step function with rise and fall times?

I'm looking for something similar to a step function where I can adjust the rise time, fall time and magnitude of the step height.

Suggestions?

Answer 1

[CD]

How exactly does one us the lsim function?

I added "step(Zo)" and "lsim(Zo, u, t)" below to compare results.

With step I see results that I am expecting though I cannot modify step rise/fall times.

I'm not seeing any results with lsim.

Used the first examplefrom the lsim page:

https://www.mathworks.com/help/control/ref/lsim.html

%% Closed Loop Zo(s) = Zout(s)/(1 + T(s))

% Zout(s) Transfer Function Setup

L1 = 1e-6; % inductance

C1 = 200e-6; % output filter capacitance

Rs = 30e-3; % series resistance RL + Ron

Resr = 0.8e-3; % capacitor equivalent series resistance

R = 1e3; % load resistance

%% Zout(s) transfer function salient features

woD = 1/(sqrt(L1*C1));

QoD = 1/( woD*((Rs+Resr)*C1 + (L1/R)));

Z0 = Rs; % Zout(s) DC gain

woN = 1/(sqrt((Resr/Rs)*L1*C1));

QoN = 1/(woN*(Resr*C1 + (L1/Rs)));

w1N = QoN*woN;

w2N = woN/QoN;

%% Open-loop output impedance transfer function

s = tf('s');

Zout = Z0*( ((1 + s/w1N)*(1 + s/w2N))/(1+(1/QoD)*(s/woD)+(s/woD)^2) );

%% Loop gain T

L1 = 1e-6; % inductance

Rs = 30e-3; % series resistance RL + Ron

C1 = 200e-6; % output filter capacitance

Resr = 0.8e-3; % capacitor equivalent series resistance

Vg = 5; % input voltage

R = 1e3; % load resistance

VM = 1; % PWM saw-tooth amplitude

Vref = 1.8; % reference voltage

H = 1; % sensing gain

%% Gvd transfer function salient features

wesr = 1/(C1*Resr); % esr zero

wo = 1/sqrt(C1*L1); % center frequency of the pair of poles

Qload = R/sqrt(L1/C1);

Qloss = sqrt(L1/C1)/(Resr+Rs);

Q = Qload*Qloss/(Qload+Qloss); % Q factor

%% Open-loop control-to-output transfer function

s = tf('s');

Gvd = Vg*(1+s/wesr)/(1+(1/Q)*(s/wo)+(s/wo)^2);

%% PID compensator (see lecture slides)

R2 = 16e+3; % Compensator

R1 = 3e+3; % Compensator

R4 = 360e+0; % Compensator

C2 = 1.3e-9; % Compensator

C4 = 1.5e-9; % Compensator

Gc0 = R2/R1;

wL = 1/(C2*R2);

wz = 1/(C4*R1);

wp1 = 1/(C4*R4);

fL = wL/(2*pi);

fz = wz/(2*pi);

fp1 = wp1/(2*pi);

wp2 = 2*pi*1e6; % Added to protect OP AMP Gain BW product

%% Open-loop Gc(s) transfer function

s = tf('s');

Gc = Gc0*(1+wL/s)*(1+s/wz)/(1+s/wp1);

T = minreal( H*(1/VM)*Gvd*Gc );

Zo = minreal( Zout/(1 + T) );

figure(1)

step(Zo)

figure(2)

[u,t] = gensig('square',4,10,0.1);

lsim(Zo, u, t)

Answer 2

[CD]

I understand how u is "shaped".

Why did you multiplied Zo by 200 (y*200)? "plot(t,y*200)"

What does function "tlim" do? Looks like you could replaced 51:end with 51:max(t)?

Ideally I would like to create a step like (trapezoid) function with various length rise and fall times:

1. Trapezoid: Rise/fall times = 1 us, On time = 20 us,
2. Trapezoid: Rise/fall times = 10 us, On time = 20 us.
3. .... on so on (shorter/longer rise/fall times)

Appears as though sample time (time step per t element/column) comes from step ([y,t] = step(Zo)).

if t(0) = 1.2884e-7 seconds then

u "on time" would be (668-50)*1.2884e-7 seconds or 79 useconds.

u "rise time" would be 50*1.2884e-7 seconds or 6.4 useconds.

If I want to get rise/fall times of .001 useconds then I would need smaller sample time.

How can adjust sample time?

I'd probably need to set sample time before running the step function.

Thank you,

Craig

figure(1)

[y,t] = step(Zo);

tlim = [min(t) max(t) numel(t)];

plot(t,y)

figure(2)

u = [t(1:50)/t(50); ones(size(t(51:end)))];

[y,t] = lsim(Zo, u, t);

plot(t,y*200)

hold on

plot(t,u, ':k')

hold off

legend('y(t)', 'u(t) \cdot 200')

[Stephen23]

@Craig Dekker: please write comments in a comment field. Answers are for answering the question (and can move around, which makes them unsuitable for a discussion thread).