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Lightweight Airplane Design

Designing a new or modifying an existing flight vehicle is a complex, time-consumingprocess with technical and process challenges. This demo uses the design of alightweight aircraft to show how to use MathWorks® products to address these and otheraircraft design challenges. It shows and discusses many of the steps involved indesigning a flight vehicle.

To run this demo, you need Aerospace Blockset™ software and its required products.Additional products you will need to explore this demo further are:

Control Toolbox™

Simulink® Control Design™

Simulink® Design Optimization™

Contents

Defining Vehicle Geometry

Determining Vehicle Aerodynamic Characteristics

Creating Flight Vehicle Simulation

Designing Flight Control Laws

Completing the Design Process

Summary

References

The design process is iterative; you will try many vehicle configurations before selectingthe final one. Ideally, you perform iterations before building any hardware. The challengeis to perform the iterations quickly. Typically, different groups work on different steps ofthe process. Effective collaboration among these groups and the right set of tools areessential to addressing this challenge.

Defining Vehicle Geometry

The geometry of this lightweight aircraft is from reference 1. The original design objectivefor this geometry was a four-seat general aviation aircraft that was safe, simple to fly, andeasily maintainable with specific mission and performance constraints. For more detailson these constraints, see reference 1.

Potential performance requirements for this aircraft include:

Level cruise speed

Acceptable rate of climb

asbSkyHogg.mdl

Acceptable rate of climb

Acceptable stall speed.

For the aircraft flight control, rate of climb is the design requirement and assumed to begreater than 2 meters per second (m/s) at 2,000 meters.

Figure 1: Lightweight four-seater monoplane [1].

Determining Vehicle Aerodynamic Characteristics

The aircraft's geometrical configuration determines its aerodynamic characteristics, andtherefore its performance and handling qualities. Once you choose the geometricconfiguration, you can obtain the aerodynamic characteristics by means of:

Analytical prediction

Wind tunnel testing of the scaled model or a full-sized prototype

Flight tests.

While wind tunnel tests and flight tests provide high-fidelity results, they are expensiveand time- consuming, because they must be performed on the actual hardware. It is bestto use these methods when the aircraft's geometry is finalized. Note: Analytical predictionis a quicker and less expensive way to estimate aerodynamic characteristics in the earlystages of design.

In this demo, we will use Digital Datcom, a popular software program, for analyticalprediction. The U.S. Air Force developed it as a digital version of its Data Compendium(DATCOM). This software is publicly available.

To start, create a Digital Datcom input file that defines the geometric configuration of ouraircraft and the flight conditions that we will need to obtain the aerodynamic coefficients.

aircraft and the flight conditions that we will need to obtain the aerodynamic coefficients.

Digital Datcom provides the vehicle's aerodynamic stability and control derivatives andcoefficients at specified flight conditions. Flight control engineers can gain insight into thevehicle's performance and handling characteristics by examining stability and controlderivatives. We must import this data into the MATLAB® technical computing environmentfor analysis. Normally, this is a manual process.

With the Aerospace Toolbox software, we can bring multiple Digital Datcom output filesinto the MATLAB technical computing environment with just one command. There is noneed for manual input. Each Digital Datcom output is imported into the MATLAB technicalcomputing environment as a cell array of structures, with each structure corresponding toa different Digital Datcom output file. After importing the Digital Datcom output, we can runmultiple configurations through Digital Datcom and compare the results in the MATLABtechnical computing environment.

In our example, we need to check whether the vehicle is inherently stable. To do this, wecan use Figure 2 to check whether the pitching moment described by the correspondingcoefficient, Cm, provides a restoring moment for the aircraft. A restoring moment returnsthe aircraft angle of attack to zero.

In configuration 1 (Figure 2), Cm is negative for some angles of attack less than zero.This means that this configuration will not provide a restoring moment for those negativeangles of attack and will not provide the flight characteristics that are desirable.

This means that this configuration will not provide a restoring moment for those negativeangles of attack and will not provide the flight characteristics that are desirable.Configuration 2 fixes this problem by moving the center of gravity rearward. Shifting thecenter of gravity produces a Cm that provides a restoring moment for all negative anglesof attack.

Figure 2: Visual analysis of Digital Datcom pitching moment coefficients.

Creating Flight Vehicle Simulation

Once we determine aerodynamic stability and control derivatives, we can build anopen-loop plant model to evaluate the aircraft longitudinal dynamics. Once the model iscomplete, we can show it to colleagues, including those who do not have Simulink®software, by using Simulink® Report Generator™ software to export the model to a Webview. A Web view is an interactive HTML replica of the model that lets you navigate modelhierarchy and check the properties of subsystems, blocks, and signals.

A typical plant model includes the following components:

Equations of motion: calculate vehicle position and attitude from forces andmoments

Forces and moments: calculate aerodynamic, gravity, and thrust forces andmoments

Actuator positions: calculate displacements based on actuator commands

Environment: include environmental effects of wind disturbances, gravity, andatmosphere

Environment: include environmental effects of wind disturbances, gravity, andatmosphere

Sensors: model the behavior of the measurement devices

We can implement most of this functionality using Aerospace Blockset™ blocks. Thismodel highlights subsystems containing Aerospace Blockset blocks in orange. Ithighlights Aerospace Blockset blocks in red.

Figure 3: Top Level of Lightweight Aircraft Model

We begin by building a plant model using a 3DOF block from the Equations of Motionlibrary in the Aerospace Blockset library (Figure 4). This model will help us determinewhether the flight vehicle is longitudinally stable and controllable. We design oursubsystem to have the same interface as a six degrees-of-freedom (DOF) version. Whenwe are satisfied with three DOF performance, stability, and controllability, we can

subsystem to have the same interface as a six degrees-of-freedom (DOF) version. Whenwe are satisfied with three DOF performance, stability, and controllability, we canimplement the six DOF version, iterating on the other control surface geometries until weachieve the desired behavior from the aircraft.

Figure 4: Equations of Motion implemented using 3DoF Euler block from the AerospaceBlockset library.

To calculate the aerodynamic forces and moments acting on our vehicle, we use a DigitalDatcom Forces and the Moments block from the Aerospace Blockset library (Figure 5).This block uses a structure that Aerospace Toolbox creates when it imports aerodynamiccoefficients from Digital Datcom.

For some Digital Datcom cases, dynamic derivative have values for only the first angle ofattack. The missing data points can be filled with the values for the first angle of attack,since these derivatives are independent of angle of attack. To see example code of howto fill in missing data in Digital Datcom data points, you can examine the asbPrepDatcomfunction.

Figure 5: Aerodynamic Forces and Moments implemented in part with the AerospaceBlockset Digital Datcom Forces and Moment block.

We also use Aerospace Blockset blocks to create actuator, sensor, and environmentmodels (Figures 6, 7, and 8, respectively). Note: In addition to creating the following partsof the model, we use standard Aerospace Blockset blocks to ensure that we convert frombody axes to wind axes and back correctly.

Figure 6: Implementation of actuator models using Aerospace Blockset blocks.

Figure 7: Implementation of flight sensor model using Aerospace Blockset blocks.

Figure 8: Environmental effect of wind, atmosphere, and gravity using AerospaceBlockset blocks.

Designing Flight Control Laws

Once we have created the Simulink plant model, we design a longitudinal controller thatcommands elevator position to control altitude. The traditional two-loop feedback controlstructure chosen for this design (Figure 9) has an outer loop for controlling altitude(compensator C1 in yellow) and an inner loop for controlling pitch angle (compensatorC2 in blue). Figure 10 shows the corresponding controller configuration in our Simulinkmodel.

Figure 9: Structure of the longitudinal controller.

Figure 10: Longitudinal controller in Simulink model.

With Simulink® Control Design™ software, we can tune the controllers directly inSimulink using a range of tools and techniques.

Using the Simulink Control Design interface, we set up the control problem by specifying:

Two controller blocks

Closed-loop input or altitude command

Closed-loop output signals or sensed altitude

Steady-state or trim condition.

Using this information, Simulink Control Design software automatically computes linearapproximations of the model and identifies feedback loops to be used in the design. Todesign the controllers for the inner and outer loops, we use root locus and bode plots forthe open loops and a step response plot for the closed-loop response (Figure 11).

Figure 11: Design plots before controller tuning.

We then interactively tune the compensators for the inner and outer loops using theseplots. Because the plots update in real time as we tune the compensators, we can seethe coupling effects that these changes have on other loops and on the closed-loopresponse.

To make the multi-loop design more systematic, we use a sequential loop closuretechnique. This technique lets us incrementally take into account the dynamics of theother loops during the design process. With Simulink Control Design, we configure theinner loop to have an additional loop opening at the output of the outer loop controller (C1in Figure 12). This approach decouples the inner loop from the outer loop and simplifiesthe inner-loop controller design. After designing the inner loop, we design the outer loopcontroller. Figure 13 shows the resulting tuned compensator design at the final trimmedoperating point.

Figure 12: Block diagram of inner loop, isolated by configuring an additional loop opening.

Figure 13: Design plots at trim condition after controller tuning.

You can tune the controller in Simulink Control Design software in several ways. Forexample:

You can use a graphical approach, and interactively move controller gain, poles, andzeros until you get a satisfactory response (Figure 13).

You can use Simulink® Design Optimization™ software within Simulink ControlDesign software to tune the controller automatically.

After you specify frequency domain requirements, such as gain margin and phasemargin and time domain requirements, Simulink Design Optimization softwareautomatically tunes controller parameters to satisfy those requirements. Once we havedeveloped an acceptable controller design, the control blocks in the Simulink model areautomatically updated. See the demos "Getting Started with the SISO Design Tool" inControl Systems Toolbox demonstrations and "Tuning Simulink Blocks in theCompensator Editor" in Simulink Control Design demonstrations for more information ontuning controllers.

We can now run our nonlinear simulation with flight control logic and check that thecontroller performance is acceptable. Figure 15 shows the results from a closed-loop

We can now run our nonlinear simulation with flight control logic and check that thecontroller performance is acceptable. Figure 15 shows the results from a closed-loopsimulation of our nonlinear Simulink model for a requested altitude increase from 2,000meters to 2,050 meters starting from a trimmed operating point. Although a pilot requestsa step change in altitude, the actual controller altitude request rate is limited to provide acomfortable and safe ride for the passengers.

Figure 14: The final check is to run nonlinear simulation with our controller design andcheck that altitude (purple) tracks altitude request (yellow) in the stable and acceptablefashion.

We can now use these simulation results to determine whether our aircraft design meetsits performance requirements. The requirement called for the climb rate to be above 2m/s. As we can see, the aircraft climbed from 2,000 to 2,050 meters in less than 20seconds, providing a climb rate higher than 2.5 m/s. Therefore, this particular geometricconfiguration and controller design meets our performance requirements.

In addition to traditional time plots, we can visualize simulation results using theAerospace Blockset interface to FlightGear (Figure 15).

Figure 15: Visualizing simulation results using the Aerospace Blockset interface toFlightGear.

We can also use the Aerospace Toolbox interface to FlightGear to play back MATLAB datausing either simulation results or actual flight test data.

Completing the Design Process

The next steps involve

Building a hardware-in-the-loop system to test real-time performance

Building the actual vehicle hardware and software

Conducting the flight test

Analyzing and visualizing the flight test data.

Because these steps are not the focus of this demo, we will not describe them here.Instead, we will simply mention that they can all be streamlined and simplified using theappropriate tools, such as Embedded Coder™, xPC Target™, Simulink® Verification andValidation™, and Aerospace Toolbox software.

Summary

In this demo we showed how to:

In this demo we showed how to:

Use Digital Datcom and Aerospace Toolbox software to rapidly develop the initialdesign of your flight vehicle and evaluate different geometric configurations.

Use Simulink and Aerospace Blockset software to rapidly create a flight simulation ofyour vehicle.

Use Simulink Control Design software to design flight control laws.

This approach enables you to determine the optimal geometrical configuration of yourvehicle and estimate its performance and handling qualities well before any hardware isbuilt, reducing design costs and eliminating errors. In addition, using a single tool chainhelps facilitate communication among different groups and accelerates design time.

References

[1] Cannon, M, Gabbard, M, Meyer, T, Morrison, S, Skocik, M, Woods, D. "SwineworksD-200 Sky Hogg Design Proposal." AIAA®/General Dynamics Corporation Team AircraftDesign Competition, 1991-1992.

[2] Turvesky, A., Gage, S., and Buhr, C., "Accelerating Flight Vehicle Design", MATLAB®Digest, January 2007.

[3] Turvesky, A., Gage, S., and Buhr, C., "Model-based Design of a New LightweightAircraft", AIAA paper 2007-6371, AIAA Modeling and Simulation Technologies Conferenceand Exhibit, Hilton Head, South Carolina, Aug. 20-23, 2007.

Copyright 2007-2011 The MathWorks, Inc.Published with MATLAB® 7.14

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