# Bode plot or Bode Diagram

#### Luiz Fernando Vieira

Joined Aug 24, 2015
61
Hello I am having difficulty understanding the Bode diagram, which I have understood so far: that depending on the angle of the phase, where the system becomes unstable or stable. I just don't know what the practical applications are when using this system in a closed loop.
I mean a practical example how to change the control, such as a robotic arm, or a mechanism that can be more sensitive (control)?

#### Papabravo

Joined Feb 24, 2006
18,978
The Bode diagram has two parts:
1. A plot of the magnitude of a transfer function as a function of frequency
2. A plot of the phase difference of the transfer function, also as a function of frequency
When considering stability you have to consider BOTH the magnitude and the phase.

• Luiz Fernando Vieira

#### crutschow

Joined Mar 14, 2008
30,438
To determine the stability of a closed-loop feedback control system you need to determine the gain and phase margin of the loop
That can be seen from the gain/phase of the loop displayed in a Bode plot.

For a typical control system the feedback compensation values are selected to obtain the desired margins.

• Luiz Fernando Vieira

#### LvW

Joined Jun 13, 2013
1,478
To determine the stability of a closed-loop feedback control system you need to determine the gain and phase margin of the loop
That can be seen from the gain/phase of the loop displayed in a Bode plot.
For a typical control system the feedback compensation values are selected to obtain the desired margins.
Yes - that´s OK. Just to avoid misunderstandings : You have to analyze the loop when it is opened! That means: The gain and phase of all parts/blocks within the loop in series. This gain is called "loop gain".

• Luiz Fernando Vieira

#### Luiz Fernando Vieira

Joined Aug 24, 2015
61
Vou te dizer o que entendi. '' A partir dessa análise, você pode derivar a margem de estabilidade, que diz se o circuito fechado será estável e quantas "margens" o sistema de circuito fechado tem até se tornar instável. ''
Ok, muito obrigado. Mas entendi o conceito de aplicação prática na área. Exemplo um braço robótico com sensor, quando ocorre uma anomalia no sistema por causa do sinal que está instável (a operação está fora de controle), quando está funcionando normalmente o sistema fica estável.
O exemplo que você disse sobre o braço robótico está correto?
Na prática, não sei onde é aplicado.

#### Papabravo

Joined Feb 24, 2006
18,978
Vou te dizer o que entendi. '' A partir dessa análise, você pode derivar a margem de estabilidade, que diz se o circuito fechado será estável e quantas "margens" o sistema de circuito fechado tem até se tornar instável. ''
Ok, muito obrigado. Mas entendi o conceito de aplicação prática na área. Exemplo um braço robótico com sensor, quando ocorre uma anomalia no sistema por causa do sinal que está instável (a operação está fora de controle), quando está funcionando normalmente o sistema fica estável.
O exemplo que você disse sobre o braço robótico está correto?
Na prática, não sei onde é aplicado.
Your English is probably better than my Portuguese, but here goes:

I'll tell you what I understand. '' From this analysis, you can derive the stability margin, which says whether the closed loop will be stable and how many "margins" the closed loop system has until it becomes unstable. '' OK thank you. But I understood the concept of practical application in the area. Example a robotic arm with sensor, when an anomaly occurs in the system because of the signal that is unstable (the operation is out of control), when it is working normally the system is stable. Is the example you said about the robotic arm correct? In practice, I don't know where it is applied.

For a linear system it is fairly easy to determine the stability for ALL bounded inputs. They do not loose control as you suggest if the control system has sufficient gain and phase margin. A non-linear system, on the other hand, can become unstable in the presence of unexpected inputs. An excessive perpendicular gust load on the vertical tail of an airplane comes to mind, which renders the vertical tail incapable of controlling yaw.

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• Luiz Fernando Vieira

#### Luiz Fernando Vieira

Joined Aug 24, 2015
61
Your English is probably better than my Portuguese, but here goes:

I'll tell you what I understand. '' From this analysis, you can derive the stability margin, which says whether the closed loop will be stable and how many "margins" the closed loop system has until it becomes unstable. '' OK thank you. But I understood the concept of practical application in the area. Example a robotic arm with sensor, when an anomaly occurs in the system because of the signal that is unstable (the operation is out of control), when it is working normally the system is stable. Is the example you said about the robotic arm correct? In practice, I don't know where it is applied.

For a linear system it is fairly easy to determine the stability for ALL bounded inputs. They do not loose control as you suggest if the control system has sufficient gain and phase margin. A non-linear system, on the other hand, can become unstable in the presence of unexpected inputs. An excessive perpendicular gust load on the vertical tail of an airplane comes to mind, which renders the vertical tail incapable of controlling yaw.
kkkkk. Sorry I thought I would translate into English.
My debt is still open. But if you didn't understand I can simplify my doubt. I have an automated machine (automation). What has been said above, where can it be applied in practice (effect) and how? I understood the functions of signals, but what their practical application is.

#### LvW

Joined Jun 13, 2013
1,478
kkkkk. Sorry I thought I would translate into English.
My debt is still open. But if you didn't understand I can simplify my doubt. I have an automated machine (automation). What has been said above, where can it be applied in practice (effect) and how? I understood the functions of signals, but what their practical application is.
For application of the mentioned analysis you need the block diagram of the system under discussion and the transfer functions for each block. Hardware is not sufficient at all.

• Luiz Fernando Vieira

#### Papabravo

Joined Feb 24, 2006
18,978
kkkkk. Sorry I thought I would translate into English.
My debt is still open. But if you didn't understand I can simplify my doubt. I have an automated machine (automation). What has been said above, where can it be applied in practice (effect) and how? I understood the functions of signals, but what their practical application is.
I don't exactly know how to answer your question, but the analysis tools we are talking about apply to systems that can be described by ordinary linear differential equations. The Laplace transform is often used to turn the problem of solving an ordinary linear differential equation into the problem of solving an algebraic equation. Solving the algebraic equation allows you to write down the solution to the differential equation. Once you have the transfer function (Laplace transform) of the differential equation you can use the bode plot to express it's behavior in polar form by computing the magnitude and the phase as functions of frequency. This will allow you to identify potential frequencies where misbehavior might occur, or put you mind at ease that your system is stable under all conditions.

The transfer function has a 3-dimensional representation by adding a real valued z-axis perpendicular to the complex plane. The Bode magnitude plot is the slice of the 3-dimensional function along the jω-axis. Same for the phase. That is why you don't see any exponential decay along the jω-axis because the real part is identically zero.

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• Luiz Fernando Vieira

#### Luiz Fernando Vieira

Joined Aug 24, 2015
61
I don't exactly know how to answer your question, but the analysis tools we are talking about apply to systems that can be described by ordinary linear differential equations. The Laplace transform is often used to turn the problem of solving an ordinary linear differential equation into the problem of solving an algebraic equation. Solving the algebraic equation allows you to write down the solution to the differential equation. Once you have the transfer function (Laplace transform) of the differential equation you can use the bode plot to express it's behavior in polar form by computing the magnitude and the phase as functions of frequency. This will allow you to identify potential frequencies where misbehavior might occur, or put you mind at ease that your system is stable under all conditions.

The transfer function has a 3-dimensional representation by adding a real valued z-axis perpendicular to the complex plane. The Bode magnitude plot is the slice of the 3-dimensional function along the jω-axis. Same for the phase. That is why you don't see any exponential decay along the jω-axis because the real part is identically zero.
guys thank you very much you are helping me a lot in the theoretical part and feeding more knowledge on this subject. But I don't know if the language barrier is getting in the way. I'll send you an example image.

Regarding the image, in practice in the Bode Diagram (signals, gain, lag ...) can influence the practice of the equipment. Attention I'm using a generic image, I don't know if I'm using a correct example of the subject

#### MrAl

Joined Jun 17, 2014
9,344
Hello I am having difficulty understanding the Bode diagram, which I have understood so far: that depending on the angle of the phase, where the system becomes unstable or stable. I just don't know what the practical applications are when using this system in a closed loop.
I mean a practical example how to change the control, such as a robotic arm, or a mechanism that can be more sensitive (control)?
Do you mean something like you have a robotic arm that is currently unstable and you want to add a compensator circuit to the design to make it stable?

• Luiz Fernando Vieira

#### Luiz Fernando Vieira

Joined Aug 24, 2015
61
Do you mean something like you have a robotic arm that is currently unstable and you want to add a compensator circuit to the design to make it stable?
That's right, I was wondering if that really, because I didn't find any practical application literature, the books simply said the goat diagram, but not its practical application. Where it is really used.

#### Papabravo

Joined Feb 24, 2006
18,978
That's right, I was wondering if that really, because I didn't find any practical application literature, the books simply said the goat diagram, but not its practical application. Where it is really used.
So in order to know how to fix a problem you have to understand the problem. Given an arbitrary control system you must understand how to describe the deviations from the requirements. For example:
1. The system will overshoot the setpoint.
2. The error signal never reaches zero.
3. The system response is too slow.
You use a variety of tools to observe and characterize the system behavior. Then you change the system dynamics by modifying the closed loop transfer function so the problem is mitigated. Besides the Bode plot there are:
1. Nyquist plot
2. Nichols chart
3. Root Locus
In the good old bad old days these had to be constructed manually with pen, paper, and slide rule. Software abounds to render these tasks trivial.

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#### LvW

Joined Jun 13, 2013
1,478
That's right, I was wondering if that really, because I didn't find any practical application literature, the books simply said the goat diagram, but not its practical application. Where it is really used.
Have look into Richard C. Dorf: Modern Control systems.
Here you can find many practical applications (Control systems for satellites, airplanes,..)

#### MrAl

Joined Jun 17, 2014
9,344
That's right, I was wondering if that really, because I didn't find any practical application literature, the books simply said the goat diagram, but not its practical application. Where it is really used.
If i can get a chance i will show an example from the book that @LvW suggested in the post just before this one.

#### Luiz Fernando Vieira

Joined Aug 24, 2015
61
thank you gave a better on the concept, but my question it was a little more simplistic, because I do not find a material book an industry website that says this type of situation is applied to such a situation. Why the books talk like they do, but I don't see an application, the example above the robotic arm.
Last example of classic electronics [I quit]:
Where does the capacitor apply?

Response (generic): to filter the signal, leaving less noise, usually applied in a linear or switching source. [this is a practical example].

That kind of example I wanted to know.

(I don't know if in the English language the word '' application '' has another meaning).

#### LvW

Joined Jun 13, 2013
1,478
In "Modern Control Systems" (Richard C. Dorf, Addison-Wesley, 6th edition, 1992) there is a chapter (12.5) "The design of a Robot Control system) and "The Design of a Mobile Control system" (12.6).

#### MrAl

Joined Jun 17, 2014
9,344
thank you gave a better on the concept, but my question it was a little more simplistic, because I do not find a material book an industry website that says this type of situation is applied to such a situation. Why the books talk like they do, but I don't see an application, the example above the robotic arm.
Last example of classic electronics [I quit]:
Where does the capacitor apply?

Response (generic): to filter the signal, leaving less noise, usually applied in a linear or switching source. [this is a practical example].

That kind of example I wanted to know.

(I don't know if in the English language the word '' application '' has another meaning).
Hi,

It is a little hard to understand what it is exactly you are looking for.
A filter?
There are various filters depending on what you are doing. From a simple RC filter to an LC fitler to a Kalman filter. RC simple signal filters, LC simple power filters, Kalman more advanced signal filters.
The capacitor is usually used with at least a resistor for signal filters, and with an inductor for power solution filters. An RC filter can be as simple as a resistor in series with a capacitor where the output is taken from across the capacitor. A lead or lag compensator can be RC also or perhaps with multiple R's and C's.

You probably should get a book on this though if you really want to study this.