using $this->$Var to call an existing method-Collection of common programming errors

I’m in the process of creating a controller to display pages. I currently have this;

 $request  = str_replace("/Smarty/", "", $_SERVER['REQUEST_URI']); 
   $params = explode("/", $request);  

  function FormatArr ($Arr){
        $Array_Keys = array ("PageName","Username");
        if (count($Arr) > 2){
            trigger_error("Unexpected Params",E_USER_ERROR);
        }
        return array_combine($Array_Keys,$Arr);
    }
    $New_Params = FormatArr($params);

On the setup.php page, then on my libs:

class testing {
        protected $Smarty;
        protected $fixpath;
        public function __construct($Template_Name){
            $this->Smarty = new Smarty;
            $this->fixpath = dirname(__FILE__)."./Templates/".$Template_Name;           
            $this->Smarty->compile_dir=$this->fixpath."/compile";
            $this->Smarty->template_dir=$this->fixpath."/html";
        }
        public function index(){
            $this->Smarty->assign("name","test");
            $this->Smarty->assign("test","../test/");   
        }
        public function Display_Page($PageName){
            $this->$PageName();
            $this->Smarty->display($PageName.".html");

        }
    }
    $Test = new testing('Testing/');

I have it sucessfully working, but I want to dynamically call pages which will render the correct variables on the smarty template. The problem is caused by:

$this->$PageName;

I’m struggling on finding the way of making this sucessfully call the necessary method