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Nonlinear Robust Control of an Highly Manoeuvrable Missile

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Nonlinear Robust Control of an Highly Manoeuvrable Missile “Sapienza” Universita` di Roma Facolta` di Ingegneria DIS - Dipartimento di Informatica e Sistemistica “Antonio Ruberti” Nonlinear Robust Control of an Highly Manoeuvrable Missile supervisor: candidate: Chiar.mo Prof. Salvatore Monaco Giovanni Mattei co-supervisor: Ing. Emidio Pizzingrilli A.Y. 2010-2011 Introduction Automatics and control theory should be considered at the top of modern engineering science. Control systems are everywhere and, over time, they are going to be more and more essential (not just incidental, as happens now) for the proper functioning of any system. This thesis is about control system design for a generic air-to-air missile autopilot and guidance system. For the autopilot, a nonlinear recursive approach is proposed, beginning from a simpler, nominal, implementation to arrive, in the end, to a more complicated robust one. The first two control systems proposed are based on a wiser version of Backstepping, which uses a non-quadratic Lyapunov function to achieve in a more natural way some necessary dynamic cancellations. A faster version of these two autopilots is also designed, including nonlinear damping terms. Then, nonlinear robust control theory is introduced, highlighting the structure of the generic nonlinear uncertain system. A nonlinear robust roll autopilot is designed, including in the robust recursive approach, that shall represent the baseline for the robust versions of the autopilot, also a revisited version of Lyapunov redesign, which has no counterpart in control theory literature. For pitch and yaw dynamics are, finally, proposed the static and dynamic robust recursive designs, two rigorous and systematic approaches to the problem of controlling a nonlinear uncertain system, which seem to be well suited to handle the structure of the missile vector-fields. To derive the equations of all the nonlinear controllers, a complete, nonlinear dynamical model of the missile is necessary: this is very important, because nonlinear control represents a model based design methodology. The simulation model was developed in the first part of the work, together with the simplified models used for control design. Also, an accurate and very physical-oriented open-loop analysis of the missile behaviour is presented, with some simulations regarding the statically unstable dynamics, the phenomenon of peaking related to finite time explosions and the non-minimum phase. The final part of the work is dedicated to the guidance system design. A nonlinear, Lyapunov-based, approach is used to guarantee the finite-time convergence to zero of the line-of-sight angular rates. The guidance loop is closed around the dynamic robust recursive controller, which in simulation will show the best performance. In this way, the guidance system and the autopilot will be both of energetic and nonlinear nature, and 9 INTRODUCTION 10 their integration and coupled functioning shall be really good, as simulations will show in the last part of the thesis. Part I Overview on rocket science 11 Chapter 1 A brief history As a presentation to this work, it seems convenient to introduce the reader to the world of rocket science by means of its history, its development as a stronghold for modern warfare and its pretty recent employment in space exploration. This part of the work is freely taken by [28]. Rockets have been used as early as A.D. 1232, when the Chinese employed them as unguided missiles to repel the Mongol besiegers of the city of Pein-King (Peiping). Also, in the fifteenth century, Korea developed the sinkijon1 (or Sin-Gi-Jeon) rocket. Manufactured from the early fifteenth to mid-sixteenth century, the sinkijon was actively deployed in the northern frontiers, playing a pivotal role in fending off invasions on numerous occasions. Once out of the rocket launcher, the fire-arrows were set to detonate automatically near the target area. Also, the high-powered firearm was utilized in the southern provinces to thwart the Japanese marauders. The main body of the sinkijons rocket launcher was five to six meters long, the largest of its kind at that time. A sinkijon was capable of firing as many as one hundred fire-arrows or explosive grenades. The fire-arrow contained a device equipped with gunpowder and shrapnel, timed to explode near the target. The introduction of gunpowder made possible the use of cannon and muskets that could throw projectiles at great distances and with high velocities. It was desirable (in so far as the study of cannon fire is desirable) to learn the paths of these projectiles, their range, the heights they could reach, and the effect of muzzle velocity. Several years later, the sinkijon went through another significant upgrade, which enabled it to hurl a fire-arrow made up of small warheads and programmed to detonate and shower multiple explosions around the enemy. In 1451, King Munjong ordered a drastic upgrade of the hwacha (a rocket launcher on a cartwheel). This improvement allowed as many as one hundred sinkijons to be mounted on the hwacha, boosting the overall firepower and mobility of the rocket. Since those early times and in one form or another, rockets have been used as weapons and machines of war, for amusement through their colorful aerial bursts, as life-saving 1Sinkijon means “ghost-like arrow machine”. 12 CHAPTER 1. A BRIEF HISTORY 13 equipment, and for communications or signals. The lack of suitable guidance and control systems may have accounted for the rockets slow improvement over the years. Strangely enough, it was the airplane rather than the rocket that stimulated the development of a guided missile as it is known today. In the twentieth century, the idea of using guided missiles came during World War I. Specifically, and as stated above, the use of the airplane as a military weapon gave rise to the idea of using remote-controlled aircraft to bomb targets. As early as 1913, Ren´e Lorin, a French engineer, proposed and patented the idea for a ramjet powerplant. In 1924, funds were allocated in the United States to develop a missile using radio control. Many moderately successful flights were made during the 1920s with this control, but by 1932 the project was closed because of lack of funds. Radio-controlled target planes were the first airborne remote-controlled aircraft used by the Army and Navy. Dr. Robert H. Goddard was largely responsible for the interest in rockets back in the 1920s. Early in his experiments he found that solid-propellant rockets would not give him the high power or duration of power needed for a dependable supersonic motor capable of extreme altitudes. On March 16, 1926, Dr. Goddard successfully fired the first liquid-propellant rocket, which attained an altitude of 56 m and a speed of 97 km/h. Later, Dr. Goddard was the first to fire a rocket that reached a speed faster than the speed of sound. Moreover, he was the first to develop a gyroscopic steering apparatus for rockets, first to use vanes in the jet stream for rocket stabilization during the initial phase of a rocket in flight, and the first to patent the idea of step rockets. The first flight of a liquid-propellant rocket in Europe occurred in Germany on 14 March 1931. In 1932 Captain Walter Dornberger (later a general) of the German Army obtained the necessary approval to develop liquid-propellant rockets for military purposes. Subsequently, by 1936 Germany decided to make research and development of guided missiles a major project, known as the “Peenem¨unde Project” , at Peenem¨unde, Germany. The German developments in the field of guided missiles during World War II were the most advanced of their time. Their most widely known missiles were the V-1 and V-2 surface-to-air missiles (note that the designation V1 and/or V2 is also found in the literature). As early as the spring of 1942, the original V-1 had been developed and flight-tested at Peenem¨unde. In essence, then, modern weapon (missile) guidance technology can be said to have originated during World War II in Germany with the development of the V-1 and V-2 (German: A-4 ; the A-4 stands for Aggregat-4, or fourth model in the development type series; the V stands for Vergeltungswaffe, or retaliation weapon, while some authors claim that initially, it stood for Versuchsmuster or experimental model) surface-to-surface missiles by a group of engineers and scientists at Peenem¨unde. In the spring of 1942 the original V-1 (also known by various names such as buzz bomb, robot bomb, flying bomb, air CHAPTER 1. A BRIEF HISTORY 14 torpedo, or Fieseler Fi-103) had been developed and flight-tested at Peenem¨unde. Thus, the V-1 and V-2 ushered in a new type of warfare employing remote bombing by pilotless weapons launched over a hundred miles away through all kinds of weather, day and night. The V-1 (Fig. 1.1) was a small, midwing, pilotless monoplane, lacking ailerons but using conventional airframe and tail construction, having an overall length of 7.9 m and a wingspan of 5.3 m. It weighed 2180 kg, including gasoline fuel and an 850 kg warhead. Powered by a pulsejet engine and launched from an inclined concrete ramp 45.72 m long and 4.88 m above the ground at the highest end, the V-1 flew a preset distance, and then switched on a release system, which deflected the elevators, diving the missile straight into the ground. The engine was capable of propelling the V-1 724 km/h. A speed of 322 km/h had to be reached before the V-1 propulsion unit could maintain the missile in flight. The range of the V-1 was 370 km.
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