Model Predictive Control Toolbox 3.1.1

Constrained Multivariable (2x2) MPC Control of an AFTI-F16 Aircraft

Contents

This demonstration shows how to use Model Predictive Control Toolbox™ to control a simplified model of the dynamics of an AFTI-F16 aircraft with saturating actuators [1,2].

Reference: [1] P. Kapasouris, M. Athans and G. Stein, "Design of feedback control systems for unstable plants with saturating actuators", Proc. IFAC Symp. on Nonlinear Control System Design, Pergamon Press, pp.302--307, 1990 [2] A. Bemporad, A. Casavola, and E. Mosca, "Nonlinear control of constrained linear systems via predictive reference management," IEEE® Trans. Automatic Control, vol. AC-42, no. 3, pp. 340-349, 1997.

Define the MPC Object

if ~mpcchecktoolboxinstalled('simulink')
    disp('Simulink(R) is required to run this demo.')
    return
end

The linearized open-loop dynamic model for the attack and pitch angles as a function of the elevator and flaperon angles is

Ts=.05;        %Sampling time
Tstop=40*Ts;   %Simulation time

A=[-.0151 -60.5651 0 -32.174;
     -.0001 -1.3411 .9929 0;
     .00018 43.2541 -.86939 0;
      0      0       1      0];
B=[-2.516 -13.136;
     -.1689 -.2514;
     -17.251 -1.5766;
     0        0];
C=[0 1 0 0;
     0 0 0 1];
D=[0 0;
     0 0];

sys=ss(A,B,C,D);
x0=zeros(4,1);

The manipulated variables are the elevator and flaperon angles, the attack and pitch angles are measured outputs to be regulated. The open-loop response of the system is unstable.

Both inputs are constrained between +/- 25 deg. The task is to get zero offset for piecewise-constant references, while avoiding instability due to input saturation. We also add constraints on the outputs to limit undershoots.

clear MV OV
MV(1)=struct('Min',-25,'Max',25);
MV(2)=struct('Min',-25,'Max',25);
OV(1)=struct('Min',-0.5,'Max',0.5);
OV(2)=struct('Min',-100,'Max',100);
Weights=struct('Input',[0 0],'InputRate',[0 0],'Output',[10 10]);

p=10;     % Prediction horizon
moves=3;  % Control horizon

mpcafti=mpc(sys,Ts,p,moves);
mpcafti.Weights=Weights;
mpcafti.MV=MV;
mpcafti.OV=OV;

-->The "Weights.ManipulatedVariables" property of "mpc" object is empty. 
Assuming default 0.00000.
-->The "Weights.ManipulatedVariablesRate" property of "mpc" object is emp
ty. Assuming default 0.10000.
-->The "Weights.OutputVariables" property of "mpc" object is empty. Assum
ing default 1.00000.

Simulation in Simulink®

open_system('mpc_afti16')
sim('mpc_afti16',Tstop)

-->Converting model to discrete time.
-->Integrated white noise added on measured output channel #1.
-->Integrated white noise added on measured output channel #2.
-->MPC problem is constrained and "ManipulatedVariables.RateMin" is not c
ompletely specified or has infinite values.
   Setting values to -10 to prevent numerical problems in QP.
-->The "Model.Noise" property of the "mpc" object is empty. Assuming whit
e noise on each measured output channel.

bdclose('mpc_afti16')