**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).**

**Chapter 5.3 Youtube about Xcose**

The **PID** control scheme will be edited and tested in the movie.

The movie shows:

– Object **Go(s)**, input generator signal **x(t)**, **PID** controller… charging from so-called **pallette browser**

– Connecting these devices by drawing the “cables”-lines

– Testing the control scheme – step response

Click show movie.

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