Introducing the algorithm that ruled the adaptive flight control system of the first manned hypersonic aircraft, the North American X-15.

We live in a world where control engineering is more important than ever.

In the last 10 years, we have seen how cars are able to drive autonomously, how the cost to access space has drastically decreased thanks to reusable rockets that can re-enter the atmosphere and land vertically, and how airplanes can operate without human intervention at all.

None of these incredible breakthroughs would have been possible without modern control systems. Practically every aspect of our day-to-day life is affected by some type of control algorithm.

Within the wide spectrum of the existing control techniques, there is a very…


This is the North American X-15, a legend, a pioneer, an engineering marvel born to boost the scientific research which helped to put men on the moon

It was a sunny morning in the Rogers Dry Lake on October 7, 1967. Only the sound of wind and dust dared timidly to break the silence. Suddenly, a big “bang” came out of the blue.

It was the “sonic-boom” of the North American X-15, soaring high at an incredible speed of Mach 6.7 (6.7 times the speed of sound!) at 102,100ft.

Exactly fifty-four years ago, on that morning, USAF test pilot William J. …


From multitasking tricks to shortcuts that will save you precious time, here you have my Top-5 functions and aliases for those “Bash-days”

Bash is a powerful command-line interface, but in my opinion, many times its syntax is way too cumbersome.

For the newcomers, it’s common to get stuck trying to remember what was the correct spelling of that “magical” but odd command to do a specific task.

Honestly, when I started using Bash, I had only two options: google for answers or open my “unix_recipes.txt” file. Simple as that.

With time, I learned how to define functions in the ~/.bashrc file, and started to migrate my old recipes to a more elaborated set of handy functions.

After a couple of years of…


Add some salt and pepper to your optimizer with quasi-random numbers generators

Many computer programs rely on random numbers to work.

This is the case of global optimization algorithms, which belong to a branch of applied mathematics and numerical analysis that studies how to efficiently find the global minima/maxima of a function f(x) on a given optimization hyper-space.

In every global optimization algorithm, the optimization process starts with the generation of a randomly sampled population of N individuals of dimension D.

Each one of these individuals represents a candidate solution to the optimization problem to be solved.

Many studies have shown that the spatial distribution of the first generation of candidate solutions…


Beating the Fast Fourier Transform algorithm for a small number of selected frequencies is possible. Here you will learn how.

The frequency-domain analysis allows extracting information that is not obvious by simply observing a signal in time.

Nowadays frequency-domain algorithms are the backbone of many lossy compression data methods like the JPEG for image files or the MP3 for music files.

Most of these algorithms are a derivation of the Continuous Fourier Transform (CFT), originally proposed in 1822 by Jean-Baptiste Joseph Fourier, the father of modern engineering.

The problem with CFT is that it can only be applied to analogical signals, and we all live in a digital/discrete world.


How A.I. helped NASA to improve modern flight control systems

At the beginning of this century, from 1999 to 2008, NASA Dryden Flight Research Center started a novel research program to investigate applications of Artificial Intelligence (AI) to reduce pilot’s workload after a flight controls failure.

With this research, NASA aimed to prove that the symbiosis between AI and state-of-the-art control algorithms could render a self-healing control software.

The AI was intended to be a key element of the digital “fly-by-wire” system of the aircraft, providing real-time estimations of the aerodynamic derivatives of the aircraft, that were then used to redesign in real-time the flight control strategy. …


How to build from scratch a Simulink model of the famous MH-96, the X-15's Adaptive Flight Control System

Welcome to the second chapter of this series about Adaptive Control.

In the previous article, we made a one-way trip to the past, more specifically to the early 60s, the era of the firsts adaptive flight control system, and the beginning of hypersonic manned flights with the North American X-15.

In this new issue, we will make the way back trip to the present.

Using nowadays technology, we will build up a simplified simulation model of the X-15’s Adaptive Flight Control System (AFCS), the MH-96.

It’s curious to think that you could even simulate the X-15’s flight dynamics in your…


How to build the definite animation tool that will help you analyze in detail the complex dynamics of an aircraft’s movement

They say data is gold.

However, raw-data on its own will never be as valuable as gold. It’s the post-processing and visualization tools that allow us to exploit all the added value that the data hides.

In the aerospace industry, we analyze a vast amount of raw data generated by high-fidelity simulators. When it comes to the validation and verification of flight control systems, the number of simulations required to be performed to check the aircraft’s controllability and handling qualities starts to build-up.

In some cases, we simulate millions of maneuvers to check that the aircraft never departs from a…


How frequency hybridization of inertial and air-data measurements can provide enhanced control robustness against turbulence, without impairing the controller stability margins

Atmospheric perturbations are evil for every pilot. It takes guts and magic touch to land an airliner with a wind shear profile and severe turbulence. And believe it or not, it takes even more expertise to land a Cessna under the same adverse conditions.

The lower the flight speed, the higher the effect of turbulence on the aircraft’s movements. If you have ever flown a drone or an RC plane in windy weather, you know what I’m talking about.

When I started working in the aerospace industry, one of the first problems I had to deal with was closely related…


Introducing one of the most simple frequency estimation algorithms for digital signal processing applications

GPS, radar systems, or even satellite communications; all these applications and devices have one thing in common: they work using frequency-encoded data. In order to decode the valuable information, all these systems use special algorithms to accurately estimate the main frequency of the digital signals they work with.

Many of these algorithms have been proposed throughout the second half of the 20th century and are used to estimate the main frequency of a certain digital signal in real-time, however, only a bunch of them are simple enough (in terms of numerical complexity) to be fit for the embedded software of…

Rodney Rodríguez

Aerospace engineer, flight dynamics and control expert, amateur writer, and cutting-edge technology advocate.

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