The Arduino is the best microcontroller to do so. Lots of example is code is available, and we are glad to help.
A closed loop is software that controls motion with sensors. For example a balancing robot.http://en.wikipedia.org/wiki/Closed_loop
(read the 'feedback' and the 'PID controller')
An IMU is a few sensors together, needed to control for example that balancing robot.http://en.wikipedia.org/wiki/Inertial_measurement_unit
I guess you need an IMU, but also a few motors or servo motors.
Search for "arduino balancing" or "arduino self leveling", you will find many projects.
Here are a few:https://sites.google.com/site/onewheeledselfbalancing/Home/easy-build-low-cost-arduino-self-balancerhttp://sebastiannilsson.com/en/k/projekt/selfbalancing-robot/
But I think you don't have to make a robot, but something like this self-leveling project:
For some IMU boards is good code available, and for others not.
Boards at Sparkfun have good code, https://www.sparkfun.com/search/results?term=imu&what=products
The MPU-6050 sensor board is very cheap on Ebay. Jeff Rowberg wrote a good library for that, https://github.com/jrowberg/i2cdevlib/tree/master/Arduino/MPU6050
And this is the 'teapot' example using that:
You also need motors or servo motors. Servo motors can be easily connected to the Arduino, and the Servo library provides an easy way to control them, http://arduino.cc/en/Reference/Servo
It all starts with an Arduino board. I would suggest the Arduino Uno board, that is the most common and easiest board.http://arduino.cc/en/Main/arduinoBoardUno
Follow the instructions to set it up, see "Getting Started" on the home page, http://www.arduino.cc/
First thing to do is to get the 'Blink' example running on the Arduino.