Implementation of Time Optimal Control Law

Implementation of time optimal control law (bang-bang controller) for a double integral system

This is an example of bang-bang controller. The problem statement is taken from Optimal Control Systems by D.S. Naidu, page no. 306, which is about the simple motion of a block of mass 'm' in a frictionless environment when subjected to an external force f(t). The motion is described as:
m*y''(t) = f(t)
where, y(t) is the position of the block at time t, so that, y'(t) and y"(t) represents the velocity and acceleration of the block, respectively.
In the Simulink model, x_1 is the state variable for the position of the block (y), and x_2 is the state variable for the velocity of the block (y'). The initial conditions can be altered in their respective blocks. Control input can be visualized from the scope labeled as 'Control Input'.