trier les éléments d'une jlist

Je suis en train de trier une JList lorsque vous appuyez sur le bouton de tri mais je peux pas comprendre comment le faire.
C'est mon code:

Classe Song:

package song;

public class Song implements Comparable<Song>{
    private String name;
    private String artist;

    public Song(String name, String artist){
        this.name = name;
        this.artist = artist;
    }

    public String getName(){
        return name;
    }

    public String getArtist(){
        return artist;
    }

    public void setArtist(String artist){
        this.artist = artist;
    }

    public void setName(String name){
        this.name = name;
    }

    public int compareTo(Song s){
        return this.name.compareTo(s.getName());
    }

    public String toString(){
        return name + " " + artist;
    }
}

Liste Modèle:

package song;

import java.util.ArrayList;
import java.util.Collections;

import javax.swing.AbstractListModel;

public class ListModel extends AbstractListModel{
    ArrayList<Song> songs;

    public ListModel(ArrayList<Song> array){
        songs = array;
    }

    public int getSize(){
        return songs.size();
    }

    public Object getElementAt(int index){
        return (Song)songs.get(index);
    }

    public ArrayList<Song> getSongList(){
        return songs;
    }

    public void setList(ArrayList<Song> array){
        this.songs = array;
    }

    public void getSortedList(ArrayList<Song> array){
        Collections.sort(array);
        songs = array;
    }
}

La classe App:

    package song;
import java.awt.BorderLayout;
import java.awt.Color;
import java.awt.Dimension;
import java.awt.GridLayout;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.Reader;
import java.util.ArrayList;
import java.util.Collections;
import javax.swing.JButton;
import javax.swing.JFrame;
import javax.swing.JLabel;
import javax.swing.JList;
import javax.swing.JPanel;
import javax.swing.JTextField;
import javax.swing.ListSelectionModel;
public class App extends JFrame{
JFrame frame;
JList<Song> list;
ArrayList<Song> songList;
ListModel songModelList;
private static final String FILE =  "songs.txt";
JPanel loadPanel, addBtnPanel;
JButton btnLoad, btnSort, btnAdd, btnSave;
JTextField txtArtist, txtName;
public static void main(String[] args){
App a = new App();
}
public App(){
frame = new JFrame("Playlist");
loadPanel = createLoadPanel();
loadPanel.setBackground(Color.BLUE);
JPanel btnPanel = createButtonPanel();
btnPanel.setBackground(Color.ORANGE);
frame.getContentPane().add(btnPanel,BorderLayout.EAST);
frame.getContentPane().add(loadPanel,BorderLayout.CENTER);
frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
frame.setSize(300, 300);
//     frame.pack();s
frame.setVisible(true);
}
public JPanel createButtonPanel(){
JPanel panel = new JPanel();
btnLoad = new JButton("Load List");
btnSort = new JButton("Sort list");
btnAdd = new JButton("Add");
btnSort.addActionListener(new ActionListener() { //here is the action listener for the button used for sorting
@Override
public void actionPerformed(ActionEvent e) {
//             Collections.sort(songList);
//             songModelList.setList(songList);
songModelList.getSortedList(songList);
list.updateUI();
}
});
btnLoad.addActionListener(new ActionListener() {
@Override
public void actionPerformed(ActionEvent e) {
loadPanel.setVisible(true);
}
});
btnAdd.addActionListener(new ActionListener() {
@Override
public void actionPerformed(ActionEvent e) {
addBtnPanel = createAddPanel();
}
});
panel.add(btnLoad);
panel.add(btnSort);
panel.add(btnAdd);
return panel;
}
public JPanel createAddPanel(){
JFrame frame = new JFrame();
JPanel panel = new JPanel(new GridLayout(3,2));
JLabel lblName = new JLabel("Name");
JLabel lblArtist = new JLabel("Artist");
txtName = new JTextField(15);
txtArtist = new JTextField(15);
panel.add(lblName);
panel.add(txtName);
panel.add(lblArtist);
panel.add(txtArtist);
btnSave = new JButton("Save");
panel.add(btnSave);
btnSave.addActionListener(new ActionListener() {
@Override
public void actionPerformed(ActionEvent e) {
String name = txtName.getText();
String artist = txtArtist.getText();
Song s = new Song(name, artist);
songModelList.getSongList().add(s);
list.updateUI();
}
});
frame.getContentPane().add(BorderLayout.CENTER,panel);
frame.setVisible(true);
frame.setSize(new Dimension(300,100));
return panel;
}
public JPanel createLoadPanel(){
JPanel LoadPanel = new JPanel();
list = new JList<Song>();
songList = loadFromFile();
songModelList = new ListModel(songList);
songList = new ArrayList<Song>();
list.setModel(songModelList);
list.getSelectionModel().setSelectionMode(ListSelectionModel.SINGLE_SELECTION);
LoadPanel.add(list);
LoadPanel.setVisible(false);
return LoadPanel;
}
public ArrayList<Song> loadFromFile(){
ArrayList<Song> array = new ArrayList<Song>();
try{
BufferedReader reader = new BufferedReader(new FileReader(FILE));
String line = null;
while((line = reader.readLine()) != null){
String[] parts = line.split(" - ");
if(parts.length == 2){
String name = parts[0];
String artist = parts[1];
Song s = new Song(name, artist);
array.add(s);
}
else{
System.out.println("Invalid line!");
}
}
reader.close();
}catch(IOException e){
System.out.println("File not found");
e.printStackTrace();
}
return array;
}
}

Donc, la JList desplays les éléments dans l'ordre où ils sont ajoutés. Mais si l'utilisateur veut les trier, j'ai fait un bouton de tri et lorsque le bouton est appuyé, la JList affiche les éléments dans l'ordre de tri. Comment puis-je gérer pour le faire? J'ai essayé maintes et maintes fois, mais il ne fonctionne pas.