## Preliminary Automatics Course

Chapter 5.1 About dynamic object G(s) shortly
You will use one Scilab application–>Xcos . It’s Simulink equivalent from Matlab. The world is ruled by differential equations (university, engineering college…) not by algebraic equations (high school, grammar school…). Are you high school pupil and you don’t know differential calculus? Never mind. I will try to explain it as simple as possible.

What is the main job of the basic Xcos unit–>integrator? It inegrates! The differential unit differentiates analogously.
See Fig.1-2 chapter 1. You will do this experiment personally! You will say “dervative is easy” then!
Every dynamic object is described by differential equations and by so-called transfer functions–>Go(s). It isn’t very strictly but differential equations and transfer functions describing dynamic object are equivalent for me. This simplification is too big probably, so my friendly advice is “don’t say it during exams.”
The simplest transfer function is a proportional unit Go(s)=K. Everybody knows it. It’s a amplifier with gain K=10 for example.
The input signal x(t)=1 V causes sharpish output signal y(t)=10 V. Without any delays. It’s described by algebraic equation y(t)=10*x(t).
The next, not so simple transfer function is a inertial unit Go(s)=K/(1+s*T). The input signal so-called step x(t)=1 V causes y(t)=10 V but with delay, more strictly with inertia. This unit is described by differential equation and not by algebraic as proportional. The s symbol in this Go(s) means that first derivative appears in the differential equation.

Chapter 5.2 What does Xcos do with the dynamic object G(s) ?

Fig. 5-1
Xcos window
The input x(t)=1 is a step signal
The object G(s) is a inertial unit with gain K=1 and time constant T=3 seconds
What is the output signal y(t)? The answer for this question is a job for Xcos

What does Xcos do when you push the start experiment button?
1. Xcos analyses input signal x(t) and Go(s) parameters–>K=1 and T=3 sec. It means that scheme is a input for the Xcos!
2. Xcos changes x(t) and Go(s) parameters K and T for differential equation–>k*x(t)=y(t)+T*y'(t) *
3. Xcos solves the differential equation swiftly but draws the output y(t) in real time. You observe on your computer the RC loading process for example, and not a ready time diagram!
*Note
The differential equation knowledge is very usefull, but not necessary. My goal is to feel dynamic object Go(s) parameters.
You will see difference between 2 similar looking objects G1(s)=3/(1+7*s) and G2(s)=7/(1+3*s) for example

Xcos is as a laboratory on your desk. This laboratory is equipped with the different devices–>signal generators, Go(s) object models, oscilloscopes… Your job is only to wiring the devices and push the button. The wiring is the scheme drawing by special Editor. It’s similar to simple windows PAINT editor
The detailed Xcos and his master Scilab knowledge isn’t necessary too. You have ready experiments (ready schemes) included in PID folder.
Your job is only to push the button and observe the output signal y(t).