Preface
Complemented with Some Background to the Closed Loop

The subject matter discussed in this book concerns automatic control, or more specifically, control in system dynamics. It is an educational work, both theoretical and applicative in nature, featuring a number of solved problems.

The personalization of the presented content results from a well-known past (which nourishes the present), a desire for innovation and simplifcation, and a long-standing deep thinking based on experience. It is true to say that thinking on this subject has always been conducted based on acquired experience in electronics and automation, through teaching, research and technological-transfer activities within the framework of partnerships with the industrial sector. Driven by a concern for balance, these activities can also be credited for favorably supporting my career, first as an assistant in electronics and automation at the University of Bordeaux from 1978 to 1990, and then as an automation professor at the engineering schools of ENSEIRB (École Nationale Supérieure d’Électronique et de Radioélectricité de Bordeaux) and the Polytechnic Institute of Bordeaux, from 1991 to 2018.

Having had the privilege of presenting the foundations of the control loop at the prestigious Les Houches summer school in physics (France), I had the opportunity very early on to become aware of the favorable perception of our discipline by physicists, who indeed concluded my presentation by interpreting automation as a veritable science, even if my talk remained limited to the subject of the control loop itself. But in the context of the control loop, is automation not considered consistent with automation building based on the famous closed loop, better known by electronics engineers for its feedback (or negative reaction), and the open loop, which simultaneously determines stability and performance in terms of frequency?

The history of the closed loop answers this question, providing testimony through founding works, their context and their development, associated with the main dates. In fact, several elements are drawn in large part from one synthesis document produced by Jean-Claude Trigeassou, based on a contribution by Bennett, a science historian [BEN 79, BEN 93].

In its most widely accepted version, the closed loop can take different forms, notably that of the control loop (with controller), as studied in tracking and regulation in the automation control domain. The concept of the closed loop appears to date back to the 18th century, with the introduction of the mechanical device known as the Watt regulator, by Boulton and Watt in 1788. This device was regularly improved upon, notably by Siemens, and analyzed by physicists interested in its operation: Young in 1807, Airy in 1840 and 1851, and Maxwell in 1868 in his renowned article, “On Governors”, the first ever article on the subject of automation.

As the transcontinental telephone between the East and West Coasts of the United States required reamplification of the signal by repeaters (relay amplifiers for telephone lines), “Bell Laboratories” worked to replace the first (magnetic) amplifiers with low-frequency electronic amplifiers, made possible by the invention of the triode. Black was recruited to Bell in 1925 to improve on electronic tube repeaters, whose main shortcoming was their narrow bandwidth, associated with significant distortion. His idea of introducing a negative reaction to widen the bandwidth and reduce distortion was patented in 1927 and published in 1934 in the Bell System Technical Journal. Even if the concept of a closed loop appears to date back more than a century prior, it is Black specifically who can be credited for introducing the closed loop into the electronics field, through the shaping of feedback, as it is still used today.

But the feedback that could be at the origin of an oscillation, or indeed an instability, led Nyquist, also at Bell, to develop his famous criterion established based on Cauchy's theory and published in 1932 under the title, “Regeneration Theory”. In the case of a stable control loop in open loop, where the Nyquist criterion required the critical point (–1) to not be surrounded for closed-loop stability, a significant decrease in gain accompanied by an (illusory) low phase rotation was then sought.

In 1934, the problem was put to Bode, who demonstrated, for minimal phase-shifting systems (or systems with minimum phase), that a gain curve corresponded to a single phase curve, with this link between gain and phase already presenting a naturally admitted constraint in terms of synthesis and therefore performance: complementary to the Bode diagrams dating back to 1938, this contribution, associated with that of Nyquist, was published in 1940, and went on to be included in a book, published in 1945. Furthermore, the first proposition for the systematic adjustment of the P, I and D actions of the PID regulator should be attributed to Ziegler and Nichols, who published their widely known method in an article back in 1942.

Finally, the control loop was also used for temperature and pressure regulation, as well as for servomechanisms (notably for speed and position), according to the principles set out by Hazen in 1934, very similar to those of Black, although not inspired by them. Research into servomechanisms, which was developed significantly to support the armament effort in the Second World War, was given particular impetus in areas that were a priority for armament, including the domain of control and guidance of anti-aircraft defense guns. In 1940, Brown specified the performances of servo-controls, most specifically in transient state, through the damping coefficient and natural frequency. One of Brown’s researchers, Hall (thesis published in 1943), constructed a chart, known as the Hall chart, plotted in the complex plane (also known as the Nyquist plane), to change from the frequency response in open loop to the frequency response in closed loop. To change directly to closed loop based on the Bode diagrams in open loop, Nichols had the idea of transposing the Hall chart into a new plane, known as the Nichols plane, whose gain in decibels is applied on the ordinate, and whose phase in degrees is applied on the abscissa [JAM 47]. An even older origin of the Nichols plane and chart can be found in the Black plane and chart, dating back to 1934, in the sense that the Nichols plane results from the permutation of the Black gain and phase axes, accompanied by the expression of the gain in decibels (in compliance with the Bode representation). Yet these works, which contributed to the precision (in position and speed) of servomechanisms, were not enough to address the more general problem of pursuit of target, which also required the anticipation of the movements of the target and a prediction of its future behavior. So Wiener developed his famous filter, known as the Wiener filter (1942), used to guide DCA artillery based on radar information, thus replacing manual guiding. Section 1.10.4 provides additional details of a more technical nature.

Having gone through these major points in its history, let us now present the control loop in the context of the present book, specifying that by studying all aspects of the control loop, we are able to present, in a clear, structured manner, all of the functions, properties and performances that can characterize all other controls.

Moreover, the unification exercise considered in Chapter 4, which consists of developing a control loop equivalent to any other control among a set of controls, makes it possible to demonstrate an absence of specific contribution in terms of performances, even with the synthesis method differing, depending on the control.

Certainly expressing a change with respect to the control loop, this methodological contribution, which, in principle, allows us to assume a bonus in terms of performance, and which, subsequently, retains this in the best case scenario, leads us at the very least to think of the principle, according to which it is advisable to change the form (here, the methodology) to preserve the substance (here, performance). It is true that evolution is de rigueur, so if a change is inevitable when it is not necessary, is it not preferable to opt for a change of form that is fundamentally the least detrimental?

With the control loop thus all the more reinforced, as indeed confirmed by its usage in all robustness approaches, it is widely developed in the first two chapters of this book, which accord it due credit. This didactic choice should help the reader to obtain a measure of the major interest of the command loop, in the sense of its own interest and the interest it represents for other controls through the often-implicit place that it occupies, and which is highlighted by establishing the equivalent control loop. This same loop, through the nature of its regulator, makes it possible to objectively appreciate the richness of control strategy, with the control loop thus appearing as an absolute reference. This means that the control loop, which is the proven substrate of automation, must be very widely known to all, including specialists of other controls, at the risk of rediscovering lukewarm water, or even making cold water from it, by achieving less success than the control loop.

The innovative contribution in terms of performance undoubtedly lies in the so-called robust controls, including the CRONE control (the French abbreviation for the Robust Control of Non-Integer Order), which combines three significant advantages in terms...