How to read XML-Data into a dataTable via Powershell and force using correc types via a given XmlSchema?

I am currently struggling to read XMLdata into a dataTable by enforcing a given XmlSchema. Whatever I do, after the Data-Import all Types are set back to "string". I need to force the below ID-column to be of type "int" (not "string" or "byte"):

$schema = '
<xs:schema xmlns:xs="http://www.w3.org/2001/XMLSchema">
  <xs:group name="r">
    <xs:sequence>
      <xs:element name="id" type="xs:int" />
      <xs:element name="name" type="xs:string" />
    </xs:sequence>
  </xs:group>
  <xs:complexType name="body">
    <xs:group ref="r" />
  </xs:complexType>
</xs:schema>'

$data = '
<body>
    <r>
        <id>9</id>
        <name>AAA</name>
    </r>
    <r>
        <id>10</id>
        <name>BBB</name>
    </r>
</body>'

# read the schema:
$set = [System.Data.Dataset]::new()
$sr =[System.IO.StringReader]::new($schema)
$set.ReadXmlSchema($sr)

# read the data:
$sr =[System.IO.StringReader]::new($data)
$set.ReadXml($sr)

cls
$set.Tables | ft -AutoSize
write-host "type of column 'id' in table : " $set.Tables[0].Columns[0].DataType

$list = [System.Collections.ArrayList]::new($set.Tables[0].GetList())
write-host "type of column 'id' in list  : " $list[0].id.GetType()

I also did some tests with the XMLReadMode, but the only change appears, when I use [System.Data.XmlReadMode]::InferTypedSchema, but this changes the type to "byte" or something else depending on the data for that column.

Any help is more than welcome here! Thanks you in advance.

Solution

Thanks to the hints I finally solved it. First I found out, that I dont need to create a dedicated XMLSchema before the data-import - just creating the proper table-structure did the same thing with less code.

Here the final code-sample:

cls
$set =[System.Data.DataSet]::new()
$set.tables.Add('r')
$table = $set.Tables[0]
[void]$table.Columns.Add('id', [int])
[void]$table.Columns.Add('name', [string])

$data = '
<body>
    <r>
        <id>9</id>
        <name>AAA</name>
    </r>
    <r>
        <id>10</id>
        <name>BBB</name>
    </r>
</body>'

# read the data:
$sr =[System.IO.StringReader]::new($data)
[void]$set.ReadXml($sr)

$set.Tables | ft -AutoSize
write-host "type of column 'id' in table : "   $table.Columns['id'].DataType

$list = [System.Collections.ArrayList]::new($table.GetList())
write-host "type of column 'id' in list  : " $list[0].id.GetType()

Here the output from above script:

id name
-- ----
 9 AAA 
10 BBB 


type of column 'id' in table :  System.Int32
type of column 'id' in list  :  System.Int32