**Neuro-Knowledge Model Based on a PID Controller to Automatic Steering of Ships on a PID Controller to Automatic Steering of Ships**

José Luis Calvo Rolle and Héctor Quintián Pardo Additional information is available at the end of the chapter

**Neuro-Knowledge Model Based**

Additional information is available at the end of the chapter

José Luis Calvo Rolle and Héctor Quintián Pardo

http://dx.doi.org/10.5772/50316

## **1. Introduction**

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[20] Shneiderman, B., & Plaisant, C. (2009). Designing the User Interface: Strategies for Ef‐ fective Human-Computer Interaction, (5th edition). Reading, MA: Addison-Wesley

[21] Souto, M. A. M. (2003). Diagnóstico on-line do estilo cognitivo de aprendizagem do aluno em um ambiente adaptativo de ensino e aprendizagem na web: uma aborda‐ gem empírica baseada na sua trajetória de aprendizagem. PhD thesis. Universidade

[22] Siqueira, C., & Gurgel-Giannetti, J. (2011). Mau desempenho escolar: uma visão

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In the area of control engineering, it is necessary to work in a continued form in obtaining new methods of regulation to remedy deficiencies that already exist, or to find better alternatives to which they were used previously, for example [1, 2]. This dizzying demand of applications in control, is due to the wide range of possibilities developed until this moment.

Despite this upward pace of discovery of different possibilities, it has been impossible up to now to derail relatively popular techniques, such as the "traditional" PID control. Since the discovery of such regulators by Nicholas Minorsky in the area of automatic steering of ships [3, 4] since 1922 by now, many studies on this regulator are made. It should be noted that there are numerous usual control techniques for the process in any field, where innovations were introduced, for example thanks to the inclusion of artificial intelligence in this area, [5]. Despite this, the vast majority of its implementation uses PID controllers, raising the utilization rate up to 90% [6], according to different authors. Their use continues to be very high for different reasons such as ruggedness, reliability, simplicity, error tolerance, etc.

In the conventional PID control [6, 7] there are many contributions made by scholars as a result of investigations conducted on the subject,. There are many expressions among them, for obtaining the parameters that define this control, achieved by different routes and operating conditions specific for the plant that tries to control.

Emphasize that formulas developed to extract terms, which are sometimes empirical, always go out to optimise a particular specification. On the other side often happens that when one of the parameters is improved, other gets worse. We need to indicate that the parameters obtained applying the formulas of different authors are a starting point for setting the regulator. Usually it is necessary to proceed afterwards to a finer tuned test-error.

properly cited.

Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Luis Calvo Rolle and Quintián Pardo; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is © 2012 Luis Calvo Rolle and Quintián Pardo; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

©2012 Rolle and Pardo, licensee InTech. This is an open access chapter distributed under the terms of the

The vast majority of real systems are not linear. This occurs notably in the steering of ships, from which long time ago emerging models as the first or second order Nomoto model [8], the Norbbin model [9] or the Bech model [10]. Nowadays this feature remains a cause for study [11, 12] according to their working point, certain specifications will be required to be equal in all areas of operation. Thus different values of the regulator parameters will be needed in each of these areas. Having this in mind, self and adaptive PID regulators [5, 13–15] are a good solution to reduce this problem. Though it should be noted that its implementation is quite difficult, expensive and closely linked to the type of process which purports to regulate, being sometimes difficult to establish a general theory in this type of PID controllers.

where *u* is the control variable and y is the control error given by *e* = *YSP* − *y* (difference between the reference specified by the input and the output measured in the process). Thus, the control variable is a sum of three terms: the term P, which is proportional to the error, the term I, which is proportional to the integral error, and the term D, which is proportional to the derivative of error. The controller parameters are: the proportional gain K, the integral

There are multiple ways for the representation of a PID controller, but to implement the PID controller used and defined in the formula above, and more commonly known as the

D

There are infinite processes that exist in industries whose normal function is not adequate for certain applications. The problem is often solved by using this controller, by which the system is going to obtain certain specifications in the process control leading them to optimal settings for the certain process. The adjustment of this controller is carried out by varying the proportional gain, and the integral and derivative times commented in its different forms.

**3. Adjustament methods of parameters controller with gain scheduling**

On many occasions this method is known as the process dynamic changes with the process operating conditions. One reason for the changes in the dynamic can be caused, for example, by the well-known nonlinearities of processes. Then it will be possible to modify the control parameters, monitoring their operation conditions and establishing rules. The methodology will consists of first application of Gain Scheduling, analyzing the behaviour of the plant in question at different points of work and establishing rules to program gains in the controller, so that it will be possible to obtain certain specifications which remain, in the possible extent, constant throughout the whole range of operation of the process. This idea can

The Gain Scheduling method can be considered as a non-linear feedback of a special type; it has a linear controller whose parameters are modified depending on the operation conditions, with some rules extracted and previously programmed. The idea is simple, but its implementation is not easy to carry out, except in computer controlled systems. As it is shown in Figure 3, operating conditions that indicate the working point that is the process,

with the specific rules learned, program in the controller, the parameters selected.

Neuro-Knowledge Model Based on a PID Controller to Automatic Steering of Ships

http://dx.doi.org/10.5772/50316

103

standard format [6, 7], shown in representation bloc, it is shown in Figure 1.

P I

time *Ti* and the derivative time *T* − *d*.

**Figure 1.** PID controller in standard format

be schematically represented as shown in Figure 2.

To alleviate these difficulties it can be applied the well-known Gain Scheduling method, which is easier to implement, and with which are obtained highly satisfactory results. The concept of Gain Scheduling arises at the beginning of the 90t's [16], and it is considered as part of the family of adaptive controllers [13]. The principle of this methodology is to divide a non-linear system in several regions in which its behaviour is linear. Thus we obtain parameters of the controller that allow having some similar specifications around the operating range of the plant.

To implement the Gain Scheduling at first it is necessary to choose the significant variables of the system according to which it is going to define the working point. Then it is necessary to choose operating points along the entire range of operation of the plant. There is no systematic procedure for these tasks. Often at first step are taken those variables that can be measured easily. The second step is more complicated because of the points that have to be selected. The system can be stable at them for the parameters of the controller deducted, but it does not have to be stable between the selected points. This problem has no simple solution, and when it exists, there is usually particularized, that is why a subject has been studied by researchers, see for example [17–19].

A way to solve the problem is using artificial neural networks, which is a known side of the Artificial Intelligence that is in general difficult and uses other techniques. There are some similar cases where their work is to be resolved by this technique [20, 21], as well as other techniques of artificial intelligence [22, 23]. As it will be shown throughout this document, the use of the proposed method may be feasible in many cases.

This document is structured starting with a brief introduction of the topology of PID controller, which it is used to show an explanation of the method proposed above. Then is exposed a description of its application to the model of a ship, which is a non-linear system, to carry out the steering control with the proposed methodology. That is applicable in different steering models of existing ships regardless of the complexity. It ends with the validation of the method, making simulations under different conditions.

## **2. The PID controler**

There are multiple representation forms of PID controller, but perhaps the most widespread and studied is the one given by the equation 1

$$u(t) = K\left[e(t) + \frac{1}{T\_l} \int e(t)dt + T\_d \frac{de(t)}{dt}\right] \tag{1}$$

where *u* is the control variable and y is the control error given by *e* = *YSP* − *y* (difference between the reference specified by the input and the output measured in the process). Thus, the control variable is a sum of three terms: the term P, which is proportional to the error, the term I, which is proportional to the integral error, and the term D, which is proportional to the derivative of error. The controller parameters are: the proportional gain K, the integral time *Ti* and the derivative time *T* − *d*.

There are multiple ways for the representation of a PID controller, but to implement the PID controller used and defined in the formula above, and more commonly known as the standard format [6, 7], shown in representation bloc, it is shown in Figure 1.

**Figure 1.** PID controller in standard format

2

PID controllers.

operating range of the plant.

**2. The PID controler**

studied by researchers, see for example [17–19].

and studied is the one given by the equation 1

*u*(*t*) = *K*

the use of the proposed method may be feasible in many cases.

validation of the method, making simulations under different conditions.

*<sup>e</sup>*(*t*) + <sup>1</sup> *Ti* 

The vast majority of real systems are not linear. This occurs notably in the steering of ships, from which long time ago emerging models as the first or second order Nomoto model [8], the Norbbin model [9] or the Bech model [10]. Nowadays this feature remains a cause for study [11, 12] according to their working point, certain specifications will be required to be equal in all areas of operation. Thus different values of the regulator parameters will be needed in each of these areas. Having this in mind, self and adaptive PID regulators [5, 13–15] are a good solution to reduce this problem. Though it should be noted that its implementation is quite difficult, expensive and closely linked to the type of process which purports to regulate, being sometimes difficult to establish a general theory in this type of

To alleviate these difficulties it can be applied the well-known Gain Scheduling method, which is easier to implement, and with which are obtained highly satisfactory results. The concept of Gain Scheduling arises at the beginning of the 90t's [16], and it is considered as part of the family of adaptive controllers [13]. The principle of this methodology is to divide a non-linear system in several regions in which its behaviour is linear. Thus we obtain parameters of the controller that allow having some similar specifications around the

To implement the Gain Scheduling at first it is necessary to choose the significant variables of the system according to which it is going to define the working point. Then it is necessary to choose operating points along the entire range of operation of the plant. There is no systematic procedure for these tasks. Often at first step are taken those variables that can be measured easily. The second step is more complicated because of the points that have to be selected. The system can be stable at them for the parameters of the controller deducted, but it does not have to be stable between the selected points. This problem has no simple solution, and when it exists, there is usually particularized, that is why a subject has been

A way to solve the problem is using artificial neural networks, which is a known side of the Artificial Intelligence that is in general difficult and uses other techniques. There are some similar cases where their work is to be resolved by this technique [20, 21], as well as other techniques of artificial intelligence [22, 23]. As it will be shown throughout this document,

This document is structured starting with a brief introduction of the topology of PID controller, which it is used to show an explanation of the method proposed above. Then is exposed a description of its application to the model of a ship, which is a non-linear system, to carry out the steering control with the proposed methodology. That is applicable in different steering models of existing ships regardless of the complexity. It ends with the

There are multiple representation forms of PID controller, but perhaps the most widespread

*e*(*t*)*dt* + *Td*

*de*(*t*) *dt* 

(1)

There are infinite processes that exist in industries whose normal function is not adequate for certain applications. The problem is often solved by using this controller, by which the system is going to obtain certain specifications in the process control leading them to optimal settings for the certain process. The adjustment of this controller is carried out by varying the proportional gain, and the integral and derivative times commented in its different forms.
