Flight Control Systems and Autopilots
Brian Jewell
Department of Engineering, CalvinCollege
Engineering 315 Final Paper
Professor Ribeiro
Abstract: Autopilot systems have been crucial to
flight control for decades and have been making flight easier, safer, and more efficient. However, these autopilot systems are complex devices that require precise control and stability. These systems usually include a form of digital control systems to allow for easier implementation. One example, the Beaver Autopilot system, uses an inner, outer loop system to maintain control while simpler systems often only require something as simple as a PID controller to keep the aircraft stable.
1. Introduction
Since the creation of the first aircraft, the ability for people to travel large distances in relatively short periods of time has drastically increased. However, in the beginning of the airplane age, traveling on these craft was difficult as there are many components of air travel and controlling these components can be an extremely difficult task for a pilot. In modern aircraft, there are simply too many things for the pilot to control them all so some form of automation must be done. Also, long air trips can cause problems for the pilots. While the plane is traveling along the same trajectory, flying can and does become a rather monotonous job for the pilot and the pilot runs a higher risk of falling asleep or suffering from a reduced response time. For these reasons, autopilot systems have become a blessing to the aerospace industry.
However, these autopilot systems are not simple systems. They require complex control systems with robust measuring equipment. The scope of this paper is to give an overview of autopilot systems (with a description of digital controls), to examine the Beaver Autopilot System, and to explore a simple flight control example.
2. History
The earliest form of autopilots have been in existence for decades. The first systems were created an implemented about ten years after the Wright Brothers flew the very first airplane: the Kitty Hawk. These earlier systems were simply a gyroscope that gave the plane a smoother flight path. The only control that these systems gave was in the altitude and pitch. They kept the plane from flying with its nose pointed down and from flying crooked.
Around the time of Second World War, the very first fully functional autopilot systems were designed and tested. These earlier systems had the capability to keep the flight path level as well as launch and land the aircraft. This revolutionary system, however, was not a simple task and it was prone to failure. The systems would often break down and crash the plane (by making the plane point straight down as opposed to straight forward. To keep the systems operating properly, the plane required a crew that was more than twice as large as the original autopilot-less planes. This caused problems because it took far more work to keep the autopilot working than it did to actually fly the plane without such a device. For this reason, the autopilot was not used very often for many years. It wasn’t until the 1960’s that the device really took off (to use an atrocious pun). At this point, more sophisticated systems were being introduced and a new form of flight control was in the works: a computer controlled flight. This technique called “fly by wire” didn’t become a standard until closer to the 80s but it had its beginnings in the late 60s.
The basic concept of the “fly by wire” systems is digital control systems. To understand this form of autopilot a brief description of digital control systems must be discussed.
3. Digital Control Systems
In a typical control system, the equipment to measure and control signals can be extremely complicated and can require enormous levels of sophistication. However, if it were possible to use a computer to control the systems, a simple “off the counter” processor could be able to handle complex control systems. For example, a system that requires complicated mathematical algorithms for control could simply digitize the signal and send it to a processor to take care of the calculations. The processor (usually called a “minicomputer”) is usually inexpensive and relatively easy to implement. The control system using these sorts of devices is shown below in Figure 1: Digital Control System Block Diagram.
Figure 1: Digital Control System Block Diagram
In this system, the digital computer reads in the digital signals from the feedback loop and the input and it sends them to the D/A converter. This converter takes the digital values from the computer and converts the signals into a usable value for the actuator and process. The signals are then sent via the feedback loop through the measurement sensors until it reaches the analog to digital convert. This portion takes the measured value and converts it into a binary digital signal that can be read by the computer.
This digitizing is where the real challenge enters into the picture. Since computers cannot read the same kind of signals that an analog device can, some method of transforming the analog data to readable digital data must be introduced. This is done through a method called sampling. A simple circuit is set up with a switch (shown below in Figure 2: Switch Digitizer). The switch samples the value of the signal at regular intervals.
Figure 2: Switch Digitizer
These samples must be at a high enough frequency to accurately represent the input signal. This process takes the signal and breaks it up into a step like function. An example of this is shown below in Figure 3: Discrete Signal.
Figure 3: Discrete Signal
As can be seen, the resulting function is no longer a smooth signal but it is a series of step functions that represent the original signal.
To deal with these functions, the z-Transform must be used. The z-Transform is an extension of the LaPlace transform and is of the following form: Z = esT where s is the value from the LaPlace transform and T is the period of the sampler (how many seconds between samples). In the z-Plane, there are several methods of stability analysis. For example, a sampled system is stable if all of the poles of the closed loop transfer function T(z) lie within the unit circuit of the z-plane.
These systems can readily be constructed in MATLAB. The function can be defined as it would in any transfer function however the sampling time is also included (so the definition is as follows: sys=tf(num,den,Ts) where Ts is the sampling time). The systems can be converted from continuous to digital and back again using the c2d and d2c commands. Below, in Figure 4: Discrete Step Response the following MATLAB code was entered:
> num=[1];den=[1 1 0];
> sysc=tf(num,den);
> sysd=c2d(sysc,1,'zoh');
> sys=feedback(sysd,[1]);
> T=[0:1:20];step(sys,T)
This code yields the following graph:
Figure 4: Discrete Step Response
As can be seen by the above plot, the digital signal is no longer a smooth curve. Depending on the sampling rate (in this case, once every second) the value is measured and then held constant until the next value is measured. For a digital control system, this value is converted into a binary number that is then fed into the minicomputer for analysis.
This sort of system is extremely beneficial to the aviation industry. With a digital control system, the autopilots can have a much more precise control of the flight path of the aircraft. Rather than feed the controlled signal (such as altitude or yaw) through a complex process (which would be extremely difficult to design), the signal can be converted to a digital signal and sent to the minicomputer. In the minicomputer, the signal can be operated on with a higher level of ease because the computer can directly run the algorithms on the digital numbers. This method can yield a higher quality control system for the aircraft. Although it does require more circuitry (the minicomputer) it is usually smaller and easier to implement backup systems.
With this general understanding of digital control systems, the Beaver Autopilot System is the focus of the rest of this paper. This digital control system overview will help understand some of the mystery of the proprietary (and therefore undisclosed) portions of the Beaver system.
4. Beaver Autopilot System
The Beaver autopilot document that is used for this report entitled “A Simulink Toolbox for Flight Dynamics and Control Analysis” and is written by Marc Rauw. This document describes the Beaver system in great detail and discusses its implementation in the Flight Dynamic Control toolbox for SIMULINK. However, since this toolbox was not written by the SIMULINK people, the standard SIMULINK package does not contain this toolbox. Therefore, for any attempted simulations, regular SIMULINK will be utilized and any unknown functions will be estimated as best as is capable by this author.
4.1 Functions
The functions of an autopilot system can be broken down into two major categories: guidance and control. The guidance function of an auto-pilot determines the speed and the course to be followed by the craft. This is done by measuring the current actual values and comparing them to some reference system. The control function is the function that takes the data from the guidance system and applies the proper corrections. For example, if the guidance says that the altitude of the aircraft is 200m too high, the control function would move the wing flaps to bring the craft back down to the appropriate level. The control does not usually contain any sort of measuring devices as this function is delegated entirely to the guidance function. The guidance loop acts as a commander to the control loop and the control loop commands the physical movement and response of the aircraft. As is evident, it is desirable for these control systems to have a fast and stable response. They must also be able to withstand any disturbances from the surrounding environment. This is extremely important because, if a disturbance caused a critical control system to become unstable, the autopilot would cease to function and possibly put the lives of the passengers at risk.
The best way to describe the two functions is to think of them as two interrelated loops. The control loop is the inner loop as it is controlled by the outer loop guidance system. This is best shown in Figure 5: Basic Block Diagram of Autopilot.
Figure 1: Basic Block Diagram of Beaver Autopilot
These two controllers (guidance and control) control two major areas of the flight path of the aircraft: Longitudinal and Latitudinal direction. The Longitudinal Mode is discussed below. The Latitudinal mode is of a similar format with slightly different constants and different control blocks.
Figure 6: Block Diagram of Longitudinal Mode
4.1.1 Longitudinal Mode Overview
This portion of the auto-pilot controls the pitch angle and the altitude of the aircraft. The complete block diagram for this portion of the autopilot is shown above in Figure 6: Block Diagram of Longitudinal Mode. As can be seen by the above diagram, there are several components that make up this portion. The main three blocks of the system are the controllers of this function. They take the values from the outer loops which pass through constants and integrators and output the appropriate controls for the aircraft. The input signal Href is the current altitude as measured from the guidance systems. This value then is taken with the control’s new altitude as well as the pitch angle (θ) and fed into the control blocks of the diagram. It should be noted that the gains shown in the feedback loops of the system are all variable and depend on the velocity of the aircraft. This happens because the control to the aircraft will change as the speed does. Wind resistance and other factors contribute to this.
The final portion of the longitudinal mode of the aircraft is the Approach mode. It should be noted that the Glideslope device is a unique device to the Beaver autopilot mode. This portion of the control system is a feedback loop from the Hdot output (from Figure 6) to the input Hdotref signal.
The glideslope receiver is an on-board measurement device that interacts with a transmitter on the airport runway. This system is an extra feedback loop that has more control over the descent of the aircraft. To properly operate, the distance to the runway is calculated using Distance Measurement Equipment (DME). However, this equipment doesn’t often work well with autopilot modules because of hardware limitations. Therefore, a different approach must be used. The three dimensional distance to the runway is calculated using the following equation.
In this equation, R is the three dimensional distance to the runway, Href is the height above the runway, and γgs is the reference flight path angle or, the angle the plane makes when flying along the nominal path. Generally, a radio altimeter is used to determine the value of Href.
During a glideslope approach, there are two different modes of operation. The first is the “glideslope armed mode. As the authors of the Beaver document say: “This phase is engaged as the approach mode is selected by the pilot. The longitudinal autopilot mode in which the aircraft flew before selecting the approach mode, usually ALH, will be maintained until the aircraft has reached the glideslope reference plane” (Rauw, 177). This mode simply tells the aircraft that it is going to be landing soon and that it needs to get ready for landing. It does not affect any of the current flight paths.
The second mode is the glideslope coupled mode. The author describes this mode by saying that “This phase is initiated as soon as the aircraft passes the glideslope reference plane for the first time. In this phase the control laws of the GS mode take over the longitudinal guidance task of the autopilot” (Rauw, 177). In this mode, the GS actually takes over the rest of the autopilot. It does this by adding its own signals with the Hdotref input signal. When the GS is not engaged, the signal that is the output of the GS is zero allowing the aircraft to operate as it normally would. The timing of the coupling of the GS is extremely important. If the GS is coupled too earlier, the aircraft will follow the path as shown below in Figure 7: Result of Early GS Coupling
Figure 7: Result of Early GS Coupling
As can be seen by the above figure, the timing is important because, if the GS is coupled too early, the aircraft tries to approach the reference line (the slanted dotted line in the figure) before it is supposed to. The result of this is that the plane will rise to the reference line and then have to suddenly shift down after the line is crossed. To properly couple the GS, the mode controller is constantly examining the state of the aircraft. When the aircraft reaches the correct point, the mode controller immediately switches to coupled mode and the aircraft can land. This system is not perfect and it does yield a slight overshoot but the resulting overshoot is far more desirable than the overshoot shown in Figure 7.
4.1.2 Longitudinal Mode Simulation
To get a better picture of how exactly this autopilot system works, it became desirable to simulate the system in MATLAB. All of the K values (as seen in Figure 6) are given in the Beaver document and can be constructed in Simulink. However, there are still a few different blocks that are not explained in the Beaver document. This is due to the fact that the autopilot system is proprietary information (or if it isn’t, the authors of the document don’t disclose the information). Because of this, the following assumptions are made. The first is in the Computational Delay block. This block is assumed to be a simple signal delay and is set to delay the signal by one second. The next block is the Actuator and Cable Dynamics block. This block, for the sake of the simulation is assumed to be a simple transfer function (a second order is used). At the heart of the block diagram is the Beaver Dynamics. This block is the portion of the control system that reads in the measured values and operates on them. For the sake of simulation, the block was assumed to be three transfer functions: one of which is a simple constant value, the second is an integrator function, and the third is a derivative function. After the system was constructed, the outputs were examined. The θplot is shown below in Figure 8: θ Simulink Plot.
Figure 8: θ Simulink Plot
As can be seen, this is invalid data. The plot shows nothing and every one of the outputs looks about the same. Changes made in the functions of the control system yielded no results either. The system would either be zero and then drop off to negative infinity or the signal would be zero and rise to positive infinity. The system did not compensate for anything. The reason that these simulations did not yield valid results is because of the fact that the setup of the Beaver Dynamics is unavailable for research. The actual system for the Beaver Dynamics I probably not actually a simple transfer function. If it was a simple transfer function, changes to the simulated system would have had a larger effect. The Beaver Dynamics is probably a control system in and of itself. Since the system is a moderately complex system, it can probably be assumed that the Beaver Dynamics is a digital control system. There is probably a minicomputer (as discussed earlier) at the heart of the system that does all of the actual control for the aircraft. For this reason, it cannot be adequately simulated for this paper. For that to happen, more information about the Beaver Dynamic would have to be available for study. To make up for this lack of simulation, a simple aircraft flight control system is examined in the final portion of this paper.