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:

1. Sense Pilot Intention: Convert the push/pull and deflection actions of the control stick into clear flight targets (such as “climb”, “turn”).
2. 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.
3. Drive Control Surfaces: Send commands to elevators, ailerons, and rudders to generate aerodynamic forces that change the flight trajectory.
4. 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:

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:2px

Key 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_System is 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 Pilot module outputs Nz_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) and Ylat = +30 (right rudder) to simulate a banked dive.

Phase 2: Intelligent Calculation (t=0.5-1.0s)

• Cmd_Alpha sub-module: Converts -40 load into -12° angle of attack command.
• Cmd_Q sub-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_Lon receives 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_Lat responds 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_System in real-time.
• If the angle of attack changes too slowly, the elevator deflection angle is automatically increased (Gain Kp_q_cmd=1.7 acts).
• If approaching the target attitude, the control surface is reduced in advance to prevent overshoot (Feedback gain Kp_q_FB=0.3 acts).
• 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_cmd

Parameter 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:

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:

Coordinated Turn Implementation:

• Command Generation: FUN_BETA_CMD lookup 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)

Lateral Flight Quality Verification

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;