The inertia of a rotating mass can be computed (or measured: see the section II of this paper,). We know that the torque required to accelerate that inertia is equal to the product of inertia and the acceleration rate: (t = I.a). If we assume a frictionless system, and that the inertia and the desired acceleration rate is known, the torque required to accelerate the mass to a desired speed without closing a speed loop can be computed. Why is this? We know that acceleration is the derivative of speed. This implies that the derivative of a clean speed reference will yield the acceleration rate. That rate can be multiplied by the known inertia to yield the torque required to accelerate the inertia such that the rotational speed tracks the speed reference (known as inertia compensation ). The system will track the speed reference without closing a speed loop. This is considered an open loop speed controller, and it works based on the computed feedforward torque reference.

Unfortunately the real world is full of non-linearities that limit the effectiveness of such feed forward control schemes. In the above example, if we do not add some extra torque (or, over time, energy) to compensate for the non-linear friction and windage losses, these losses will consume the energy that was intended to be used for accelerating the mass, and result in a difference between the actual speed and the speed reference. By using a feed-forward loss compensation signal for friction losses, this can be overcome. A simple way to accomplish this is to set the speed reference of a temporarily closed speed loop controller to a set of specified values, and tabulate the time-averaged value of the torque reference at each speed. This look-up table (known as friction compensation ) can then be used with an input pointer of speed reference, and an output of feed-forward friction and windage loss torque to effectively compensate for these energy losses.

If you have set-up the two above feed-forward signals perfectly, and the friction losses are predictable and non time-varying, the actual speed will match the speed reference. However real world implementations cannot exactly compensate for time varying friction losses, and the actual speed will vary with the time varying friction and windage losses. Friction and windage in a given system will vary with temperature, humidity, bearing-grease age etc. Usually the above compensation terms are utilized to assist a closed speed loop by maintaining the speed "in the ballpark" and thereby minimizing the output of the loop PI regulator. This is very desirable in some applications, because the integrator (which is an energy storage device) in the loop is maintained with a minimal storage value, enabling it to be reset with a minimum disturbance to the system. See this paper for more insights into the weaknesses of feed-forward control.

The tension on the outflow side of a driven roll (or bridle) in a properly configured section of web (paper and converting industries) or strip (metals industries) is known to be: T_OUT = T_IN – t_M.GR/R. Or in other words: The tension on the OUTPUT side of a driven roll is equal to the tension on the INPUT side minus the motor shaft torque that is reflected to the driven roll surface. If the motor is "motoring" it will lower the tension on the output side, if it is "regenerating" or absorbing power, it will increase the tension on the output side. Here again, if we know (from measurement for example) what the tension on the input side of the driven roll is, and we know what tension we want on the output side, we can compute the torque we need to generate the desired tension control.

Friction and windage losses will consume energy in tension control designs as well (see this paper). They will consume energy that was supposed to be used for holding tension. The result of this is that the actual tension will differ from the tension reference. This can be overcome by implementing the same feed-forward friction/windage loss compensation signal described in Example 1 above. However, note that if there is no closed speed loop, the feed-forward terms described above will be required to compensate for the energy needed to accelerate the roll inertia during line speed changes. If this is not done the system will not maintain tension and the web/strip may "bottom out" when discharging from winders/unwinders, or web breaks may occur during changes in line speed.

Assume that a process is devised where, in order to accelerate a mass, air must be blown into a sail-like device. We know that F = P.A (Force = pressure times area) and F = m.A (Force = mass times acceleration). If the effective surface area, the mass, and the desired acceleration rate are know, the Pressure needed to meet that desired acceleration rate can be computed. In addition, if the relationship between the pressure and the fan torque, and speed are known, the same techniques described above can be implemented to predict the fan motor torque that is required to meet the desired application acceleration rate. designs similar to these demonstrate the usefullness of feed forward controls techniques. They can be deployed to solve many difficult controls problems. See this report for an example.

In these applications the design engineer must also develop feedforward compensation schemes to compensate for the energy losses associated with the movement of air in pipes. Since this kind of windage loss term is highly non-linear and poorly understood it is best to close a speed loop around the feed forward pressure loop, and let the speed controller compute the difference.

The bandwidth (see the introduction here) of a speed loop varies linearly with inertia, the bigger the inertia, the lower the bandwidth for a given fixed gain. If the application reflected inertia varies a from very small value to a very large value (for example: a paper machine winder) and the controls engineer implements a fixed gain regulator, the loop may be stable at core, but wildly unstable at full roll. Or the loop may be stable at full roll, but the drive gets very "noisy" and chatters and growls at core. In these applications, where the change in inertia is significant, the controls engineer will always have to design the speed controller to schedule the gain of the loop as a function of the roll inertia (which can be computed based on a known density, a measured diameter, and a roll width). In essence, the gain is increased proportional to the increase in roll inertia, or until a gain limit is reached (all systems are gain limited due to noise, read Section II of this paper for more information about gain limitations due to system noise, and torque jitter). When a proportional gain limit is reached the controller must be designed to decrease the integral gain as inertia increases in an inversely proportional manner, this will keep the loop stable over the entire roll build-up.

If a PI (proportional plus integral) position loop is closed around a torque loop, without a closed speed loop between the position and torque loops. This loop has two integrations in the forward path (from torque to speed, and then from speed to position), and then a third one from the PI regulator. That equals -270 [deg] of phase shift from DC to the first lead frequency. With only one "zero" (+90 [deg]); in the PI regulator, their will always be 180 [deg] of phase shift at the loop crossover frequency. A crossover that is 180 [deg] phase shifted, no-matter what the gain value is, will be unstable at or about the crossover frequency. If a derivative term (i.e. a PID regulator) is used to close the loop, the extra "zero" helps by adding phase margin (+90 [deg]). However for most untrained field service engineers, PID regulators are difficult to tune. A better approach is to close the position PI loop around a closed speed loop. The speed loop acts like a low-pass filter in the outer position loop, and a fixed gain position loop tuning (albeit an optimally "slow" tuning) can be found that will be stable at all inertia values. An even better approach is to use gain and frequency scheduling to guarantee that the controller is optimally "hot" for all inertia values. If you have trouble understanding "poles" and "zeroes". Try taking the first course of our 10 volume/20-course Advanced Dynamic Simulation course. Or ask us to help you out with your particular controls problem.