Figure 1: |
Fly-by-wire (FBW) is the generally accepted term for flight control systems in which a computer processes the pilot's control movements and sends electric signals to the flight control surface actuators without any mechanical linkage. While enhancing aircraft performance and flying qualities, today's fly-by-wire systems present their own unique hazards and risks. Aviation safety officers and accident investigators need to become "fly-by-wire literate" to be effective today. Here, I briefly introduce fly-by-wire concepts, acquaint you with some of the FBW lingo, and look at safety applications.
As aircraft design progressed to high-speed, swept-wing jets, capable of flying over a broad flight envelope, flight control designers faced new problems. Airplane handling qualities varied tremendously with speed, fuel burn, or external stores configuration. Improved stability and handling precision were needed, and fly-by-wire technology provided the solution. To understand how this technology makes modern airplanes fly, we'll look first at the concept of electronic feedback control.
Feedback control systems
Feedback compensation is essentially error control. It regulates a system by comparing output signals to input signals. Any error between the two becomes a command to the flight control surface until output equals input.
A computer measures an aircraft's motion parameter, conditions the signal, amplifies it, and sums it up with an input command, forming a closed "loop" (see Figure 1).
In an FBW schematic diagram of this process, called a block diagram, the upper line is called the forward path while the lower loop is called the feedback loop or path. Gain is the amplification (or attenuation) that is applied to the signal to adjust the aircraft response as desired. A filter may be used to block feedback of signals or motion of an undesired frequency. The diagram's circle, or summer, indicates algebraic summation according to the arrows and signs.
An advantage of a feedback system is that the flight control system (FCS) can be used to reduce sensitivity to changes in basic aircraft stability characteristics or external disturbances. Autopilots, stability augmentation systems (SASs), and control augmentation systems (CASs) are feedback control systems.
In an SAS, the damper function is formed in the feedback loop and usually has low gain, or authority, over a control surface. CAS, implemented in the forward path, is high-authority "power steering," providing consistent response over widely varying flight conditions.
CAS and SAS were used extensively before fly-by-wire, as in the A-7 and the F-15, but fly-by-wire provides more precision and much greater flexibility. Uniform aircraft response is achieved over a broad flight envelope through CAS gains that are programmed as functions of airspeed, mach, center-of-gravity position, and configuration.
Control laws
Modern flight control computers are programmed with control laws that govern the feedback control system. Control laws are commonly named after the primary feedback parameter as "___feedback" or "___command." For the pitch channel, common feedbacks are vertical load factor (Nz or just "g"), pitch rate (q), pitch angle (q or attitude), and angle of attack (a or alpha). Common lateral feedbacks are bank angle (f) and roll rate (p). Typical directional feedbacks are yaw rate (r), sideslip angle (b or "beta feedback"), and rate of change of sideslip angle (b with a dot over it, or "beta dot feedback").
G command, desirable at high speeds, means for a particular amount of stick force, you get the same "g" regardless of airspeed (energy permitting). In a pitch-rate command system, you get the same amount of pitch rate for a given stick force regardless of speed. (Pitch-rate feedback and its effects are presented in detail in Figure 2--the concepts apply to any feedback control law.)
The pilot applies a certain control force, demanding pitch rate, and that becomes the flight control computer's command for a particular pitch rate. Because the pilot's control input "demands" a certain maneuver parameter, such an arrangement is often termed a "maneuver demand" system. The computer, not the pilot, then moves the control surfaces as required to meet the pilot's demand.
To provide immediate response to pilot input, the computer provides a direct path to the elevator via the proportional line (called the "feed forward gain" in the B-777). For precision over time, an integrator produces a control surface command until the feedback signal is equal to the pilot's command signal.
Pure integral control, or too much integrator gain (K), causes excessive lag in the aircraft response, hence the use of the proportional circuit. This arrangement, called "proportional plus integral" control, is found in most fly-by-wire designs, including the B-777 and the A320.
In a block diagram, "1/s" or "K/s" denotes an integrator, the "K" indicating some gain value. FBW engineers must "tune" the integrator gain to prevent excessive lag.
Lag causes delay in changing directions--for example, nose-up to nose-down, which is a classic cause of pilot-involved oscillation, or PIO. Engineers can mathematically analyze control laws for such instabilities. Thorough flight testing is still required, however, to validate an FBW system.
So how does an airplane with a pitch-rate command or g command fly? Essentially, it gives you attitude hold with controls free, similar to an autopilot's control wheel steering feature. If you change pitch attitude and release control pressure at the desired attitude, the system holds that new attitude because the FCS reacts to bring pitch rate to zero. The airplane should fly nicely with pleasant control forces and precise attitude control.
A side benefit of either pitch-rate or g feedback is autotrim in that you can change speed without needing to retrim for level flight. And you don't have to retrim for thrust or configuration changes either. Autotrim gives you apparent neutral-speed stability. Even though positive speed stability was a generally accepted design requirement for more classical airplanes, the lack of it doesn't seem to bother Airbus pilots. However, Boeing opted to retain conventional trim "feel" in its B-777 design.
C Star
C* (pronounced "C Star") is the popular name for a control law in which Nz (g) and pitch-rate feedback are blended. (In the late 60s and early 70s, Nz feedback was called the C law. NASA space shuttle approach studies added pitch-rate feedback, which was called C*.) At low speed in a C* airplane, pitch rate is primary; at higher speeds, g is primary. The changeover is transparent and occurs at about 210 knots in the A320 ("Fly-By-Wire for Commercial Aircraft: The Airbus Experience," C. Favre, 1991).
C*U ("U" represents forward velocity in flight equations) is a modified C* control law used in the B-777 to provide apparent speed stability. The trim switches set a reference speed that is summed with the actual speed in the feedback loop in such a way that the pilot feels conventional control force cues as speed changes. You "trim a speed," not the stabilizer (weight off wheels). Because the max trim reference speed is 330 knots, you would have to push on the control wheel to further increase speed toward Vmo. This provides a tactile high-speed cue.
Fly-by-wire allows designers to optimize the effective dynamics for different flight tasks--for example, an approach mode or a flare mode. This is called task tailoring and produces a multi-mode FCS.
In both the A320 and the B-777, the control laws are not fully active during takeoff until after liftoff because the sensors used for feedback would sense a lot of vibration and "noise" during the ground roll. Landing requires other transitions. Accident investigators should thoroughly understand mode transition points and effects.
Landing with C*
Because C* doesn't "see" ground effect and would require a forward control movement to land, flare compensation may be introduced to the control law. In the B-777, the control law generates a nose-down pitch command at 30 feet radio altitude, requiring aft stick to flare, duplicating conventional ground effect.
The B-777 control laws also improve derotation characteristics over those of the B-757/767. This was achieved by fine-tuning the C*U integrator gain during flight tests and required absolutely no hardware or tooling changes!
Redundancy management
Want a mechanical backup system for all this fly-by-wire magic? This is a popular discussion issue, but the need for such a backup system is really a function of how much redundancy the computers and the sensors have. With today's technology, money is generally better spent on electrical and sensor system integrity and redundancy.
Some military aircraft, because they get shot at, have a quadraplex FCS; that is, they have four each of every essential component. airliners, such as the B-777 and A340, generally use triplex FCSs. Boeing and Airbus both provide limited mechanical backup to ensure a period of survivability at cruise to sort out any electrical problems. Duplex FBW systems should generally have a full mechanical backup.
With all components operative, an FCS is commonly said to be operating in normal law. Various failures usually cause autoreversion to some degraded, but still computed, FCS mode. The lowest level of FBW backup modes normally features analog electronic signals that bypass the primary computers and go directly to the actuators, hence the term direct mode. Direct modes have no feedback control and may have fixed gains to provide acceptable control forces proportional to control surface deflection. The gain selected may optimize control forces for the landing configuration only, or the design might provide different gains for cruise and landing, switched through the flap handle, for example.
Envelope protection
Feedback control of airspeed, mach, attitude, and angle of attack can be used to keep the FBW airplane within a design envelope. Two strategies have been pursued.
With "hard limits," control laws have absolute control (unless the pilot selects direct mode); this is the Airbus strategy.
With "soft limits," the pilot can override envelope protection and so has final authority for the operation of the airplane; this is the Boeing philosophy (and that of the former McDonnell Douglas).
Hazards
Now for the bad news. While FBW technology could make an aerodynamically unstable aircraft flyable, it can also destabilize an otherwise stable airframe.
FBW flight control laws may not be stable for all values of gain or phase angle (the difference between pilot input and airplane response in terms of frequency; exactly opposite would be a 180-degree phase angle) that can be applied. Now costarring with static margin as stability factors are "gain margin" and "phase margin"--measures of how much additional gain or phase-angle lag are available until the system becomes unstable. Computer simulation or flight testing can determine these two margins. But these data are often the manufacturer's proprietary information, so don't look for it on your weight-and-balance sheet.
Highly augmented aircraft, in which fly-by-wire transforms the basic aircraft aerodynamics, can exhibit cliff-like handling qualities.
One reason is that fly-by-wire systems are susceptible to time delay, from a number of causes, which can seriously degrade the pilot's ability to control the aircraft. Time delay may vary for different sizes or frequencies of inputs. U.S. military standards suggest that time delays should be less than one tenth of a second for good handling qualities and that loss of control may occur with delays more than one quarter of a second (MIL STD 1797).
Another factor seen in a number of FBW aircraft accidents involving loss of control is actuator rate limiting, which occurs when the control actuator is commanded to move faster than it is physically capable of moving. Large or rapid control inputs, causing the actuator to lag or not respond to commands, can induce rate limiting in FBW airplanes. Rate limiting can also occur when multiple functions are trying to control the same surface; for example, during rapid pilot pitch commands while the pitch damping function is working hard during turbulence.
Some FBW designs may have a software rate limit placed on the pilot's inputs in the command path. In this case, commands faster than the software limit cause a delay between control movement and resulting aircraft response (Aircraft Control System Rate Limiting, L. Knotts, M. Parrag, E. Ohmit, Calspan Corp., 1993).
While your basic Cessna also has rate limits, the control stops provide some cues that are totally lacking in an FBW airplane. With cable and/or pushrod controls, pilots don't and can't move the controls opposite the surfaces; in FBW, it could happen without the pilot's being aware. Furthermore, time delay and rate limiting can occur with all equipment components operating normally--you don't need a failure somewhere to get these effects.
These factors can lead to an inadvertent or unwanted flightpath motion, aircraft-pilot coupling (APC). Formerly called "pilot-induced oscillations," APC is preferred as it removes the pilot-blaming implicit in "PIO." A good safety program for an FBW airplane should have a reporting system to track APC events. Any unusual handling problems or aircraft motions should be reported. Without tracking APC events, control law deficiencies may go uncorrected.
Safety applications
Fly-by-wire means adding a few new chapters to our accident investigation handbooks. I'll cover just one accident investigation application--detecting rate limiting. This has been the cause of some FBW loss-of-control accidents, including the August 1993 Gripen airshow crash at Stockholm. If loss of control or aircraft handling qualities are suspected in an FBW accident, first assume that the FCS--and not the pilot--induced it until proven otherwise (it might be "designer error").
Your investigation team should include an FBW flight controls expert capable of evaluating phase and gain margins of the system. Also, you may need a manufacturer's FCS engineer who has access to proprietary control law details and flight test data.
One "smoking gun" that investigators should look for is the unmistakable signature of rate limiting. Using the flight data recorder data, compare control surface position to pilot control force (or position). If these data are not available, suspect flight conditions might be repeated in a simulator and computer time histories analyzed, but simulators don't respond like the real airplane outside of a small envelope. (See Figure 3 for the characteristic shapes to look for--this is not an actual data trace.)
A "sawtooth" shape of the data trace of the control surface position, as in Figure 3, indicates that the actuator is moving "stop to stop"--the distinct indication of rate limiting. If actuator-rate or rate-signal data are available, you will see a "checker" shape over the control surface position; the flat spots are the actual rate-limit value. For a software rate limit upstream of the actuator, the sawtooth shape may not be detectable on the control surface time history, and other signals may need to be analyzed. In any case, look for a time delay between input and output.
If you see the sawtooth, try to find a "trigger" that caused rapid or full deflection pilot inputs. For example, in the case of a YF-22 landing accident at Edwards AFB, the trigger was raising the gear for a go-around with afterburner engaged. This caused a step control law gain change to the stick forces and activated thrust vectoring. With the sudden change in aircraft response, the pilot became immediately involved in an oscillatory APC event with rate limiting.
In closing, this article has tried to acquaint the aviation accident investigator with safety aspects of fly-by-wire flight control systems. Now, you should be able to "talk fly-by-wire" with the best of them. The FBW glossary (page 20) defines, with additional explanation, the fbw terms used in the article.
FLY-BY-WIRE GLOSSARY
* Aircraft–pilot coupling (APC)--Inadvertent, unwanted flightpath and attitude motions, usually oscillatory, caused by abnormal interactions between the aircraft FCS and the pilot. Also known as "PIO" for "pilot-induced oscillation," with pilot-blaming implied. APC, or "pilot-involved oscillation," implies the FCS may be at fault.
* Alpha feedback--Feedback of angle-of-attack (denoted by the Greek letter a, alpha). Because accurate alpha measurement at high angles of attack is difficult with airflow vane-type systems due to airframe buffeting and structural flexing, alpha values for feedback are often derived from inertial sensor data.
* Apparent neutral speed stability--FBW feature such that the pilot doesn't have to trim to maintain level flight during speed changes; autotrim.
* Augmentation--Enhancing an aircraft's natural aerodynamic response though the internal design characteristics of the flight control system. SAS, CAS, and FBW (see below) all provide augmentation.
* Augmented aircraft--The combination of the aircraft's natural aerodynamic response plus the additional dynamics and characteristics provided by the flight control system; augmentation systems turned on. Conversely, the "unaugmented aircraft" would have the augmentation systems turned off.
* Autotrim--No pilot trim inputs required to maintain level flight when speed is changed. Autotrim can be a side-effect of a pitch rate command or g command FBW system, which is called "apparent neutral speed stability" (note: pitching moments due to the thrust changes that would effect the speed change are compensated for without the need for pilot trim inputs as well).
* Beta--Sideslip angle, b, as measured with respect to the relative wind (often called the wind-axes, aerodynamic-axes, or stability-axes coordinate system). Sideslip angle is different from the yaw angle (y), which is measured relative to the body axes coordinate system that is rigidly fixed in the airplane; the two are essentially numerically equivalent only at low angles of attack.
* Beta dot--Rate of change of sideslip angle, b with a dot over it (the dot means derivative or rate of change of the parameter). Beta dot and yaw rate are often used as feedback signals in the lateral–directional modes, depending on the application. For example, the B-777 yaw damper control law uses Beta dot feedback at low angles of attack and switches to yaw-rate feedback at high angles of attack.
* Block diagram--A schematic diagram illustrating a basic control law, the signal flow, and associated sensors and feedbacks. As with electrical schematics, a block diagram may be represented by equations and analyzed mathematically for system stability characteristics.
* Body axes--Set of three mutually perpendicular directions (x,y,z), rigidly fixed to the body of an aircraft. Commonly, the axes originate at the cg and are defined as the longitudinal (roll) or x axis, measured positive forward and negative to rear; the lateral (UK= "transverse") (pitch) or y axis, measured positive to the right and negative to the left; and the vertical (yaw) or z axis, measured positive downward and negative upward. The x axis may be parallel to the thrust line, the wing aerodynamic chord, or some other longitudinal reference line. The xz plane is the plane of symmetry for the aircraft.
* C*--Pronounced "C Star," a pitch-axis control law in which pitch-rate and load-factor (g) feedback are blended. Pitch rate dominates at low speed, load factor at higher speed. Used in the Airbus A320/330/340.
* C*U--Modified C* pitch-axis control law with forward velocity feedback included to give apparent speed stability. Used in the Boeing 777.
* CAS--Control (or "command") augmentation system; provides "power steering" and consistent aircraft response over a broad flight envelope. CAS functions originate in the forward path of the FCS block diagram. It essentially boosts the pilot's initial control force and makes flying the airplane easier and more precise. Sensors in the CAS circuit provide feedback signals (typically load factor, pitch rate, or roll rate) to a computer, which compares the aircraft response to the pilot's command signal to make the airplane respond as desired.
* Command path--The portion of a control law, as shown on a block diagram, before summation with feedback. Here, the pilot's command input may be shaped, filtered, or limited.
* Compensation--FBW feature by which control laws automatically prevent unwanted flightpath excursions. Typically, compensation is provided to eliminate trim changes due to configuration changes (extending or retracting landing gear, flaps, and/or speed brake) or thrust changes, to automatically coordinate the rudder required during roll into a turn, to adjust pitch attitude to maintain level flight during a turn, and to provide gust alleviation. An example is the B-777 thrust asymmetry compensation system, which automatically adds rudder to minimize yaw due to engine failure.
* Direct mode, aka direct link--A backup FBW mode in which analog electrical signals bypass the computers and go straight to the control actuators, producing deflection proportional to stick input. The ratio of control surface deflection to stick deflection/force is often fixed, called fixed gains, as a function of configuration, with more deflection provided with flaps down, for instance. Alternatively, gains may be optimized only for landing.
* Envelope protection--FBW feature by which flight envelope limits are implemented through the flight control system's control laws. Protections provided might include g limiting (2.5 gs on A320), angle-of-attack limiting, overspeed protection, low-speed limiting, or bank-angle limiting.
* Feedback--Motion output parameter such as pitch rate, angle of attack, or g that is measured, amplified (or attenuated), and then summed with the original input command. Named for the given parameter; for example, "pitch-rate feedback."
* Feedback control system--Flight control system circuit in which performance in maintaining a desired output parameter is substantially improved by feeding back the output for comparison with the input. If the output differs from the desired value, corrective signals are automatically sent to the flight control surface actuators without any pilot action required. Feedback circuits may consist of one or more "loops."
* Feedback loop--The portion of a block diagram that shows the path of the feedback signals that forms a "loop," usually depicted as the lower part of a block diagram.
* Filter--Modifies a feedback signal according to the frequency content of the parameter of interest to eliminate unwanted feedback effects. A "noise filter" can block nuisance variations in the feedback parameter; for example, pitch rate due to atmospheric turbulence. A "notch filter" can block feedback of structural bending effects occurring at some specific frequency.
* Fly-by-wire (FBW)--Flight control system in which a computer processes the pilot's commands and sends them to the flight control surface actuators by electrical signals rather than mechanical linkage; backup modes may bypass the computer. FBW also includes "fly-by-light," in which the same effects are accomplished through fiber-optic cables. "power-by-wire," means the actuators themselves are electric.
* Forward path--In a block diagram, the path for pilot inputs and their modification upstream of the flight control actuator.
* G command--Pitch-axis control law by which the pilot gets the same "g" for a particular amount of stick force, regardless of speed (energy permitting).
* Gain--Ratio of output to input, or amplification (or attenuation), of a feedback control system element. Pilot gain is often used to describe the magnitude and rapidity (frequency) of pilot control inputs. An urgent or high-effort task, such as flaring and touching down in a gusty crosswind, is often called a high-gain task.
* Gain margin--Amount of additional gain that could be applied to a control law before the system becomes unstable, in the same manner as "static margin" affects static pitch stability. Note: FBW flight control laws are not stable for all values of gain that could be applied.
* Hard limits--FBW envelope protection scheme by which the pilot cannot override the control law limits (in normal mode). Airbus designs use hard limits.
* Inertial Axes--A set of axes used for analysis of inertial effects (that is, the effects of weight distribution) on an aircraft's flightpath during maneuvering flight. In sustained maneuvers, the aircraft would actually rotate about the inertial axes. The longitudinal inertial axis need not be the same as the body x axis or wind x axis; however, the y and z axes usually coincide for a symmetrically loaded aircraft.
* Integrator--Circuit in an FBW flight control system that reduces response
errors over time. It "remembers" the pilot's command and continues to move the
control surfaces until the desired response is achieved and no further "error
signal" is present. Represented by a "1/s" term in a block diagram.
Important: integrator circuits often know only the pilot's maneuver request and may have
no clue as to what the aircraft's physical capability to respond might
be. Additionally, integrators remember the pilot's request as of some time ago, which may
differ significantly from the pilot's instantaneous request during rapid control inputs.
This may cause system lag and instability.
* Lag--Delay between pilot inputs and the aircraft's response. The severity of the lag is described by a parameter called phase lag or phase angle specified in angular degrees. Exactly opposite input and output would be a 180-degree phase lag/angle. Phase margin describes the additional amount of phase lag, measured in degrees, the system can have before it becomes unstable.
* Load factor (also g, Nz, or vertical-load factor)--Ratio of lift generated to aircraft weight, which pilots call "gs." Accelerometers that measure g for FBW feedback functions are not usually located at the cg, since it moves fore and aft during flight, but rather are located near the pilot's station; g accelerometers located aft of the cg can induce feedback control system problems.
* Maneuver demand--Because the pilot's control input "demands" a certain maneuver response in a FBW flight control system, it is often referred to as a "maneuver demand" system.
* Multimode FCS--FBW flight control system in which the effective dynamics change for different flight phases or tasks. The aircraft response is optimized, or "tailored," for various events, such as in an approach mode or flare mode, for example. Each mode has a different control law; mode changes may be enabled through gear/flap/throttle position.
* Normal mode--Normal control laws are in effect, all SAS and CAS functions working normally. Loss of certain sensors or components may cause automatic reversion to some degraded mode and control laws.
* Pitch attitude--Pitch angle, represented in block diagrams by the Greek letter theta, q. Note: "Nose up" is usually positive, but the sign convention for corresponding elevator deflection varies. For instance, in NASA sign convention, a negative elevator deflection is trailing-edge-up, which produces a positive pitch motion.
* Pitch rate--Rate of change of pitch attitude measured relative to the body "y" axis, represented in block diagrams by the letter "q."
* Pitch-rate command--Pitch-axis control law in which the pilot gets the same pitch rate for a particular amount of stick force (or deflection in some designs), regardless of speed.
* Proportional plus integral (PPI)--Popular FBW arrangement that includes a "proportional" path to produce immediate control surface response to stick input while an "integrator" continues control surface commands until the feedback signal equals the pilot's command signal, yielding precision over time. Used in the B-777 and A320 pitch-axis control laws.
* Rate limiting--A phenomenon in FBW FCSs that causes handling difficulties ranging from unintended flightpath changes to loss of control. A flight control surface can be moved at some maximum rate, depending on the actuator's capability to reposition the surface (hardware limit) or on some lower rate limit imposed by the FBW flight control system (software limit). When the FCS commands exceed this limit, surface movement can significantly lag the pilot's inputs and go "stop-to-stop" trying to catch up with pilot commands. A data recorder time history would show the control surfaces moving back and forth in very unpilot-like straight lines, in a "sawtooth" fashion.
* Redundancy management--Describes the level of backup capability. Quadraplex means four of all essential components and computers--common on military aircraft (because of battle damage potential). A "fail-operate" system can be produced with a triplex system (as on B-777 and A320/330/340). Duplex FBW provides a low level of redundancy and should probably require a full mechanical backup.
* Roll rate--Rate of change of bank angle measured about the body "x" axis, represented by the letter "p." Usually, right roll and right stick are positive. Note: roll rate about the velocity vector (stability axis) may also be used.
* Sign convention--Establishes the positive and negative directions for control surface deflections and pitch, roll, and yaw motions used in a control law. Conventions vary among manufacturers. Caution: You must know the manufacturer's sign convention to evaluate its block diagram algebraically. For example, elevator trailing edge up (nose up) may be either a positive or a negative deflection depending on the sign convention adopted. Understanding the sign convention is imperative for accident investigation.
* Soft limits--FBW envelope protection scheme in which the pilot can override the control law limits. The B-777 design philosophy used soft limits.
* Stability augmentation system (SAS)--Feedback control system that provides pitch, roll, or yaw damping; sometimes called a "damper." Older aircraft with an SAS use an electrical, single-loop feedback signal in parallel (stick moves) or series (stick doesn't move) with the mechanical flight control system.
* Summer--In a block diagram, indicates the algebraic summation of the input quantities according to the arrows and the signs; represented by a circle or by a circle and an x.
* Time delay--Delay from pilot input to FBW aircraft response. Caused by many factors including the effect of filters, computer processing time, task time-sharing by computers and signal processors, "higher order" effects of the feedback control system, digital sampling effects, and/or actuator rate limiting. Time delays of more than 0.25 second can cause enough lag to make the FBW aircraft unstable during certain tasks, especially in "high gain" situations.
* Wind axes (aka aerodynamic axes and stability axes)--Set of three mutually perpendicular axes (u,v,w), usually with origin at the cg. The wind axes differ from the body axes in that the longitudinal axis is parallel to the flight path (relative wind) and not a fuselage reference line; the angle between the two longitudinal axes would be the angle of attack.
* Yaw damper--SAS system that damps unwanted yawing motions. A "body axis yaw damper" might use feedback from a yaw rate gyro or accelerometer and can be effective in eliminating "Dutch roll" tendency. However, these might be detrimental when roll about the velocity vector is desired (requires a "conical" motion with body axis roll and yaw rates) because it would oppose body axis yaw rate. Hence, Beta dot feedback might be used to provide damping about the velocity vector.
* Yaw rate--Rate of change of yaw angle as measured about the airplane's "z" body axis, denoted by "y."
