我的单选按钮没有从foreach循环中获得值，表单验证返回'；必填字段'；即使已检查

我正在使用codeigniter。验证错误一直说"需要主席字段"，尽管在元素检查时，单选按钮有一个值。所以我想问题是没有看到单选按钮输入字段。

以下是我的观点：

 <form method="" action="" id="vote_results" >
 <?php if (isset($vchairman_records)) : foreach ($vchairman_records as $v_chairman_row) : ?>
 <input type="radio" id="chairman" name="chairman"  value="<?php echo $chairman_row->registration_number ?>" /> 
  <?php endforeach; ?>
     <?php else : ?>
      <p class="">No records were returned</p>
    <?php endif; ?>
 
 <button type="submit" class="btn btn-success btn-lg alert-info sb_button" id="vote">
  <span id="sending_btn" style="display: none">Sending....</span>
  <span class="" id="profesional-btn">Submit</span>
 </button>
 </form>

## My Controller ##
    $this->form_validation->set_rules('chairman', 'Chairman', 'required|xss_clean');
    
        if (!$this->form_validation->run() == FALSE) {
            $data = array(
                'success' => FALSE,
                'errors' => validation_errors()
            );

            echo json_encode($dat

a） ；

Ajax

function loader_doc(v) {
            if (v === 'on') {
                $('#sending_btn').show();
                $('#profesional-btn').hide();
            } else {
                    $('#sending_btn').hide();
                    $('#profesional-btn').show();
                }
            }
     $(document).ready(function () {
                $('form#vote_results').submit(function (e) {
                    e.preventDefault();
                    loader_doc('on');

                    var vote_data = new FormData();
                    vote_data.append('chairman', $('#chairman').val());
                  
                    $.ajax({
                        url: '<?php echo base_url('StartPageController/get_results'); ?>',
                        method: 'post',
                        contentType: false,
                        processData: false,
                        cache: false,
                        dataType: 'json',
                        data: vote_data,
                        success: function (data) {
                            if (!data.success) {
                                $('.n').modal('show');
                                $('.m').append(data.errors);
                                loader_doc('off');

                            } else {
                                
                                alert(data.msg);
                                loader_doc('off');
                            }
                            loader_doc('off');
                        },
                        error: function () {
                        }
                    });
                });
            });