Matlab Control Systems Cheat Sheet

Matlab Functions

Symbolic Toolbox

Function	Description
numden(sym_eqn) → [N, D]	Extracts the numerator and denominator of a symbolic equation
simplify(sym_eqn) → [eqn]	Simplifies the symbolic equation
expand(sym_eqn) → [eqn]	Expands the symbolic equation
solve([eqn ..], [var ..])	Solves the equations(s) for the given variable(s) symbolically
vpasolve([eqn ..], [var ..])	Solves the equations(s) for the given variable(s) numerically
laplace(sym_ft) → [Fs]	Finds the Laplace transform of the given symbolic equation
ilaplace(sym_Fs) → [tf]	Finds the inverse Laplace transform of the given symbolic equation
ztrans(sym_ft) → [Fz]	Finds the z-transform of the given symbolic equation
iztrans(sym_ft) → [Fz]	Finds the inverse z-transform of the given symbolic equation.
Use syms k positive integer to avoid a cryptic answer.
limit(fx, x, a) → [val]	Returns the limit of the function fx as x approaches a. Useful to check if value is NaN meaning the function diverges to infinity.
c2d(tf, Ts, method) → [tf]	Converts continuous-time dynamic system to discrete time with the chosen method: ‘zoh’, ‘foh’, ‘impulse’, ‘tustin’, ‘matched’, ‘least-squares’, ‘damped’. Defaults to ‘zoh’ which is recommended, if method is omitted.

Matrix Operations

Function	Description
eye(N, M) → [mat]	Creates an identity matrix of N by M size
nan(N, M) → [mat]	Creates a NaN matrix of N by M size
zeros(N, M) → [mat]	Creates a zero matrix of N by M size
size(mat) → [row, col]	Returns the size of the matrix

Transfer Functions

Using s = tf(’s’) is a good way of making future equations using s become transfer function objects.

Function	Description
zpk(eqn)	Factorizes the transfer function into a zero-pole-gain model
c2d(tf)	Converts a continuous transfer function to a discrete one
tf(N, D) → [tf]
tf(N, D, Ts) → [tf]	Create a transfer function with the given numerator and denominator coefficients. May also need sym2ploy(N) and sym2ploy(D) before using tf(N, D). Adding the sampling time Ts creates a discrete-time transfer function
bode(tf)	Create a bode plot of the given transfer function
feedback(Gs, Hs) → [tf]	Adds closed loop feedback Hs to the transfer function Gs
step(tf)	Creates a plot of the transfer functions step response
stepinfo(tf) → [obj]	Returns a object with all the step response information
drmodel(N) → [N, D]	Generates a random stable test models of Nth order
drmodel(N) → [A, B, C, D]	Generates a random stable test models of Nth order
drmodel(N, P) → [N, D]	Generates a random stable test models of Nth order, P outputs
drmodel(N, P) → [A, B, C, D]	Generates a random stable test models of Nth order, P
drmodel(N, P, M) → [A, B, C, D]	Generates a random stable test models of Nth order, P outputs and M inputs
evalfr(tf, x)	Evaluates frequency response at a single frequency
dcgain(tf)	Computes the steady-state gain of the dynamic system (caution: does return a finite value for an unstable system). Should be used in conjunction with isstable(tf)
residues(N, D) → [N, D, K]	Partial fraction expansion
residuesz(N, D) → [N, D, K]	Z-transform partial fraction expansion
pzmap(tf)	Plot the pole-zero map of a dynamic system
eig(tf) or pole(tf)	The poles of the system, showing it’s stability
isstable(tf) → [bool]	Returns if the transfer function is stable or not

State-Space

Function	Description
abcdchk()	Check state-space matrices for the correct dimensions
ss2tf(A, B, C, D) → [tf]	Converts a state-space model to a transfer function

Misc

Function	Description
pretty(eqn)	Turns a command line equation in a more human readable equation
interp1(X, V, Xi) → [Vi]	1D interpolation, given the input vector X with the output vector V determine Vi from the known Xi
tic; <exp>; toc;	Times the execution of the expression