WPF KeyBinding 命令未在自定义控件中触发

我正在构建一个 WPF 自定义控件（注意：不是用户控件）。控件的c#代码定义如下：

using System.Windows;
using System.Windows.Controls;
using MvvmFoundation.Wpf;

namespace TextBoxWithInputBinding
{
    public class AutoComp : Control
    {
        static AutoComp()
        {
            DefaultStyleKeyProperty.OverrideMetadata(typeof(AutoComp), new FrameworkPropertyMetadata(typeof(AutoComp)));
        }

        public AutoComp()
        {
            DownCommand = new RelayCommand(() =>
            {
                System.Diagnostics.Debug.WriteLine("Down");
            });
            PressedCommand = new RelayCommand(() =>
            {
                System.Diagnostics.Debug.WriteLine("Pressed");
            });
        }

        public RelayCommand DownCommand
        {
            get { return (RelayCommand)GetValue(DownCommandProperty); }
            set { SetValue(DownCommandProperty, value); }
        }

        public static readonly DependencyProperty DownCommandProperty =
            DependencyProperty.Register("DownCommand", typeof(RelayCommand), typeof(AutoComp), new PropertyMetadata(null));

        public RelayCommand PressedCommand
        {
            get { return (RelayCommand)GetValue(PressedCommandProperty); }
            set { SetValue(PressedCommandProperty, value); }
        }

        public static readonly DependencyProperty PressedCommandProperty =
            DependencyProperty.Register("PressedCommand", typeof(RelayCommand), typeof(AutoComp), new PropertyMetadata(null));
    }
}

我在Generic.xaml中为控件定义模板，如下所示：

<ResourceDictionary
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:local="clr-namespace:TextBoxWithInputBinding">
    <Style TargetType="{x:Type local:AutoComp}">
        <Setter Property="Template">
            <Setter.Value>
                <ControlTemplate TargetType="{x:Type local:AutoComp}">
                    <Border Background="{TemplateBinding Background}"
                            BorderBrush="{TemplateBinding BorderBrush}"
                            BorderThickness="{TemplateBinding BorderThickness}"
                            >
                        <StackPanel>
                            <TextBox>
                                <TextBox.InputBindings>
                                    <KeyBinding Key="Down" Command="{TemplateBinding DownCommand}"/>
                                </TextBox.InputBindings>
                            </TextBox>
                            <Button Content="Press me" Command="{TemplateBinding PressedCommand}"/>
                        </StackPanel>
                    </Border>
                </ControlTemplate>
            </Setter.Value>
        </Setter>
    </Style>
</ResourceDictionary>

当我按下“按下我”按钮时，会触发 PressedCommand（输出窗口中出现“按下”一词 - 但是，当我输入文本框并按下向下键时，没有任何反应。

我需要做什么才能使 DownCommand 火起来？