fmrlc_tanker.m

一个用MATLAB编写的优化控制工具箱

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% Fuzzy Model Reference Learning Control (FMRLC) System for a Tanker Ship
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%
% By: Kevin Passino 
% Version: 4/26/01
%
% Notes: This program has evolved over time and uses programming 
% ideas of Andrew Kwong, Jeff Layne, and Brian Klinehoffer.
%
% This program simulates an FMRLC for a tanker
% ship.  It has a fuzzy controller with two inputs, the error
% in the ship heading (e) and the change in that error (c).  The output
% of the fuzzy controller is the rudder input (delta).  The FMRLC 
% adjusts the fuzzy controller to try to get tanker ship heading (psi) 
% to track the output of a "reference model" (psi_m) that has as an 
% input the reference input heading (psi_r). We simulate the tanker 
% as a continuous time system that is controlled by an FMRLC that 
% is implemented on a digital computer with a sampling interval of T=1 sec.  
%
% This program can be used to illustrate:
%  - How to code an FMRLC (for two inputs and one output, 
%    for the controller and "fuzzy inverse model").
%  - How to tune the input and output gains of an FMRLC.
%  - How changes in plant conditions ("ballast" and "full" and speed) 
%    can affect performance and how the FMRLC can adapt to improve
%    performance when there are such changes.
%  - How the effects of sensor noise (heading sensor noise) and plant 
%    disturbances (wind hitting the side of the ship) can be reduced
%    over the case of non-adaptive fuzzy control.
%  - The shape of the nonlinearity synthesized by the FMRLC
%    by plotting the input-output map of the fuzzy controller at the
%    end of the simulation (and providing the output membership function
%    centers).
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear		% Clear all variables in memory

% Initialize ship parameters 

ell=350;			% Length of the ship (in meters)
abar=1;             % Parameters for nonlinearity
bbar=1;

% Define the reference model (we use a first order transfer function 
% k_r/(s+a_r)):

a_r=1/150;
k_r=1/150;

% Initialize parameters for the fuzzy controller

nume=11; 	% Number of input membership functions for the e 
			% universe of discourse (can change this but must also
			% change some variables below if you make such a change)
numc=11; 	% Number of input membership functions for the c 
			% universe of discourse (can change this but must also
			% change some variables below if you make such a change)

% Next, we define the scaling gains for tuning membership functions for 
% universes of discourse for e, change in e (what we call c) and 
% delta.  These are g1, g2, and g0, respectively
% These can be tuned to try to improve the performance. 

% First guess: 
g1=1/pi;,g2=100;,g0=8*pi/18; % Chosen since: 
		% g1: The heading error is at most 180 deg (pi rad) 
		% g2: Just a guess - that ship heading will change at most
		%     by 0.01 rad/sec (0.57 deg/sec)
		% g0: Since the rudder is constrained to move between +-80 deg
% "Good" tuned values:
g1=2/pi;,g2=250;,g0=8*pi/18; 

% Next, define some parameters for the membership functions

we=0.2*(1/g1);	  
	% we is half the width of the triangular input membership 
	% function bases (note that if you change g0, the base width
	% will correspondingly change so that we always end
	% up with uniformly distributed input membership functions)
	% Note that if you change nume you will need to adjust the 
	% "0.2" factor if you want membership functions that 
	% overlap in the same way.
wc=0.2*(1/g2);        
	% Similar to we but for the c universe of discourse
base=0.4*g0;      
	% Base width of output membership fuctions of the fuzzy 
	% controller

% Place centers of membership functions of the fuzzy controller:

% Centers of input membership functions for the e universe of
% discourse of fuzzy controller (a vector of centers)
ce=[-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1]*(1/g1);

% Centers of input membership functions for the c universe of
% discourse of fuzzy controller (a vector of centers)
cc=[-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1]*(1/g2);

% This next matrix specifies the rules of the fuzzy controller.  
% The entries are the centers of the output membership functions.  
% This choice represents just one guess on how to synthesize 
% the fuzzy controller.  Notice the regularity 
% of the pattern of rules (basiscally we are using a type of 
% saturated index adding).  Notice that it is scaled by g0, the 
% output scaling factor, since it is a normalized rule base.
% The rule base can be tuned to try to improve performance.

% The gain gf is a gain that can be set to one to initialize 
% the rule base with an initial guess at the fuzzy controller to be
% synthesized or to zero to initialize the rule base to all zeros
% (i.e., all centers at zero so the rules all say to put zero
% into the plant).

gf=1;

rules=[1    1     1     1    1     1    0.8   0.6   0.3    0.1     0;
  	   1    1     1     1    1   0.8    0.6   0.3   0.1    0     -0.1;
	   1    1     1     1   0.8  0.6    0.3   0.1   0     -0.1   -0.3;
	   1    1     1   0.8   0.6  0.3    0.1    0    -0.1   -0.3  -0.6;
	   1    1   0.8   0.6   0.3  0.1     0   -0.1   -0.3   -0.6  -0.8;
	   1  0.8   0.6   0.3   0.1   0    -0.1  -0.3   -0.6   -0.8   -1;
	 0.8  0.6   0.3   0.1    0   -0.1  -0.3  -0.6   -0.8   -1     -1;
	 0.6  0.3   0.1    0   -0.1  -0.3  -0.6  -0.8   -1     -1     -1;
	 0.3  0.1    0   -0.1  -0.3  -0.6  -0.8   -1    -1     -1     -1;
	 0.1   0   -0.1  -0.3  -0.6  -0.8   -1    -1    -1     -1     -1;
	   0 -0.1  -0.3  -0.6  -0.8  -1     -1    -1    -1     -1     -1]*gf*g0;

% Next, we define some parameters for the fuzzy inverse model

gye=2/pi;,gyc=10;    % Scaling gains for the error and change in error for 
					% the inverse model
					% These are tuned to improve the performance of the FMRLC
gp=0.4;	

% Scaling gain for the output of inverse model.  If you let gp=0 then
% you turn off the learning mechanism and hence the FMRLC reduces to 
% a direct fuzzy controller that is not tuned.  Hence, from this 
% program you can also see how to code a non-adaptive fuzzy controller.
% If gp is large then generally large updates will be made to the 
% fuzzy controller.  You should think of gp as an "adaptation gain."

numye=11; 	% Number of input membership functions for the ye 
			% universe of discourse
numyc=11; 	% Number of input membership functions for the yc 
			% universe of discourse

wye=0.2*(1/gye);	% Sets the width of the membership functions for 
					% ye from center to extremes
wyc=0.2*(1/gyc);	% Sets the width of the membership functions for 
					% yc from center to extremes
invbase=0.4*gp; % Sets the base of the output membership functions
				% for the inverse model

% Place centers of inverse model membership functions
% For error input for learning mechanism
cye=[-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1]*(1/gye);

% For change in error input for learning mechanism
cyc=[-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1]*(1/gyc);

% The next matrix contains the rule-base matrix for the fuzzy 
% inverse model.  Notice that for simplicity we choose it to have 
% the same structure as the rule base for the fuzzy controller.  
% While this will work for the control of the tanker 
% for many nonlinear systems a different structure 
% will be needed for the rule base.  Again, the entries are 
% the centers of the output membership functions, but now for 
% the fuzzy inverse model.

inverrules=[1   1   1    1    1    1    0.8  0.6   0.4   0.2   0;
    	    1   1   1    1    1   0.8   0.6  0.4   0.2    0   -0.2;
	        1   1   1    1   0.8  0.6   0.4  0.2    0    -0.2 -0.4;
	        1   1   1   0.8  0.6  0.4   0.2   0    -0.2  -0.4 -0.6;
	        1   1  0.8  0.6  0.4  0.2   0    -0.2  -0.4  -0.6 -0.8;
	        1  0.8 0.6  0.4  0.2   0   -0.2  -0.4  -0.6  -0.8  -1;
	      0.8  0.6 0.4  0.2   0   -0.2 -0.4  -0.6  -0.8   -1   -1;
	      0.6  0.4 0.2   0   -0.2 -0.4 -0.6  -0.8   -1    -1   -1;
	      0.4  0.2  0  -0.2  -0.4 -0.6 -0.8   -1    -1    -1   -1;
	      0.2   0  -0.2 -0.4 -0.6 -0.8  -1    -1    -1    -1   -1;
	       0  -0.2 -0.4 -0.6 -0.8  -1   -1    -1    -1    -1   -1]*gp;

% Next, we set up some parameters/variables for the 
% knowledge-base modifier

d=1;   

% This sets the number of steps the knowledge-base modifier looks
% back in time. For this program it must be an integer
% less than or equal to 10 (but this is easy to make larger)

% The next four vectors are used to store the information about 
% which rules were on 1 step in the past, 2 steps in the past, ...., 
% 10 steps in the past (so that picking 0<= d <= 10 can be used).
	   
meme_int=[0 0 0 0 0 0 0 0 0 0];  
	% sets up the vector to store up to 10 values of e_int
meme_count=[0 0 0 0 0 0 0 0 0 0];  
	% sets up the vector to store up to 10 values of e_count
memc_int=[0 0 0 0 0 0 0 0 0 0];  
	% sets up the vector to store up to 10 values of c_int
memc_count=[0 0 0 0 0 0 0 0 0 0];  
	% sets up the vector to store up to 10 values of c_count

% Now, you can proceed to do the simulation or simply view the nonlinear
% surface generated by the fuzzy controller that is now fully defined.

flag1=input('Do you want to simulate the \n FMRLC for the tanker?  \n (type 1 for yes and 0 for no) ');

if flag1==1, 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Next, we initialize the simulation:

t=0; 		% Reset time to zero
index=1;	% This is time's index (not time, its index).  
tstop=20000;	% Stopping time for the simulation (in seconds)
step=1;     % Integration step size
T=10;		% The controller is implemented in discrete time and
			% this is the sampling time for the controller.
			% Note that the integration step size and the sampling
			% time are not the same.  In this way we seek to simulate
			% the continuous time system via the Runge-Kutta method and
			% the discrete time fuzzy controller as if it were
			% implemented by a digital computer.  Hence, we sample
			% the plant output every T seconds and at that time
			% output a new value of the controller output.
counter=10;	% This counter will be used to count the number of integration
			% steps that have been taken in the current sampling interval.
			% Set it to 10 to begin so that it will compute a fuzzy controller
			% output at the first step.
			% For our example, when 10 integration steps have been
			% taken we will then we will sample the ship heading
			% and the reference heading and compute a new output
			% for the fuzzy controller.  
eold=0;     % Initialize the past value of the error (for use
            % in computing the change of the error, c).  Notice
            % that this is somewhat of an arbitrary choice since 
            % there is no last time step.  The same problem is
            % encountered in implementation.  
			
psi_r_old=0; % Initialize the reference trajectory
yeold=0; 	 % Intial condition used to calculate yc
ymold=0; 	 % Initial condition for the first order reference model

x=[0;0;0];	% First, set the state to be a vector            
x(1)=0;		% Set the initial heading to be zero
x(2)=0;		% Set the initial heading rate to be zero.  
			% We would also like to set x(3) initially but this
			% must be done after we have computed the output
			% of the fuzzy controller.  In this case, by
			% choosing the reference trajectory to be 
			% zero at the beginning and the other initial conditions
			% as they are, and the fuzzy controller as designed
			% we will know that the output of the fuzzy controller
			% will start out at zero so we could have set 
			% x(3)=0 here.  To keep things more general, however, 
			% we set the intial condition immediately after 
			% we compute the first controller output in the 
			% loop below.
			
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Next, we start the simulation of the system.  This is the main 
% loop for the simulation of fuzzy control system.

while t <= tstop

% First, we define the reference input psi_r (desired heading).

if t>=0, psi_r(index)=0; end			    % Request heading of 0 deg
if t>=100, psi_r(index)=45*(pi/180); end     % Request heading of 45 deg
if t>=1500, psi_r(index)=0; end    			% Request heading of 0 deg
if t>=3000, psi_r(index)=45*(pi/180); end    % Request heading of -45 deg
if t>=4500, psi_r(index)=0; end    			% Request heading of 0 deg
if t>=6000, psi_r(index)=45*(pi/180); end     % Request heading of 45 deg
if t>=7500, psi_r(index)=0; end    			% Request heading of 0 deg
if t>=9000, psi_r(index)=45*(pi/180); end     % Request heading of 45 deg
if t>=10500, psi_r(index)=0; end    			% Request heading of 0 deg
if t>=12000, psi_r(index)=45*(pi/180); end    % Request heading of -45 deg
if t>=13500, psi_r(index)=0; end    			% Request heading of 0 deg
if t>=15000, psi_r(index)=45*(pi/180); end     % Request heading of 45 deg
if t>=16500, psi_r(index)=0; end    			% Request heading of 0 deg
if t>=18000, psi_r(index)=45*(pi/180); end     % Request heading of 45 deg
if t>=19500, psi_r(index)=0; end    			% Request heading of 0 deg

% Next, suppose that there is sensor noise for the heading sensor with that is
% additive, with a uniform distribution on +- 0.01 deg.
%s(index)=0.01*(pi/180)*(2*rand-1);
s(index)=0;					  % This allows us to remove the noise.

psi(index)=x(1)+s(index);     % Heading of the ship (possibly with sensor noise).

if counter == 10,  % When the counter reaches 10 then execute the 
				   % FMRLC

counter=0; 			% First, reset the counter

% Reference model calculations:
% The reference model is part of the controller and to simulate it
% we take the discrete equivalent of the
% reference model to compute psi_m from psi_r (if you use
% a continuous-time reference model you will have to augment 
% the state of the closed-loop system with the state(s) of the 
% reference model and hence update the state in the Runge-Kutta 
% equations).
%
% For the reference model we use a first order transfer function 
% k_r/(s+a_r) but we use the bilinear transformation where we 
% replace s by (2/step)(z-1)/(z+1), then find the z-domain 
% representation of the reference model, then convert this 
% to a difference equation:

ym(index)=(1/(2+a_r*T))*((2-a_r*T)*ymold+...
                                    k_r*T*(psi_r(index)+psi_r_old));

ymold=ym(index);  
psi_r_old=psi_r(index);

	% This saves the past value of the ym and psi_r so that we can use it
	% the next time around the loop
	
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Fuzzy controller calculations:
% First, for the given fuzzy controller inputs we determine
% the extent at which the error membership functions