Is your input field and TextBox in same page or different I guess both are in same page.If they are not in same page you can apply little trick according to this solution.
You need to add runat="server" in your input as well as add id to it simultaneously you have to add OnTextChanged event and AutoPostBack="true" to the property of your TextBox as it is run at server then you can copy using code behind code give below
Code in ASPX:
<form id="form1" runat="server">
<div>
<asp:textbox id="atxt" ontextchanged="atxt_TextChanged" autopostback="true" runat="server" ></asp:textbox>
</div>
<input id="aID" type="text" runat="server" name="ainput" />
</form>
Code behind in .cs:
protected void atxt_TextChanged(object sender, EventArgs e)
{
aID.Value = atxt.Text;
}