Tuning PID Constants Over a Range

[Ether]

Originally Posted by wesleyac

The RoboRIO has the power required to calculate motion profiles on-the-fly. In fact, despite not having any changing setpoints last year, we still did trapezoidal motion profiling largely on-the-fly.

Let's say at some time t_i your setpoint changes to x_s, and your present position, velocity, and acceleration are x_i, v_i, and a_i.

What formulas are you using to compute the new motion profile given these non-zero initial conditions?