Why my custom sub-category SEARCH FILTER don't work ?

Hi,

I edit my wordpress page searchform.php in theme to add filter by subcategories. And i add a add_filter(‘the_search_query’,’search_filter’) in my function.php

But when run a search : result dont care about my dropdown…

==> My question : How to make search (filter) works with my catégory filter ?

Hi have this :
https://i.stack.imgur.com/x0kEM.jpg

This in my searchpage.php :

<?php
$options_type = array(
 'name'               => 'subcat_type',
 'hierarchical'       => 1,
 'parent'             => get_category_by_slug('action-type')->term_id,
 'show_option_none'   => ("Type d’action"),
 'selected'           => (isset($_GET['subcat_type']) ? $_GET['subcat_type'] : ''),
 'hide_empty'   => 0  ); 

.......

?>

<form method="get" id="search-form" action="<?php echo home_url(); ?>/">
    <input class="search-box vntd-boxed-content" name="s" id="s" type="text" value="<?php echo isset($_GET['s']) ? $_GET['s'] : '' ?>" placeholder="<?php _e('Que recherchez vous ?','vntd_renown') ?>">
    <?php wp_dropdown_categories($options_type); ?>
    <?php wp_dropdown_categories($options_thematiques); ?>
    <?php wp_dropdown_categories($options_public); ?>
    <?php wp_dropdown_categories($options_territoire); ?>
    <input type="hidden" id="my_search" name="my_search" value="c_search" />
    <input type="submit" id="searchsubmit" value="Rechercher" />
</form>

this in my functions.php :

<?php
// Define search filter
function search_filter( $query ) {
    // only modify your custom search query.
    if ( $query->is_search &&  $_post['my_search'] == "c_search") {
        $args = array(
                'relation' => 'AND',
            array(
                'taxonomy' => 'category',
                'field' => 'id',
                'terms' => array( $_post['subcat_public']),
                'operator' => 'IN'
            ),
            array(
                'taxonomy' => 'category',
                'field' => 'id',
                'terms' => array( $_post['subcat_territoire']),
                'operator' => 'IN'
            ),
            array(
                'taxonomy' => 'category',
                'field' => 'id',
                'terms' => array( $_post['subcat_thematiques']),
                'operator' => 'IN'
            ),
            array(
                'taxonomy' => 'category',
                'field' => 'id',
                'terms' => array( $_post['subcat_type']),
                'operator' => 'IN'
            )
        );
        $query->set( 'tax_query', $args);
    }
    return $query;
}
add_filter( 'the_search_query','search_filter');
?>