Hi,
Depending on the situation, I recommend two possible solutions:
1. You can set the search to redirect to a custom URL, where you can add a static parameter, like ?s={phrase}&cat=1
2. To use the redirection to custom URL, and add the parameters conditionally via custom code based on this example. In your case, something like this:
// Use this to change the "redirect to url" parameter
add_filter( 'asp_redirect_url', 'asp_add_params_to_url', 1, 10 );
// Use this to change the "show more results url" parameter
add_filter( 'asp_show_more_url', 'asp_add_params_to_url', 1, 10 );
function asp_add_params_to_url( $url ) {
// Array of param names and values
$values = array(
"cat" => "1"
);
// Merge them together
foreach ( $values as $k => $v )
$url .= "&".$k."=".$v;
return $url;
}