From the control system perspective, I find it interesting that we continue to model most industrial applications of motors with trapezoidal “time displacement” curves and PID (proprotional integral and derivative) tuning algortihms. It seems that we should have better definitions for things after all the time and effort that goes into it.
It is important to see that the graphical representation of motion in “time displacement” plot is also a very literal representation of the mechanical aspect of motion. The area under the curve is the mechanical work done by the system.
The acceleration leg of the trapezoid is the energy needed to bring the load from rest to a constant speed. The acceleration profile is expressed simply as a scalar changing velocity that is increasing in value until the desired speed is reached. The first derivative of velocity is acceleration, or the rate of increase of velocity over the unit change in time.
What might be of interest here is that the acceleration changes from a positive value to zero when the desired speed is reached. Then acceleration is zero, because the system command will be for a constant speed with no acceleration. And in PID type controls, the transition from positive acceleration to a zero acceleration invariably causes velocity overshoot.
Since everything can be mapped with respect to time, isn’t it more straightforward to consider the inflection points along the way and change the control methodology according to what is going on in the real world?
So coming up to the transition from accelerating to not accelerating, we know that the first derivative value is decreasing to zero. Maybe our control strategy should be to switch from the velocity loop control and switch to the torque loop so we can decrease the current going to the motor. This will soften the transition point and minimize overshoot without the use of PID control.
Torque control during fixed position control also has some intuitive benefits. Any disturbance in position is countered by an opposing torque, or current control through the servoamplifier, to restore position. This behavior can be embedded in the amplifier and does not require intervention from the controller, minimizing control system loading.
PID control, while enormously successful over the years, is a sort of averaging solution. We will apply gain values across a wide range of motion conditions in hope that they will work satisfactorily for all states over the time of the move . But if we consider other possibilities, other strategies for control become possible.
This has been the goal of “adaptive gain” solutions which exist today and have evolved over the years as control technology has become cheaper and more powerful and the industry has acknowledged the weaknesses of PID control. By paying attention to the “inflection points” along the trajectory fo the motion, different control strategies are made possible that are simple, reliable and in some cases, more robust than what is possible with conventional control.