Airframe Trim and Linearize with Simulink® Control Design
by admin in Aerospace , Control Systems & Aerospace , Simulink Family on April 3, 2019This code shows how to trim and linearize an airframe using Simulink® Control Design™ software Designing an autopilot with classical design techniques requires linear models of the airframe pitch dynamics for several trimmed flight conditions. The MATLAB® technical computing environment can determine the trim conditions and derive linear state-space models directly from the nonlinear Simulink® and Aerospace Blockset™ model. This step saves time and helps to validate the model. The Simulink Control Design functions allow you to visualize the motion of the airframe in terms of open-loop frequency or time responses. All the down described equations and steps are exists in the Matlab files, that you will download after the checkout.
Contents
- Initialize Guidance Model
- Define State Values
- Set Operating Point and State Specifications
- Search for Operating Point, Set I/O, Then Linearize
- Select Trimmed States, Create LTI Object, and Plot Bode Response
Initialize Guidance Model
The first problem is to find the elevator deflection, and the resulting trimmed body rate (q), which will generate a given incidence value when the missile is traveling at a set speed. Once the trim condition is found, a linear model can be derived for the dynamics of the perturbations in the states around the trim condition.
open_system('aeroblk_guidance_airframe');
Define State Values
h_ini = 10000/m2ft; % Trim Height [m] M_ini = 3; % Trim Mach Number alpha_ini = -10*d2r; % Trim Incidence [rad] theta_ini = 0*d2r; % Trim Flightpath Angle [rad] v_ini = M_ini*(340+(295-340)*h_ini/11000); % Total Velocity [m/s] q_ini = 0; % Initial pitch Body Rate [rad/sec]
Set Operating Point and State Specifications
The first state specifications are Position states. The second state specification is Theta. Both are known, but not at steady state. The third state specifications are body axis angular rates, of which the variable w is at steady state.
opspec = operspec('aeroblk_guidance_airframe');
opspec.State(1).Known = [1;1];
opspec.State(1).SteadyState = [0;0];
opspec.State(2).Known = 1;
opspec.State(2).SteadyState = 0;
opspec.State(3).Known = [1 1];
opspec.State(3).SteadyState = [0 1];
Search for Operating Point, Set I/O, Then Linearize
op = findop('aeroblk_guidance_airframe',opspec); io(1) = linio('aeroblk_guidance_airframe/Fin Deflection',1,'input'); io(2) = linio('aeroblk_guidance_airframe/Selector',1,'output'); io(3) = linio(sprintf(['aeroblk_guidance_airframe/Aerodynamics &\n', ... 'Equations of Motion']),3,'output'); sys = linearize('aeroblk_guidance_airframe',op,io);
Operating point search report:
---------------------------------
Operating point search report for the Model aeroblk_guidance_airframe.
(Time-Varying Components Evaluated at time t=0)
Operating point specifications were successfully met.
States:
----------
(1.) aeroblk_guidance_airframe/Aerodynamics & Equations of Motion/3DOF (Body Axes)/Position
x: 0 dx: 968
x: -3.05e+03 dx: -171
(2.) aeroblk_guidance_airframe/Aerodynamics & Equations of Motion/3DOF (Body Axes)/Theta
x: 0 dx: -0.216
(3.) aeroblk_guidance_airframe/Aerodynamics & Equations of Motion/3DOF (Body Axes)/U,w
x: 968 dx: -14.1
x: -171 dx: -7.44e-08 (0)
(4.) aeroblk_guidance_airframe/Aerodynamics & Equations of Motion/3DOF (Body Axes)/q
x: -0.216 dx: 3.36e-08 (0)
Inputs:
----------
(1.) aeroblk_guidance_airframe/Fin Deflection
u: 0.136 [-Inf Inf]
Outputs:
----------
(1.) aeroblk_guidance_airframe/q
y: -0.216 [-Inf Inf]
(2.) aeroblk_guidance_airframe/az
y: -7.44e-08 [-Inf Inf]
Select Trimmed States, Create LTI Object, and Plot Bode Response
% find index of desired states in the state vector names = sys.StateName; q_idx = find(strcmp('q',names)); az_idx = find(strcmp('U,w(2)',names)); airframe = ss(sys.A([az_idx q_idx],[az_idx q_idx]),sys.B([az_idx q_idx],:),sys.C(:,[az_idx q_idx]),sys.D); set(airframe,'inputname',{'Elevator'}, ... 'outputname',[{'az'} {'q'}]); ltiview('bode',airframe);
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