MataveControl V13.0

MataveControl is a basic toolbox for control engineering. The toolbox can be used for both GNU Octave and MATLAB®. Easy to use and easy to install. The main focus of MataveControl is to offer a control toolbox which can be used in both GNU Octave and MATLAB®. MataveControl has the same function names as MATLAB®'s Control System Toolbox, but the time discrete functions are included in the time continuous functions. Also the library is a very basic library so other developers can fast dive into the code.

TODO

• reg.m This need to be fixed so it is the same as MATLAB
• lqgreg.m I don't know if Matavecontrol should keep it. It do the same as reg.m.
• More work on gensig.m
• Make linprog.m faster by using vectorization and not C-code style
• Make arma.m return a transfer function with discrete time 1
• ARMA models should be simulated with Euler-method, instead of filter.

Typical use

To use MataveControl, you should allways start with to create a transfer function or a state space model. Then you can use that mathematical model in almost all the function of MataveControl.

Here is some examples when I use MataveControl. MATLAB pictures are from Umeå University.

Creating a transfer function in MATLAB®

Creating a transfer function in GNU Octave

Create a bode diagram plot in MATLAB®

Create a bode diagram plot in GNU Octave

Create a state space model in MATLAB®

Create a state space model in GNU Octave

Do a step simulation in MATLAB®

Do a step simulation in GNU Octave

Convert a time continuous transfer function to a discrete transfer function in MATLAB®

Convert a time continuous transfer function to a discrete transfer function in GNU Octave

Do a nyquist diagram plot in MATLAB®

Do a nyquist diagram plot in GNU Octave

Model Predictive Control - Linear programming & Quadratic programming with integral action

MataveControl have both linear programming MPC and quadratic programming MPC. There is equivalent C code at CControl if you want to apply them to embedded hardware. Select the programming method, quadratic or linear, that works with your situation. Both works fine, but quadratic programming (Hildreth's Method) is faster than linear programming (Simplex Method) in MATLAB. In C-code, it depends on your C-compiler. I have done more work on qmpc.m file, compared to lmpc.m, even if they both can do the same job.

If you want to understand practical and proper MPC without theory, you should:

• Acquire all the math from the thesis Model Predictive Control for an artifical pancreas - Matias Sørensen og Simon Kristiansen.pdf (Download it here at MataveControl)
• Stody the chapters 1 and 2 from Model Predictive Control System Design and Implementation Using MATLAB® by Liuping Wang (Important that must be chapter 1 and 2, ignore the rest of the chapters)
• Throw away your lecture notes/literature from your MPC class, they just wasting your time

MataveControl/examples/mpcExample.m

Lines 1 to 26 in 03df47f

	close all
	clear all
	clc
	sys = mc.ss(0, [0 1; -1 -1], [0;1], [1 0]); % SISO state space model
	sysd = mc.c2d(sys, 0.5); % To discrete
	R = [6]; % Reference for the SISO model. If MIMO -> R need to be a vector
	N = 10; % Horizon predict constant
	T = 35; % Horizon time constant
	lambda = 7; % Regularization for smoother inputs u
	[y, t, x, u] = mc.lmpc(sysd, N, R, T, lambda); % Simulate MPC with linear programming
	hold on
	plot(t, u)
	I = 0.2; % Integral action constant
	Umax = [0.4]; % Maximum input signal vector
	S = [2]; % Slack variable says that the output can be +2 over the reference R, in this case: 6+2 = 8
	lambda = 0.2; % Regularization for smoother inputs u
	figure(2); % New figure
	x0 = [-8; 20];
	[y, t, x, u] = mc.qmpc(sysd, N, R, T, lambda, Umax, S, I, x0); % Simulate MPC with quadratic programming
	hold on
	plot(t, u)

Model Predictive Control with Kalman-Bucy filter and plant simulation

This MPC is different from the above. This MPC contains a kalman filter and is meant to be used for implementation of MPC for micro controllers. This have a unique integral action, were the integral is added the reference vector R before optimizing with the QP-solver. The code follows the paper "Model Predictive Control for an artificial pancreas. Matias Sørensen og Simon Kristiansen", which can be found in this repository.

Ther is also an equivalent C code example here: CControl

MataveControl/examples/kf_qmpcExample.m

Lines 1 to 113 in 65a3e6e

	%% This is an oscillating mass-spring-damper system. Classical second order system
	% ---------------------------------------------
	% / / / / / / / / / / / / / / / / / / / / / / /
	% ---------------------------------------------
	% | |
	% | |
	% | |
	% | |
	% | |
	% | |
	% | | | /
	% | | | /
	% | | | \
	% | | | \
	% | | | \
	% | | | \
	% | | | b = 1.2 [Ns/m] / k = 10 [N/m]
	% |_|_| /
	% | | |
	% | | |
	% |_ _| |
	% | |
	% | |
	% | |
	% | |
	% ------------------------------------
	% | |
	% | |
	% | m = 10 [kg] |
	% | |---------
	% ------------------------------------ |
	% | |
	% | | x [m]
	% | V
	% V
	% F [N]
	%
	% System of equation (second order system):
	% m*ddx + b*dx + k*x = F
	%
	% State space (first order system):
	% dx1 = x2
	% dx2 = -x1*k/m - x2*b/m + F/m
	% [dx1] = [0 1]*[x1] + [0 ]
	% [dx2] = [-k/m -b/m]*[x2] + [1/m]*F
	% dx A x B u
	%
	%% Build the system plant model (The real world system plant model which we don't know)
	m = 10; % Weight of the mass (mandatory)
	k = 10; % Spring force (mandatory)
	b = 2.2; % Damper force (mandatory)
	A = [0 1; -k/m -b/m]; % System matrix (mandatory)
	B = [0; 1/m]; % Input matrix (mandatory)
	C = [2 0]; % Output matrix (mandatory)
	delay = 0;
	sysp = mc.ss(delay, A, B, C);
	%% Build the system controller model (The estimated real world model which is very similar to the real world system plant model)
	m = 13.5; % Weight of the mass (mandatory)
	k = 8.7; % Spring force (mandatory)
	b = 3.1; % Damper force (mandatory)
	A = [0 1; -k/m -b/m]; % System matrix (mandatory)
	B = [0; 1/m]; % Input matrix (mandatory)
	C = [0.5 0]; % Output matrix (mandatory)
	delay = 0;
	sysc = mc.ss(delay, A, B, C);
	%% Create the MPC parameters
	N = 20; % Control horizon (mandatory)
	r = 10; % Reference (mandatory)
	umin = 0; % Minimum input value on u (mandatory)
	umax = 60; % Maximum input value on u (mandatory)
	zmin = -1; % Minimum output value on y (mandatory)
	zmax = 100; % Maximum output value on y (mandatory)
	deltaumin = -30; % Minimum rate of change on u (mandatory)
	deltaumax = 30; % Maximum rate of change on u (mandatory)
	antiwindup = 100; % Limits for the 1/s integral (mandatory)
	lambda = 0.1; % Integral rate (optional)
	Ts = 1; % Sample time for both models (optional)
	T = 500; % End time for the simulation (optional)
	x0 = [0; 0]; % Intial state for the models sysp and sysc (optional)
	s = 1; % Regularization parameter (Faster to solve QP-problem) (optional)
	Qz = 1; % Weight parameter for QP-solver (optional)
	qw = 1; % Disturbance tuning for Kalman-Bucy filter (optional)
	rv = 0.1; % Noise tuning for Kalman-Bucy filter (optional)
	Spsi_spsi = 1; % Slackvariable tuning for H matrix and gradient g (optional)
	d = 3; % Disturbance signal at step iteration k = 0 (optional)
	E = [0; 0]; % Disturbance signal matrix for both sysp and sysc (optional)
	%% Run MPC with Kalman-bucy filter
	% d
	% |
	% |
	% ____________ _____V_______
	% + _ | | | |
	% ---r--|---|_|--R-->| MPC + KF |-------u------>| PLANT |----------y------>
	% | +Λ |____________| |____________| |
	% | | ___ |
	% | | | 1 | _ _ - |
	% | -------------------------- - |<----|λ|<----|_|<---------------
	% | | s | - |+
	% | --- |
	% -------------------------------------------------
	[Y, T, X, U] = mc.kf_qmpc(sysp, sysc, N, r, umin, umax, zmin, zmax, deltaumin, deltaumax, antiwindup, lambda, Ts, T, x0, s, Qz, qw, rv, Spsi_spsi, d, E);
	% Print the output
	R = r*ones(length(T));
	plot(T, U, T, Y, T, R, 'r--');
	legend('Input', 'Output', 'Reference')
	grid on

This is the output where the plant model and the MPC model are not identical. Still, the error tracking can be minimized and the constraints are taken into account.

Install

To install MataveControl, download the folder "matave" and place it where you want it. Then the following code need to be written inside of the terminal of your MATLAB® or GNU Octave program.

path('path/to/the/folder/matave', path)
savepath

Example of a typical path.

path('C:\Users\dmn\Documents\Octave\matave\', path)
savepath

Update

Write this inside the terminal. Then MataveControl is going to download new .m files to MataveControl from GitHub

mc.updatematavecontrol