Stiffness of the control loop

Hi mechatronics fans!

Welcome to the latest post of the Sinadrives blog.

In previous posts we’ve looked at closed-loop control systems. If you’re not familiar with them, check out this post on open-loop/closed-loop control systems.

What we mean by “stiffness” is the capacity of the control system to react to disturbances or, more specifically, to an error between the set value and the real value. The greater the stiffness of a control system, the faster it will correct an error. However, stiffness can’t be increased infinitely, since there is a risk of destabilizing the system.

PID control is quite an effective way to correct errors; indeed, control systems have been using this technology for over 100 years. As electronics and microcontrollers have evolved, the reliability and, above all, the efficacy of control systems have increased to the point where calculation capacity has enabled the incorporation of new control functions in the process.
These new functions complement PID control, making it possible to obtain a more dynamic response or to directly compensate specific error sources.

For instance, if we take the position control of a linear axis by a CNC or PLC controller, we can see that the unit generates a theoretical trajectory that serves as a reference.

In this case, conventional PID control is applied: the real position value is read by means of an encoder and the output value is corrected in order to minimize error.

This correction, in the case of a linear axis, translates into a current and voltage output. Despite taking mere milliseconds to complete, this conversion produces a delay that impacts on the effectiveness of the system.

Could the output value be corrected directly without considering the position data? Yes, it could. In fact, this is standard practice in 99% of the controllers used today.

Taking the theoretical position trajectory, a theoretical velocity reference associated with this movement can be easily obtained, on the basis of which an acceleration or force reference can then be calculated.

Velocity in a servomotor is proportional to the level of voltage applied to it, while force is proportional to the current it consumes.
The same encoder that gave us the real position can also be used to obtain the real velocity value and, consequently, to close the PID velocity loop. By measuring the output current of the unit, we can obtain the consumption value of the motor, which makes it possible to close the force or current loop.

These three control loops could be applied independently, but given the direct dependence described above, it’s much better to apply them in a cascade arrangement. The position loop corrections are added to the velocity reference, and the resulting corrections of this loop are applied to the current loop.

Through this arrangement, the control obtained is much more dynamic, making it possible to minimize errors in the trajectory of the movement.

The stiffness of the control loop has been increased automatically, without the risk of destabilization involved in increasing the gains of a single-loop PID controller.

We’ve seen how the cascade arrangement has improved the response of the control system. Nevertheless, it involves corrections based on a set of ideal theoretical references. The fact is that in real applications, various external elements always come into play that make the control task more complicated.

These disturbances are caused by unexpected circumstances, but also by the intrinsic characteristics of the application itself. For example, in the case of the linear axis where we’ve calculated a theoretical force profile according to acceleration, if the load undergoes changes due to the process (weight is carried in the outbound trajectory but no weight is carried in the return trajectory), the calculated profile ceases to be ideal.

The disturbances will be compensated by the control loops, but this will take time and a major variation could destabilize the system.

If we could anticipate events, we could act on the corrections of the control system in order to compensate the disturbances in the exact moment when they are likely to harm the system.

This is the idea behind the feed-forward concept. By measuring the value of the disturbances, we can compensate them before they affect the system, thus achieving faster and more effective error correction.

For example, if in our application we have a flow control system involving a valve to maintain a constant flow value, a variation in room temperature will have a negative impact on the control algorithm.

By measuring the temperature, we can modify the behaviour of the valve in order to compensate the effect of the temperature change before it occurs (or before the effect becomes significant).

The only essential requirement for the application of feed-forward control is that the disturbance be measurable. Other compensations based on theoretical terms or estimations (let’s suppose that the temperature will rise 1ºC per hour until midday and will then drop at the same rate) may be useful, but they can’t be classified as feed-forward control elements.

We’ve seen that in addition to classic PID control, other complementary control techniques exist that help to improve stiffness. It’s clear that to a greater or lesser degree, depending on the type of process, these techniques are highly beneficial and must be implemented in applications where dynamics and precision are the overriding specifications.

Draw your own conclusions. Decide which innovation you want to implement in your machine to be competitive. We can help you.

Your SINADRIVES Team.