introduction

In the late 1940s, two forces converged to change the field of control systems forever: a team of brilliant young engineers at North American Aviation’s Aerophysics Laboratory and one of their newest leaders, Walter Evans. These engineers were solving some of the most difficult problems of the era—designing precision navigation systems for long-range, unmanned aircraft and submarines that needed to reach the North Pole with pinpoint accuracy.

The challenge was immense. Stability and performance requirements were beyond anything designers had previously faced. Classical analysis methods—while powerful—offered little intuitive guidance, often leaving engineers with an uneasy mix of mathematics, physical intuition, and trial-and-error tinkering.

Then came the Root Locus Method.

Within months of its introduction, engineers at North American Aviation recognized its power. It provided an immediate, visual way to understand how a system’s behavior would change as design parameters varied. No longer were control engineers flying blind—they could now see at a glance, how stability and performance were affected by gain adjustments.

As word spread, root locus quickly became the default approach to control system design. Its impact was amplified by the spirule, a simple but ingenious tool that allowed engineers to construct root locus diagrams with precision and speed—long before computers could automate the task. Together, the method and the spirule embedded themselves into the culture of control engineering. For many engineers, root locus was more than a mathematical tool—it was a breakthrough that trans-formed the way they worked. One engineer captured its impact with a word: hope. 

"My task was to determine an analog autopilot that would be stable throughout the flight. Using all the classical analysis methods, I was floundering. When Walt first started discussing root locus in his class, I saw a ray of hope."

At a time when control system design was as much an art as a science, root locus provided something invaluable—clarity. It bridged the gap between frequency-domain analysis and time-domain specifications, making stability and performance requirements easier to achieve.

Its influence spread rapidly, becoming an essential part of the international culture of automatic control. Seventy-five years later, it remains a foundational design tool, still among the first steps taken when engineers tackle a new control system.

Before the advent of root locus, control system design was often a patchwork of methods—part theory, part intuition, part sheer persistence. Engineers relied on frequency-domain techniques‑Nyquist and Bode plots, but these had limitations:

• Nyquist Criterion could confirm whether a      system was stable, but it offered little insight into how to fix an      unstable design.
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• Bode plots helped engineers understand      gain and phase margins but adjusting them to meet time-domain      specifications was more art than science.
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• Trial and error were common. Engineers      manually tuned resistors, capacitors, and inductors, often testing      prototypes to see what worked.
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• Mathematical complexity made high-order systems      difficult to analyze, forcing engineers to rely on simplified      approximations that sometimes failed in practice.
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• The biggest gap? Engineers understood that poles and zeros dictated      stability and transient response, but systematic methods to      manipulate their locations in the complex plane were lacking. This      limitation made it difficult to design systems with specific dynamic      characteristics or ensure robust stability.
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Walter Evans, better known to his colleagues as Walt, was a person of remarkable insight, and a major leader in the understanding of automatic control and how to design excellent systems very well and very quickly. At the heart of the design of any automatic control system is what the natural dynamic behavior of the controlled system will be—how stable it will be, and how quick and well-damped its natural motions will be following any disturbance. (Second in order of importance—but also of course central—is how well the controlled system will follow commands.)

Evans noted that if you need to know whether a given root location is on the locus of roots of a characteristic equation, you simply need to make one calculation: You need to know whether or not the sum of the angles of the components of the factored characteristic equation of the system is 180 degrees there. In retrospect, some observers have called that insight obvious. If anyone other than Evans saw that, they failed to recognize it as the key that would unlock the door for design engineers.

His field-leading contribution of the root locus method enabled designers to see instantly the natural dynamic behavior a linear system will have, and, moreover, to see it directly in terms of the control parameters at the designer's disposal. 

The method presents—in seconds—a plot of the system's stability, speed of response, and the damping quality of all of its natural motions. It has been called by one of Evans’ contemporaries as among the greatest contributions of the post-war aerospace industry to engineering. 

Realizing Root Locusis structured into three parts:

Roots — The root locus method wasn't born from a sudden flash of insight. It emerged through deep analytical thinking, shaped by family influences, exceptional mentors, and a professional environment that thrived on innovation. This section delves into the experiences that guided Walter Evans’ approach to engineering and laid the groundwork for his insightful  method.

Feedback — No invention stands alone. After Evans introduced root locus, it evolved through the insights and contributions of colleagues, reviewers, and engineers in the field. This section reveals how an idea nurtured inside an aerospace company was openly shared with competitors rather than guarded as a competitive advantage. It explores how external influences, from resistance to enthusiasm— helped the method achieve universal acceptance.

Stability — By 1954, root locus had not only gained widespread recognition; Walter Evans' personal life had reached a steady, fulfilling rhythm. In this section, colleagues and the author share memories of Walter and Arline — a team in every sense. They stood as role models, demonstrating what it means to remain true to one’s marriage vows through life’s ups and downs.

The story of Realizing Root Locus is one of perseverance, ingenuity, and a relentless pursuit of understanding — qualities that remain as essential to engineering today as they were then. Seventy-five years after its publication, the root locus method continues to be relevant. Whether quickly sketched by hand with a Spirule or instantly generated by software, it endures as one of the most powerful tools in control system design.

This is how it was all realized.