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<h2 class="hd hd-2 unit-title">Introduction to Control Theory</h2>
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<h2>2.5.1 Introduction to Control Theory</h2>
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Describe the basic concept of a control feedback loop that keeps a rocket flying along the desired trajectory" type="button" id="LD">MO 2.5</button></p>
<p>Rocket science is about more than just propulsion. The successful launch of a rocket from the surface of the Earth also involves numerous other aerospace engineering sub-disciplines, which we discussed in <a href="/courses/course-v1:MITx+16.00x+2T2019/jump_to_id/332d759948a54053a0ecd0152cb1d025" target="[object Object]">Subsection 1.4.3</a>. In this section, we offer a brief introduction to two such sub-disciplines: control theory and <span style="line-height: 25.6000003814697px;">structural engineering. </span></p>
<p>In the video below, Prof. Hoffman motivates the importance of guidance, navigation, and control systems in rocket science. Following this introduction, we will learn about control theory from MIT AeroAstro Prof. Jonathan How, who is a leading expert in the field.</p>
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<h2 class="hd hd-2 unit-title">Control System Overview</h2>
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<h2>2.5.2 Control System Overview</h2>
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Describe the basic concept of a control feedback loop that keeps a rocket flying along the desired trajectory" type="button" id="LD">MO 2.5</button></p>
<p>Control systems are absolutely critical to the operation of aerospace vehicles. On an aircraft, there are a number of control surfaces such as the flaps, ailerons, rudder, and elevators (top figure). These surfaces are actuators that allow the pilot to change the orientation of the aircraft about the pitch, roll, and yaw axes (bottom figure), thus enabling the aircraft to climb, descend, turn, and perform other maneuvers.</p>
<p>In the following video, Prof. How introduces the concept of open-loop vs. closed-loop control systems, the implications of each for system robustness and sensitivity, as well as the notion of a block diagram.</p>
<p><img style="display: block; margin: 20px auto 20px auto;" src="/assets/courseware/v1/0364d9771b0afacf58aed056a9fe84ea/asset-v1:MITx+16.00x+2T2019+type@asset+block/airplane-control-surfaces-620.png" alt="Parts of an aircraft" type="saveimage" target="[object Object]" /></p>
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<p style="text-align: center;"><em><span style="font-family: 'Open Sans', Verdana, Arial, Helvetica, sans-serif;">Parts of an aircraft (Image credit: <a href="http://www.grc.nasa.gov/WWW/k-12/VirtualAero/BottleRocket/airplane/airplane.html">NASA</a>)</span></em></p>
<p><img style="display: block; margin: 20px auto 20px auto;" src="/assets/courseware/v1/2fdc63b98664083f0680abc666fc7995/asset-v1:MITx+16.00x+2T2019+type@asset+block/airplane-rotations-620.png" alt="Axes of rotation on an aircraft" type="saveimage" target="[object Object]" /></p>
<p></p>
<p style="text-align: center;"><em><span style="font-family: 'Open Sans', Verdana, Arial, Helvetica, sans-serif;">Axes of rotation on an aircraft (Image credit: <a href="http://www.grc.nasa.gov/WWW/k-12/airplane/rotations.html">NASA</a>)</span></em></p>
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<h2 class="hd hd-2 unit-title">Control System Design</h2>
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<h2>2.5.3 Control System Design</h2>
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<p>Now that we have an idea of what a control system entails, we can learn about how one might design such a system. In the first video below, Prof. How introduces the classical PID controller and the philosophy behind the three types of control that it involves: <strong>P</strong>roportional, <strong>I</strong>ntegral, and <strong>D</strong>erivative feedback. In the second video, an example of a PD controller is given in the context of a simple pendulum, and MIT AeroAstro graduate student Mark Cutler demonstrates how an electronic PID controller can be used to drive a pinned propeller to hover at just the right angle.</p>
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<h3 class="hd hd-2">Video: An Example of Control System Design</h3>
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<h2 class="hd hd-2 unit-title">Introduction to Structural Engineering</h2>
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<h2>2.5.4 Introduction to Structural Engineering</h2>
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<p>Aircraft and spacecraft have powerful engines that produce a lot of thrust and allow them to attain high speeds. However, to safely accomplish their missions, these vehicles must be able to maintain structural integrity in the presence of a variety of forces and torques encountered during operation. In the following video, Prof. Hoffman motivates the importance of materials and structures in aerospace engineering, and introduces the unique additional constraints that must be considered when designing aerospace vehicles.</p>
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<h2 class="hd hd-2 unit-title">Overview of Structural Engineering</h2>
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<h2>2.5.5 Overview of Structural Engineering</h2>
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<p style="font-size: 16px; line-height: 25.6000003814697px;">Structural engineering has applications to many areas of science and engineering. It is relevant to the construction of everything from airplanes to bridges to cars. There are some factors must be considered in the design of any structure: for example, a structural design is not useful unless it can be constructed. On the other hand, there are factors are specific to a particular application: for example, shaving a pound off the weight of a seat has a much greater impact if the seat were on a plane than if it were in a car.</p>
<p>In the first video below, Prof. Radovitzky defines a structure and discusses the factors that must be considered when designing a structure. He also describes different kinds of failure and the particular importance of weight to the design of aircraft and spacecraft --- structures faced with the unique requirement of operating in opposition to gravity.</p>
<p>To design complex structures without having to build and test countless prototypes, one needs to be able to predict how a structure will react to the loads to which it is subjected. In the second video below, Prof. Radovitzky discusses structural analysis, which is used to determine loads and their effects on a structure and its components.</p>
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<h2 class="hd hd-2 unit-title">The Role of Materials in Structural Engineering</h2>
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<h2>2.5.6 The Role of Materials in Structural Engineering</h2>
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<p>The ability of a structure to perform a desired task is greatly dependent on the materials of which it is composed. For example, a beam made of steel can support more weight than a wooden beam of the same size. In the next video video, Prof. Radovitzky discusses how advances in materials science make it possible to build aircraft and spacecraft that are more powerful and more efficient, and how pushing the capabilities of these vehicles in turn drives the search for new materials.</p>
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