# rsampleBlock

Randomly sample Control Design blocks in generalized model

## Description

example

Msamp = rsampleBlock(M,names,N) randomly samples a subset of the Control Design blocks in the generalized model M. The names argument specifies which blocks to sample, and N specifies how many samples to take. The result Msamp is a model array of size [size(M) N] obtained by replacing the sampled blocks with their randomized values.

example

Msamp = rsampleBlock(M,names1,N1,names2,N2,...,namesM,NM) takes N1 samples of the blocks listed in names1, N2 samples of the blocks listed in names2, and so on. The result Msamp is a model array of size [size(M) N1 N2 ... NM].

[Msamp,samples] = rsampleBlock(___) also returns a data structure containing the block replacement values for each sampling point. You can use this syntax with any of the preceding input argument combinations.

## Examples

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Create the first-order model $G\left(s\right)=1/\left(\tau s+1\right)$, where $\tau$ is a tunable real parameter.

tau = realp('tau',5);
G = tf(1,[tau 1]);

Restrain tau to nonnegative values only.

G.Blocks.tau.Minimum = 0;

Generate 20 random samples of G. The result is a 20-by-1 array of first-order models with random values of tau taken from the range of tau.

Gs = rsampleBlock(G,'tau',20);
size(Gs)
20x1 array of state-space models.
Each model has 1 outputs, 1 inputs, and 1 states.

Take random samples of a model with both tunable and uncertain blocks. Using uncertain blocks requires Robust Control Toolbox™. Random sampling of tunable blocks works the same way as shown in this example.

Create an uncertain model of $G\left(s\right)=a/\left(\tau s+1\right)$, where a is an uncertain parameter that varies in the interval [3,5], and $\tau$ = 0.5 +/- 30%. Also, create a tunable PI controller, and form a closed-loop system from the tunable controller and uncertain system.

a = ureal('a',4);
tau = ureal('tau',.5,'Percentage',30);
G = tf(a,[tau 1]);
C = tunablePID('C','pi');
T = feedback(G*C,1);

T is a generalized state-space model with two uncertain blocks, a and tau, and one tunable block, C. Sample T at 20 random (a,tau) pairs.

[Ts,samples] = rsampleBlock(T,{'a','tau'},20);

Ts is a 20-by-1 array of genss models. The tunable block C, which is not sampled, is preserved in Ts. The structure samples has fields samples.a and samples.tau that contain the values at which those blocks are sampled.

Grouping a and tau into a cell array causes rsampleBlock to sample them together, as (a,tau) pairs. Sampling the blocks independently generates a higher-dimensionality arrays. For example, independently taking 10 random samples of a and 5 samples of tau generates a 10-by-5 model array.

[TsInd,samples] = rsampleBlock(T,'a',10,'tau',5);
TsInd
TsInd =

10x5 array of generalized continuous-time state-space models.
Each model has 1 outputs, 1 inputs, 2 states, and the following blocks:
C: Tunable PID controller, 1 occurrences.

Type "ss(TsInd)" to see the current value, "get(TsInd)" to see all properties, and "TsInd.Blocks" to interact with the blocks.

In this array, a varies along one dimension and tau varies along the other.

## Input Arguments

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Model to sample, specified as a:

• Generalized model (genss or genfrd)

• Generalized matrix (genmat)

• Uncertain model (uss (Robust Control Toolbox) or ufrd (Robust Control Toolbox))

• Uncertain matrix (umat (Robust Control Toolbox))

Control Design blocks to sample, specified as a character vector or cell array of character vectors. The entries in names correspond to the names of at least a subset of the Control Design blocks in M. For example, suppose that M is a genss model with tunable blocks t1 and t2, and uncertain blocks u1 and u2. Then, {'t1','u2'} is one possible value for names.

Grouping block names together in a cell array generates samples of the group rather than independent samples of each block. For example, the following code generates a 10-by-1 array of models, where each entry in the array has a random value for the pair (t1,u2).

Msamp = rsampleBlock(M,{'t1','u2'},10);

To sample parameters independently, do not group them. For example, the following code generates a 10-by-20 array of models, where t1 varies along the first dimension and u2 varies along the second dimension.

Msamp = rsampleBlock(M,'t1',10,'u2',20);

rsampleBlock ignores any entry in names that does not appear in M.

Number of samples to take of the preceding block or blocks, specified as a positive integer.

## Output Arguments

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Array of model samples, returned as a generalized model array, ss array, frd array, or numeric array. Msamp is of the same type as M, unless all blocks are sampled. In that case, Msamp is a numeric array, ss array, or frd array. For example, suppose that M is a uss model with uncertain blocks u1 and u2. The following command returns an array of uss models, with uncertain block u2.

Msamp1 = rsampleBlock(M,'u1',10);

The following command samples both blocks and returns an array of ss models.

Msamp2 = rsampleBlock(M,{'u1','u2'},10);

rsampleBlock uses values that fall within the uncertainty range when sampling uncertain blocks, and within the maximum and minimum parameter values when sampling tunable blocks.

Block sample values, returned as a structure. The fields of samples are the names of the sampled blocks. The values are arrays containing the corresponding random values used to generate the entries in Msamp. For instance, suppose that you run the following command, where M is a genss model with tunable blocks t1 and t2.

[Msamp,samples] = rsampleBlock(M,{'t1','t2'},10);

Then, samples.t1 contains the 10 values of t1 and samples.t2 contains the 10 values of t2. If you sample a block that is not scalar valued, the corresponding field of samples contains values compatible with the block. For instance, if you sample a tunablePID block, samples contains an array of state-space models that represent PID controllers.

| | | | | (Robust Control Toolbox)

### Topics

Introduced in R2016a