Output results of get_post_type using orderby

Is it possible to list the output of get_post_type alphabetically in the following:

<?php
  $post_type = get_post_type_object( get_post_type($post) ); // GET SINGULAR NAME
    $args = array(
    'public'   => true,
    '_builtin' => false
    );
    $output = 'objects'; // names or objects, note names is the default
    $operator = 'and'; // 'and' or 'or'
    $post_types = get_post_types($args, $output, $operator);
    echo '<select class="selectboxSingle" name="post_type">';
    foreach ( $post_types  as $post_type ) {
    $exclude = array('phase1','phase2');
    if(TRUE === in_array($post_type->name,$exclude)){
    continue;
    }
    // Note: I think you need to use query_var here, rather than slug.
    echo '<option value="'.$post_type->query_var.'">' . ucfirst($post_type->labels->singular_name) . '</option>';
    }
    echo "</select>";
?>