1挠性航天器姿态机动动力学模型

2挠性航天器姿态机动PD鲁棒控制

2.1 动力学模型及PD控制律

2.2仿真模型

2.3 控制程序

function [sys,x0,str,ts,simStateCompliance] = chap7_1ctrl(t,x,u,flag)
%SFUNTMPL General MATLAB S-Function Template
%   With MATLAB S-functions, you can define you own ordinary differential
%   equations (ODEs), discrete system equations, and/or just about
%   any type of algorithm to be used within a Simulink block diagram.
%
%   The general form of an MATLAB S-function syntax is:
%       [SYS,X0,STR,TS,SIMSTATECOMPLIANCE] = SFUNC(T,X,U,FLAG,P1,...,Pn)
%
%   What is returned by SFUNC at a given point in time, T, depends on the
%   value of the FLAG, the current state vector, X, and the current
%   input vector, U.
%
%   FLAG   RESULT             DESCRIPTION
%   -----  ------             --------------------------------------------
%   0      [SIZES,X0,STR,TS]  Initialization, return system sizes in SYS,
%                             initial state in X0, state ordering strings
%                             in STR, and sample times in TS.
%   1      DX                 Return continuous state derivatives in SYS.
%   2      DS                 Update discrete states SYS = X(n+1)
%   3      Y                  Return outputs in SYS.
%   4      TNEXT              Return next time hit for variable step sample
%                             time in SYS.
%   5                         Reserved for future (root finding).
%   9      []                 Termination, perform any cleanup SYS=[].
%
%
%   The state vectors, X and X0 consists of continuous states followed
%   by discrete states.
%
%   Optional parameters, P1,...,Pn can be provided to the S-function and
%   used during any FLAG operation.
%
%   When SFUNC is called with FLAG = 0, the following information
%   should be returned:
%
%      SYS(1) = Number of continuous states.
%      SYS(2) = Number of discrete states.
%      SYS(3) = Number of outputs.
%      SYS(4) = Number of inputs.
%               Any of the first four elements in SYS can be specified
%               as -1 indicating that they are dynamically sized. The
%               actual length for all other flags will be equal to the
%               length of the input, U.
%      SYS(5) = Reserved for root finding. Must be zero.
%      SYS(6) = Direct feedthrough flag (1=yes, 0=no). The s-function
%               has direct feedthrough if U is used during the FLAG=3
%               call. Setting this to 0 is akin to making a promise that
%               U will not be used during FLAG=3. If you break the promise
%               then unpredictable results will occur.
%      SYS(7) = Number of sample times. This is the number of rows in TS.
%
%
%      X0     = Initial state conditions or [] if no states.
%
%      STR    = State ordering strings which is generally specified as [].
%
%      TS     = An m-by-2 matrix containing the sample time
%               (period, offset) information. Where m = number of sample
%               times. The ordering of the sample times must be:
%
%               TS = [0      0,      : Continuous sample time.
%                     0      1,      : Continuous, but fixed in minor step
%                                      sample time.
%                     PERIOD OFFSET, : Discrete sample time where
%                                      PERIOD > 0 & OFFSET < PERIOD.
%                     -2     0];     : Variable step discrete sample time
%                                      where FLAG=4 is used to get time of
%                                      next hit.
%
%               There can be more than one sample time providing
%               they are ordered such that they are monotonically
%               increasing. Only the needed sample times should be
%               specified in TS. When specifying more than one
%               sample time, you must check for sample hits explicitly by
%               seeing if
%                  abs(round((T-OFFSET)/PERIOD) - (T-OFFSET)/PERIOD)
%               is within a specified tolerance, generally 1e-8. This
%               tolerance is dependent upon your model's sampling times
%               and simulation time.
%
%               You can also specify that the sample time of the S-function
%               is inherited from the driving block. For functions which
%               change during minor steps, this is done by
%               specifying SYS(7) = 1 and TS = [-1 0]. For functions which
%               are held during minor steps, this is done by specifying
%               SYS(7) = 1 and TS = [-1 1].
%
%      SIMSTATECOMPLIANCE = Specifices how to handle this block when saving and
%                           restoring the complete simulation state of the
%                           model. The allowed values are: 'DefaultSimState',
%                           'HasNoSimState' or 'DisallowSimState'. If this value
%                           is not speficified, then the block's compliance with
%                           simState feature is set to 'UknownSimState'.


%   Copyright 1990-2010 The MathWorks, Inc.
%   $Revision: 1.18.2.5 $

%
% The following outlines the general structure of an S-function.
%
switch flag,

  %%%%%%%%%%%%%%%%%%
  % Initialization %
  %%%%%%%%%%%%%%%%%%
  case 0,
    [sys,x0,str,ts,simStateCompliance]=mdlInitializeSizes;

  %%%%%%%%%%%%%%%
  % Derivatives %
  %%%%%%%%%%%%%%%
  case 1,
    %sys=mdlDerivatives(t,x,u);
    sys=[];

  %%%%%%%%%%
  % Update %
  %%%%%%%%%%
  case 2,
    %sys=mdlUpdate(t,x,u);
    sys=[];
  %%%%%%%%%%%
  % Outputs %
  %%%%%%%%%%%
  case 3,
    sys=mdlOutputs(t,x,u);

  %%%%%%%%%%%%%%%%%%%%%%%
  % GetTimeOfNextVarHit %
  %%%%%%%%%%%%%%%%%%%%%%%
  case 4,
    %sys=mdlGetTimeOfNextVarHit(t,x,u);
    sys=[];
  %%%%%%%%%%%%%
  % Terminate %
  %%%%%%%%%%%%%
  case 9,
    %sys=mdlTerminate(t,x,u);
    sys=[];
  %%%%%%%%%%%%%%%%%%%%
  % Unexpected flags %
  %%%%%%%%%%%%%%%%%%%%
  otherwise
    DAStudio.error('Simulink:blocks:unhandledFlag', num2str(flag));

end

% end sfuntmpl

%
%=============================================================================
% mdlInitializeSizes
% Return the sizes, initial conditions, and sample times for the S-function.
%=============================================================================
%
function [sys,x0,str,ts,simStateCompliance]=mdlInitializeSizes

%
% call simsizes for a sizes structure, fill it in and convert it to a
% sizes array.
%
% Note that in this example, the values are hard coded.  This is not a
% recommended practice as the characteristics of the block are typically
% defined by the S-function parameters.
%
sizes = simsizes;

sizes.NumContStates  = 0;
sizes.NumDiscStates  = 0;
sizes.NumOutputs     = 1;
sizes.NumInputs      = 7;
sizes.DirFeedthrough = 1;
sizes.NumSampleTimes = 1;   % at least one sample time is needed

sys = simsizes(sizes);

%
% initialize the initial conditions
%
x0  = [];

%
% str is always an empty matrix
%
str = [];

%
% initialize the array of sample times
%
ts  = [0 0];

% Specify the block simStateCompliance. The allowed values are:
%    'UnknownSimState', < The default setting; warn and assume DefaultSimState
%    'DefaultSimState', < Same sim state as a built-in block
%    'HasNoSimState',   < No sim state
%    'DisallowSimState' < Error out when saving or restoring the model sim state
simStateCompliance = 'UnknownSimState';

% end mdlInitializeSizes

%
%=============================================================================
% mdlDerivatives
% Return the derivatives for the continuous states.
%=============================================================================
%
%function sys=mdlDerivatives(t,x,u)

%sys = [];

% end mdlDerivatives


%
%=============================================================================
% mdlOutputs
% Return the block outputs.
%=============================================================================
%
function sys=mdlOutputs(t,x,u)
thd=u(1);
th=u(2);
q1=u(3);
q2=u(4);
dth=u(5);
dq1=u(6);
dq2=u(7);
q=[q1 q2]';
dq=[dq1 dq2]';
e=th-thd;
kp=100;
kd=1000;
xite=4.0;
xite=0;
ut=-kp*e-kd*dth-xite*sign(dth);
sys = ut;

% end mdlOutputs

%
%=============================================================================
% mdlGetTimeOfNextVarHit
% Return the time of the next hit for this block.  Note that the result is
% absolute time.  Note that this function is only used when you specify a
% variable discrete-time sample time [-2 0] in the sample time array in
% mdlInitializeSizes.
%=============================================================================

2.4 被控对象程序

function [sys,x0,str,ts,simStateCompliance] = chap7_1plant(t,x,u,flag)
switch flag,
  case 0,
    [sys,x0,str,ts,simStateCompliance]=mdlInitializeSizes;
  case 1,
    sys=mdlDerivatives(t,x,u);
  case 3,
    sys=mdlOutputs(t,x,u);
  case {2,4,9}
    sys=[];
  otherwise
    DAStudio.error('Simulink:blocks:unhandledFlag', num2str(flag));

end

function [sys,x0,str,ts,simStateCompliance]=mdlInitializeSizes

sizes = simsizes;

sizes.NumContStates  = 6;
sizes.NumDiscStates  = 0;
sizes.NumOutputs     = 6;
sizes.NumInputs      = 1;
sizes.DirFeedthrough = 0;
sizes.NumSampleTimes = 1;   % at least one sample time is needed

sys = simsizes(sizes);

x0  = [0 0 0 0 0 0];
str = [];
ts  = [0 0];

% Specify the block simStateCompliance. The allowed values are:
%    'UnknownSimState', < The default setting; warn and assume DefaultSimState
%    'DefaultSimState', < Same sim state as a built-in block
%    'HasNoSimState',   < No sim state
%    'DisallowSimState' < Error out when saving or restoring the model sim state
simStateCompliance = 'UnknownSimState';

function sys=mdlDerivatives(t,x,u)
J=3250;
F1=54;
F2=6;
w1=1.2;w2=3.4;
Ks1=0.01;Ks2=0.01;

M=[J F1 F2;F1 1 0;F2 0 1];
N=[0 0 0;0 2*Ks1*w1 0;0 0 2*Ks2*w2];
K=[0 0 0;0 w1^2 0;0 0 w2^2];
B=[1 0 0]';
dt=0*3*sin(t);
ut=u(1);

x1=[x(1) x(2) x(3)]';%th q1 q2
x2=[x(4) x(5) x(6)]';%dth dq1 dq2
dx1=x2;
dx2=inv(M)*(-N*x2-K*x1+B*(ut-dt));
sys(1)=dx1(1);
sys(2)=dx1(2);
sys(3)=dx1(3);
sys(4)=dx2(1);
sys(5)=dx2(2);
sys(6)=dx2(3);


function sys=mdlOutputs(t,x,u)
sys(1)=x(1);%th
sys(2)=x(2);%q1
sys(3)=x(3);%q2
sys(4)=x(4);%sth
sys(5)=x(5);%dq1
sys(6)=x(6);%dq2

2.5 绘图程序

close all;

figure(1);
subplot(211);
plot(t,x(:,1),'r',t,x(:,2),'b','linewidth',2);
xlabel('time(s)');ylabel('angle tracking');
legend('ideal angle','practical angle');
subplot(212);
plot(t,x(:,5),'b','linewidth',2);
xlabel('time(s)');ylabel('practical angle speed');

figure(2);
subplot(211);
plot(t,x(:,3),'r','linewidth',2);
xlabel('time(s)');ylabel('Mode 1');
subplot(212);
plot(t,x(:,4),'b','linewidth',2);
xlabel('time(s)');ylabel('Mode 2');

figure(3);
subplot(211);
plot(t,x(:,6),'r','linewidth',2);
xlabel('time(s)');ylabel('speed of Mode 1');
subplot(212);
plot(t,x(:,7),'b','linewidth',2);
xlabel('time(s)');ylabel('speed of Mode 2');

figure(4);
plot(t,Th(:,1),'r','linewidth',2);
xlabel('time(s)');ylabel('Th');

2.6 结果