Gain Scheduling

6 December 10, 2024

Gain scheduling is used in the aerospace industry for designing controllers. It is required to maintain a guarantee of stability and performance in the face of off-design points.[^7] It is a form of nonlinear control. Typically increasing the gain increases the bandwidth of the system, but it leads to more instability. The gains are scheduled according to the selected scheduling variable. Due to the fact that linearized models are only accurate around the trim point, different operating points require different models, thus needing different gains for the controllers to use at these different points. Gain scheduling determines these operating points by using a scheduling variable that could be speed, altitude, or something else. Gain scheduling aims to design the simplest control design that is easy to implement, and extend it to nonlinear systems.

The nonlinear model is linearized around a number of operating points to get an ensemble of linearized models.

$$\dot{x}=A_ix+B_iu$$
Where
$$i=1,2,\dots$$
The controller gain \(K_i\) is parameterized for each of the \(i\) linearized models. These gains can be scheduled as a lookup table of interpolated values. for each of the controller gain matrices \({K_1, K_2, \dots}\) to set a suitable controller gain for the expected operating point. These gains are tuned to guarantee performance and stability around each operating point. The operating points that you select should be able to average the plant variations over the entire area. This will help the controller have the best chance of adequate performance over the entire control region. If one operating point doesn’t give enough resolution, you can separate an area into two or more operating points. A robust controller has the best chance of good performance throughout the entire operating envelope.
You can use something like interpolation or a transient-free switch to smoothly transition from one operating point to the next. Once the gains are set, typically you would assess the performance across the entire operating envelope in simulation.

VAAC Control Strategies – Used Gain Scheduling
VAAC H-Infinity Loop Shaping
[[X-29 Flight Control Modes]] – used gain scheduling
VLAT Program – used gain scheduling for adaptive flight controllers
Stability of Gain Schedules – VERY IMPORTANT!
Disadvantages of Gain Scheduling
EAP FCS – Used gain scheduling
Gain Scheduling a Pitch Controller – aircraft example
Transient-Free Switch – used in gain scheduling
JDAM Baseline Guidance System – constructed using gain scheduling
Advantages of Dynamic Inversion Controllers – DI reduces the need for gain scheduling
F-22 Lateral Directional Flight Control System – schedules gains based on AOA and speed
Advantages of DPIA Controllers – Gain scheduling doesn’t create unwanted feedback loops
Eurofighter Flight Control System
IRS-T – mu-synthesis controllers scheduled on dynamic pressure
Eurofighter Yaw Axis Feedback Loops – yaw damper gains are scheduled wrt experimental axis
Eurofighter Roll Axis Feedback Loops – scheduled wrt experimental axis
Dynamic Pressure Feedback – acts as a mechanical gain scheduler
MCLAWS-2 Gain Set
Mod BP2.7 – never use extrapolated aerodynamic data
BP4.2– Take advantage of any physical knowledge to simplify the gain scheduling
BP4.15– Beware of feedback loops and transients due to gain schedules
F-16 Aileron-Rudder-Interconnect Gain Schedule
Pressure Ventilator Controller – uses a 2 gain schedule to keep within patient pressure overshoot limits
X-29 Lateral Directional Control System– used multi-rate gain lookup structures
X-29 Air Data Sensors – AOA was used as a primary gain scheduling parameter
X-43 Longitudinal Controller – scheduled using AOA, mach number, and dynamic pressure
[[Shuttle Control Stick Steering Mode]] – gain scheduled via dynamic pressure
[[Legacy Hornet FCC OVP v10.6.1]] – had a backup set of gains
[[Function 32A]] – longitudinal forward-loop gain schedule
[[Function 100]] – speedbrake time constants are scheduled via air data
[[X-31A Flight Control Laws]] – scheduled with AOA, mach number, and altitude
[[System Robustnesss]] – robust control laws result in a simplified gain schedule
F-14 ARI Control System B – mach scheduling didn’t affect the landing
[[Command Augmentation System]] – schedules gains
[[Coolant Average Temperature Mode]] – the variable gain in the block diagram is an example of a gain scheduling function
[[F-35 Spin Recovery Mode]] – schedules gain based on lateral acceleration
[[F-117 Flight Control Laws]] – the classical flight control laws are gain scheduled
[[BP9.7]] – you can use gain scheduling after the basic system has been proven
[[Tornado SPILS Oscillations]] – SPILS is scheduled with airspeed (or dynamic pressure?)
[[Viggen Flight Control System]] – shows block diagrams for airspeed gain schedules
[[C-17 Roll Control Law]] – gain schedule caused doubling of gain which instantly saturated the actuators
[[F-106 Lateral-Directional Control System]] – gains are scheduled with dynamic pressure
[[A-7 Precision Attitude Mode]] – Longitudinal stick force was scheduled with true airspeed, other gains were scheduled with flap position
[[T-38 SAS]] – scheduled with dynamic pressure
[[F-8 Flight Control System]] – gains are scheduled with altitudes
[[Convair 200 Lateral Control Laws]] – uses AOA to schedule ARI
Roll Ratchet – roll gain contributes to roll ratchet
[[F-16XL Flight Control System]] – LE flaps are scheduled with AOA and Mach number
[[HyRaII Project]] – used gain scheduling via a lookup table for sailing speeds
[[PI Heading Controller for Sailing]] – can use gain scheduling based on wind and target direction
[[AC45 Nonlinear Compensation]] – acts sort of like an automatic gain scheduling
[[F-16 Air Data Selection]] – fail-operative to fail-fixed gain
[[B-52 Flight Control System]] – modified pitch SAS was scheduled with impact pressure
[[BQM-34 Flight Control System]] – roll-axis was gain scheduled using IAS
[[VAAC FCL005 Model Reduction]] – if adjacent controllers do not have the same structure, then you can’t schedule gains for them
[[A320 Lateral Control Law]] – gains are scheduled as a function of flap/slat position and $V_C$
[[CH-47A SAS]] – scheduled with airspeed
[[VAAC FCL005 Gain Scheduling]]
[[F-111 Stall Inhibitor System]] – gain scheduled based on AOA
[[F-8C CCV Lateral-Directional CAS]] – used gain scheduling
[[Convair 200 Longitudinal Control Laws]] – dynamic pressure

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