rtai-guide

# extract linux-3.16 to $linux
# extract rtai-4.1   to $rtai
# have .config ready at $config

# patch kernel
cd $linux
patch -p1 < $rtai/base/arch/x86/patches/hal-linux-3.16-x86-3.patch

# configure kernel
cp $config .config
make oldconfig   # press enter for every question
make menuconfig  # set local version to something like "-rtai-4.1"
                 # disable module versioning support

# compile kernel
make # make sure to use gcc < 5 for linux-3.16

# install kernel and modules
make install          # or just copy bzImage where you need it
                      # e.g. /boot/vmlinuz-linux-3.16-rtai-4.1
                      # we will refer to this path as $kernelimage
make modules_install

# create initramfs if necessary (depends on your linux distribution)
# for archlinux:
mkinitcpio -k $kernelimage -c /etc/mkinitcpio.conf -g /boot/initramfs-3.16-rtai-4.1.img

# configure boot loader and reboot with rtai-4.1 kernel
# you might need to run depmod -a after the first boot
# and reboot to get all modules to load correctly

# build and install rtai
cd $rtai
make menuconfig # make sure the path to linux source tree is correct
make
make install