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# genmat

Generalized matrix with tunable parameters

## Description

Generalized matrices (`genmat`) are matrices that depend on tunable parameters (see `realp`). You can use generalized matrices for parameter studies. You can also use generalized matrices for building generalized LTI models (see `genss`) that represent control systems having a mixture of fixed and tunable components.

## Construction

Generalized matrices arise when you combine numeric values with static blocks such as `realp` objects. You create such combinations using any of the arithmetic operators `+`, `-`, `*`, `/`, `\`, and `^`. For example, if `a` and `b` are tunable parameters, the expression `M = a + b` is represented as a generalized matrix.

The internal data structure of the `genmat` object `M` keeps track of how `M` depends on the parameters `a` and `b`. The `Blocks` property of `M` lists the parameters `a` and `b`.

```M = genmat(A)``` converts the numeric array or tunable parameter `A` into a `genmat` object.

### Input Arguments

 `A` Static control design block, such as a `realp` object. If `A` is a numeric array, `M` is a generalized matrix of the same dimensions as `A`, with no tunable parameters. If `A` is a static control design block, `M` is a generalized matrix whose `Blocks` property lists `A` as the only block.

## Properties

 `Blocks` Structure containing the control design blocks included in the generalized LTI model or generalized matrix. The field names of `Blocks` are the `Name` property of each control design block. You can change some attributes of these control design blocks using dot notation. For example, if the generalized LTI model or generalized matrix `M` contains a `realp` tunable parameter `a`, you can change the current value of `a` using:`M.Blocks.a.Value = -1;` `SamplingGrid` Sampling grid for model arrays, specified as a data structure. For model arrays that are derived by sampling one or more independent variables, this property tracks the variable values associated with each model in the array. This information appears when you display or plot the model array. Use this information to trace results back to the independent variables. Set the field names of the data structure to the names of the sampling variables. Set the field values to the sampled variable values associated with each model in the array. All sampling variables should be numeric and scalar valued, and all arrays of sampled values should match the dimensions of the model array. For example, suppose you create a 11-by-1 array of linear models, `sysarr`, by taking snapshots of a linear time-varying system at times `t = 0:10`. The following code stores the time samples with the linear models. ` sysarr.SamplingGrid = struct('time',0:10)` Similarly, suppose you create a 6-by-9 model array, `M`, by independently sampling two variables, `zeta` and `w`. The following code attaches the `(zeta,w)` values to `M`. ```[zeta,w] = ndgrid(<6 values of zeta>,<9 values of w>) M.SamplingGrid = struct('zeta',zeta,'w',w)``` When you display `M`, each entry in the array includes the corresponding `zeta` and `w` values. `M` ```M(:,:,1,1) [zeta=0.3, w=5] = 25 -------------- s^2 + 3 s + 25 M(:,:,2,1) [zeta=0.35, w=5] = 25 ---------------- s^2 + 3.5 s + 25 ...``` For model arrays generated by linearizing a Simulink® model at multiple parameter values or operating points, the software populates `SamplingGrid` automatically with the variable values that correspond to each entry in the array. For example, the Simulink Control Design™ commands `linearize` (Simulink Control Design) and `slLinearizer` (Simulink Control Design) populate `SamplingGrid` in this way. Default: `[]` `Name` System name, specified as a character vector. For example, `'mat_1'`. When you convert a static control design block such as `tunableSurface` to a generalized matrix using `genmat(blk)`, the `Name` property of the block is preserved. Default: `''`

## Examples

Generalized Matrix With Two Tunable Parameters

This example shows how to use algebraic combinations of tunable parameters to create the generalized matrix:

`$M=\left[\begin{array}{cc}1& a+b\\ 0& ab\end{array}\right],$`

where a and b are tunable parameters with initial values –1 and 3, respectively.

1. Create the tunable parameters using `realp`.

``` a = realp('a',-1); b = realp('b',3);```
2. Define the generalized matrix using algebraic expressions of `a` and `b`.

`M = [1 a+b;0 a*b]`

`M` is a generalized matrix whose `Blocks` property contains `a` and `b`. The initial value of `M` is `M = [1 2;0 -3]`, from the initial values of `a` and `b`.

3. (Optional) Change the initial value of the parameter `a`.

`M.Blocks.a.Value = -3;`
4. (Optional) Use `double` to display the new value of `M`.

`double(M)`

The new value of `M` is ```M = [1 0;0 -9]```.

## See Also

### Topics

Introduced in R2011a

## Support

#### Learn how to automatically tune PID controller gains

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