.

Ports

• u – the input, a column [m,1].
• p – the scheduling parameters, a column [d,1], one per breakpoint set in use.
• y – the output, a column [p,1].
• x – the state at this sample, [n,1].
• dx – the next state (discrete) or the state derivative (continuous), [n,1].

Parameters

• Breakpoints 1 – the first parameter's strictly increasing grid values, at least two.
• Breakpoints 2, Breakpoints 3 – the second and third parameters', or [] when the grid has fewer parameters.
• Model Type – Discrete or Continuous.
• A – one state matrix per grid point stacked vertically, [n·K, n], K the number of grid points, ordered with the FIRST parameter varying fastest (MATLAB's array order). n is 1 to 8.
• B – the input matrices stacked the same way, [n·K, m].
• C – the output matrices, [p·K, n].
• D – the feedthrough matrices, [p·K, m]. The four tables together may hold at most 4096 numbers.
• Initial State – x at the first sample, [n,1].
• Input Offset u0, Output Offset y0, State Offset x0, Derivative Offset dx0 – the operating point, [m,1], [p,1], [n,1], [n,1]; a scalar is repeated.
• Offsets Are Equilibrium – On (Simulink's default) treats the offsets as an equilibrium and ignores dx0: dx0 is taken as x0 for a discrete model and as 0 for a continuous one. Off uses dx0 as given.
• Interpolation – Flat (the breakpoint at or below), Nearest (ties go up) or Linear (one parameter after the other, the first first).
• Extrapolation – Clip holds the edge matrices; Linear extends the edge segments, and needs Linear interpolation.
• Sampling Time (s) – the block's rate; a continuous model is stepped by forward Euler at it.

Code export

All ten targets: Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog and PLC Structured Text. Each prints the same description of the step that the simulation itself runs – the grid search, the interpolation and the state update – so every target does the same arithmetic in the same order. The tables are baked in as constants.

⚠ The three HDL targets run in simulation-only real arithmetic, quantizing only at the port boundaries.

Simulink bridge

None (Support::None). Simulink's block takes its model as one ss array with a sampling grid, evaluated from a MATLAB expression, which the bridge cannot build from this block's stacked matrices or read back into them; the bridge reports this block rather than dropping it silently. Code export verification still covers it across all ten languages.

Notes

• Discrete only, and stateful: the state persists from sample to sample.
• At most three scheduling parameters. Simulink's state-space bus and offset bus outputs and its delays are not offered.