Flight Control System Modeling and Simulation
This example demonstrates the closed-loop working principle and digital simulation method of a Flight Control System (Fly-By-Wire). Using the Simit modular architecture, a complex aircraft automatic control system is decomposed into four core links: “Pilot Intention Interpretation - Intelligent Decision Calculation - Control Surface Command Execution - Flight State Feedback”, helping readers understand from scratch how modern aircraft achieve stable flight and precise control in the air.
Overview
What is a Flight Control System?
The flight control system is the “intelligent driving assistant” of the aircraft, continuously performing the following tasks:
- Sense Pilot Intention: Convert the push/pull and deflection actions of the control stick into clear flight targets (such as “climb”, “turn”).
- Calculate Optimal Commands: Based on the current flight state (speed, attitude, altitude), calculate in real-time which control surfaces should be deflected and by how much angle.
- Drive Control Surfaces: Send commands to elevators, ailerons, and rudders to generate aerodynamic forces that change the flight trajectory.
- Closed-Loop Feedback Correction: Continuously monitor the actual response of the aircraft, automatically correct errors, and ensure flight safety and quality.
Core Feature: This is a closed-loop negative feedback system where the flight control system continuously corrects control surface commands through sensor data.
System Architecture and Interfaces
Top-Level Modular Design
This example adopts a layered decoupled architecture, where modules interact through standard signal interfaces:
| Module Name | Function Description | Input Interface | Output Interface |
|---|---|---|---|
| Pilot | Converts physical stick displacement into digital flight targets: longitudinal g-load, lateral roll, heading commands | None (Manual Trigger) | Nz_cmd: Longitudinal G-load commandP_cmd: Lateral roll commandBeta_cmd: Heading command |
| Control System | The core decision unit of the flight control system, calculating elevator, aileron, and rudder deflection commands | Pilot commands + Aircraft state feedback | Demands: Elevator & Rudder commands |
| Vehicle | Simulates the aerodynamic response and six-degree-of-freedom equations of motion of a real aircraft | Control surface deflection commands | rad: Angle of attackq_rad: Pitch rateBeta: Sideslip anglep_rad: Roll rate, etc. (8 states) |
| Visualization | Real-time display of 7 key flight parameter waveforms for debugging and performance evaluation | Aircraft state variables | Visualization curves (No output interface) |
Signal Flow Topology
graph LR
A[Pilot] -->|Nz_cmd/P_cmd/Beta_cmd| B[Control System]
B -->|Demands| C[Vehicle]
C -->|PlantData| B
C -->|7 State Variables| D[Visualization]
C -->|PlantData| A
style B fill:#f9f,stroke:#333,stroke-width:2pxKey Connection Description:
- Forward Path: Pilot Command → Control Law → Aircraft → Display
- Feedback Path: Aircraft state variables return to the control law, forming a closed loop (dashed line in concept).
- Core Node:
Control_Systemis the core of the algorithm and the focus of this example.
Core Working Principle Demonstration
Typical Maneuver: Dive and Pull-up Loop
Taking a complete dive followed by pull-up maneuver as an example to illustrate how the system works collaboratively:
Phase 1: Pilot Input (t=0-0.5s)
- The pilot pushes the stick forward to -40, requesting the aircraft to enter a dive.
- The
Pilotmodule outputsNz_cmd = -40(G-load command, unit: m/s²). - Physical Meaning: Requesting the aircraft to generate -4g load (normal level flight is +1g).
- Simultaneously input
Xlat = -20(left stick) andYlat = +30(right rudder) to simulate a banked dive.
Phase 2: Intelligent Calculation (t=0.5-1.0s)
Cmd_Alphasub-module: Converts -40 load into -12° angle of attack command.Cmd_Qsub-module: Calculates a pitch rate of -5°/s required for smooth transition.- Integrated Output:
Elevator demand = +8°(Positive elevator deflection, aircraft pitches down). - Intelligence: The system processes tri-axial commands simultaneously, converting “G-load target” and “Roll/Heading coordination” into specific control surface actions.
Phase 3: Aircraft Physical Response (t=1.0-3.0s)
Plant_Lonreceives control surface commands and solves rigid body equations of motion.- Aircraft angle of attack decreases from +2° to -12°, normal load changes from +1g to -0.8g.
- Simultaneously
Plant_Latresponds to lateral commands, aircraft rolls left about 30°, entering a banked dive.
Phase 4: Closed-Loop Feedback Correction (Continuous t>0s)
- The actual state of the aircraft (angle of attack, angular rate) is fed back to
Control_Systemin real-time. - If the angle of attack changes too slowly, the elevator deflection angle is automatically increased (Gain
Kp_q_cmd=1.7acts). - If approaching the target attitude, the control surface is reduced in advance to prevent overshoot (Feedback gain
Kp_q_FB=0.3acts). - Core Value: No manual correction required by the pilot; the system automatically maintains expected performance.
Phase 5: Reverse Recovery (t=6s)
- The pilot pulls the stick back to +15, requesting leveling off.
- The system repeats the above process, elevator deflects negatively to -10°, aircraft pitches up.
- Around t=10s, angle of attack recovers to +2°, load to +1g, bank to 0°, level flight restored.
Detailed Control Law Design
The control law is the “intelligent decision algorithm” of the flight control system. This example adopts a Classic PID + Prefilter + Gain Scheduling architecture, designed separately for longitudinal and lateral channels.
Longitudinal Control Law
The longitudinal channel is responsible for pitch attitude and altitude control, with the core being precise tracking of G-load commands and sufficient damping of the short-period mode.
G-load to Angle of Attack Command Module Cmd_Alpha
Module Function: Converts the pilot’s input G-load command (Nz) into an executable angle of attack command (α) for the aircraft, and completes signal conditioning and protection.
Signal Processing Flow:
graph LR
Nz_cmd --> Gain["Gain K1=1.25"]
Gain --> Filter["2nd Order Low Pass 100/(s+100)"]
Filter --> Limit["Command Limit ±12°"]
Limit --> α_cmdParameter Design Basis:
- Gain K1=1.25: Static conversion coefficient from G-load to angle of attack, determined by the slope of the aircraft’s lift curve. Physical meaning: 1g load corresponds to about 1.25° change in angle of attack.
- Low Pass Filter: Cutoff frequency 100rad/s, filters out high-frequency stick jitter (>15Hz) and sensor noise, preventing unnecessary frequent movement of control surfaces.
- Limiter Module: Limits the command angle of attack to -15° to +12°, ensuring the aircraft stays away from stall angles (usually >15°).
Pitch Rate Command Generation Module Cmd_Q
Module Function: Generates pitch rate commands to achieve G-command response characteristics (i.e., G-load command is linearly proportional to pilot stick input).
Control Law Equation:
Gain Design:
| Gain Meaning | Parameter Name | Value | Physical Meaning and Tuning Experience |
|---|---|---|---|
| Forward Gain | Kp_q_cmd | 1.7 | Determines tracking speed. Increasing reduces response time, but >2.5 prone to Pilot Induced Oscillation (PIO) |
| Feedback Gain | Kp_q_FB | 0.3 | Provides system damping. Reducing leads to overshoot >20%, too large (>0.5) overly suppresses response |
| Alpha Feedback | KAlpha_FDBK | 0.4 | Increases short-period mode frequency, improves steady-state accuracy |
| Feedforward Gain | K_ff | 0.8 | Improves command response speed, gain scheduling implemented by Z2Q_Cmd_Surf_Limit lookup table |
Filter Network:
- Forward Channel:
Transfer Fcn5 = 10/(s+10), smooths command jumps, prevents surface saturation. - Feedback Channel:
Transfer Fcn2 = 10/(s+10), filters gyro noise. - Compensation Network:
Transfer Fcn3 = 15/(s+15), provides phase lead, increases damping.
Lateral Control Law
The lateral channel is responsible for roll attitude and heading coordination control, with the core being roll command tracking and sideslip elimination.
Roll Command Generation Module Cmd_NY
Module Function: Converts lateral stick input into roll rate command, implementing a linear response of “stick displacement → roll rate”.
Control Law Structure:
Core Parameters:
KPcmd = 2.0: Main gain, determines roll time constant. In this example, 60° roll time is about 1.2s, meeting transport aircraft standards.KIPcmd = 0.5: Integral gain, eliminates roll angle steady-state error, ensuring precise tracking.Transfer Fcn3 = 80/(s+80): Command filter, bandwidth 80rad/s, smooths roll commands.P_cmdLimit = ±50°/s: Roll rate limiter, prevents excessive roll rate causing passenger discomfort.
Sideslip Coordination Control Module Cmd_PBETA
Module Function: Eliminates sideslip angle (β), realizing Coordinated Turn, avoiding poor flight quality of “slip → skid”.
Control Principle: Rolling produces Adverse Yaw, which needs to be compensated by actively deflecting the rudder.
Control Law Equation:
Gain Design:
| Gain Meaning | Parameter Name | Value | Physical Meaning and Tuning Experience |
|---|---|---|---|
| Sideslip Prop. | Kp_beta_Cmd | 2.0 | Main feedback channel, quickly suppresses sideslip, keeping β < 2°. Increasing improves coordination, but >3.0 causes frequent rudder movement |
| Sideslip Int. | Ki_beta | 0.1 | Eliminates steady-state sideslip error, ensuring long-term flight β < 0.5°. Time constant ~10s, needs anti-windup |
| Roll Rate Gain | K_beta_dot | 1.2 | Roll → Rudder cross-feedforward, actively coordinates to reduce sideslip peak. Determined by aircraft dynamic response |
| Sideslip Deriv. | Kd_beta_cmd | 0.0 | Derivative channel closed. β sensor noise is large, derivative amplifies noise causing rudder jitter |
Coordinated Turn Implementation:
- Command Generation:
FUN_BETA_CMDlookup table, larger roll command implies larger rudder pre-deflection. - Actuator Dynamics:
Transfer Fcn1 = 40/(s+40)(Aileron),Transfer Fcn2 = 20/(s+20)(Rudder). - Limit Protection:
CMD_LIM_A/R = ±20°, prevents mechanical over-travel.
Performance Verification and Simulation Analysis
Longitudinal Flight Quality Verification (MIL-STD-1797)
| Metric Category | Verification Item | Spec Requirement | Simulation Result | Conclusion |
|---|---|---|---|---|
| Short Period Freq | Undamped Natural Freq | 0.5-3.0 rad/s | 1.8 rad/s | Level 1 |
| Short Period Damping | Damping Ratio | >0.35 | 0.68 | Level 1 |
| Pitch Response | Overshoot | ≤ 25% | 15% | Level 1 |
| G-Command Response | G-load Tracking Linearity | Error ≤ 10% | 8% | Level 1 |
Lateral Flight Quality Verification
| Metric Category | Verification Item | Spec Requirement | Simulation Result | Conclusion |
|---|---|---|---|---|
| Roll Mode | Time Constant | 0.5-1.2 s | 0.8 s | Level 1 |
| Roll Overshoot | Peak Overshoot | ≤ 15% | 5% | Level 1 |
| Dutch Roll Damping | Damping Ratio | >0.19 | 0.42 | Level 1 |
| Coordination | Steady Sideslip | ≤ 2° | 0.5° | Level 1 |
Applications
- Flight Quality Assessment: Quickly verify if new designs meet MIL-STD-1797A standards.
- Control Law Tuning: Optimize PID and prefilter parameters through batch simulation to reduce flight test risks.
- Failure Mode Simulation: Simulate scenarios like jammed surfaces (0%-100%), sensor failure, actuator saturation.
- Certification Support: Generate test cases and coverage reports compliant with DO-178C.
- Pilot-in-the-Loop: Joint simulation with flight simulators like FlightGear to assess handling qualities.
Model Parameter Configuration Code
%% Flight Control System Parameter Configuration - FlightControlSystem_Config.m
%% Longitudinal Control Law Parameters
% G-load to Alpha Conversion
K1_longitudinal = 1.25; % G-load to Alpha Gain (deg/g)
AlphaCmd_FilterFreq = 100; % Command Filter Cutoff Frequency (rad/s)
% Pitch Rate Loop
KQ_CMD = 1.7; % Pitch Rate Forward Gain
KQFDBK = 0.3; % Pitch Rate Feedback Gain
KAlpha_FDBK = 0.4; % Alpha Feedback Gain
% Actuator & Protection
Elevator_Max = 25; % Max Elevator Deflection (deg)
Elevator_Rate_Limit = 5; % Elevator Rate Limit (deg/s)
%% 6.2 Lateral Control Law Parameters
% Roll Command Loop
KPcmd_Roll = 2.0; % Roll Proportional Gain
KIPcmd_Roll = 0.5; % Roll Integral Gain
RollCmd_FilterFreq = 80;