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# trim

Compute steady-state value of MPC controller state for given inputs and outputs

## Syntax

```x = trim(MPCobj,y,u)
```

## Description

The trim function finds a steady-state value for the plant state or the best approximation in a least squares sentence such that:

$\begin{array}{l}x-{x}_{off}=A\left(x-{x}_{off}\right)+B\left(u-{u}_{off}\right)\\ y-{y}_{off}=C\left(x-{x}_{off}\right)+D\left(u-{u}_{off}\right)\end{array}$

Here, xoff, uoff, and yoff are the nominal values of the extended state x, input u, and output y.

x is returned as an mpcstate object. Specify y and u as doubles. y specifies the measured and unmeasured output values. u specifies the manipulated variable, measured disturbance, and unmeasured disturbance values. The values for unmeasured disturbances must be 0.

trim assumes the disturbance model and measurement noise model to be zero when computing the steady-state value. The software uses the extended state vector to perform the calculation.