**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 be schematically represented as shown in Figure 2.

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.

**5. Nomoto model of ship-steering process**

**Figure 4.** Coordinates and notation used to described the equations

ψ

δ

'l' the length of the ship and 'a' and 'b' are parameters of the model ship.

*dv dt* <sup>=</sup> *<sup>u</sup>*

*dr dt* <sup>=</sup> *<sup>u</sup>*

*dψ dt* = *r*

system as indicate in figure 4.

equation 3.

where,

simplified to equation 5.

To analyze a ship's dynamics as a Nomoto model it is convenient to define a coordinate

u v

V

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

y

Let 'V' be the total velocity, 'u' and 'v' the x and y components of the velocity, and 'r' the angular velocity of the ship. In normal steering the ship makes small deviations from straight-line course. The natural state variables are the sway velocity 'v', the turning rate 'r', and the heading '*ψ*'. The equations 2 are obtained, where 'u' is the constant forward velocity,

*<sup>l</sup> <sup>a</sup>*<sup>11</sup> <sup>+</sup> *ua*12*<sup>r</sup>* <sup>+</sup> *<sup>u</sup>*<sup>2</sup>

From equation 2 is determinated the transfer function from rudder angle to heading in the

*<sup>G</sup>*(*s*) = *<sup>K</sup>*(<sup>1</sup> <sup>+</sup> *sT*3)

The parameters *K*<sup>0</sup> and *Ti*<sup>0</sup> are parameters of ship model. In many cases the model can be

*<sup>G</sup>*(*s*) = *<sup>b</sup>*

*K* = *K*0*u*/*l*

*<sup>l</sup>*<sup>2</sup> *<sup>a</sup>*21*<sup>v</sup>* <sup>+</sup> *<sup>u</sup>*

*<sup>l</sup> b*1*δ*

*<sup>l</sup>*<sup>2</sup> *b*2*δ*

*<sup>s</sup>*(<sup>1</sup> <sup>+</sup> *sT*1)(<sup>1</sup> <sup>+</sup> *sT*2) (3)

*<sup>s</sup>*(*<sup>s</sup>* <sup>+</sup> *<sup>a</sup>*) (5)

*Ti* <sup>=</sup> *Ti*0*l*/*u i* <sup>=</sup> 1, 2, 3 (4)

*<sup>l</sup> <sup>a</sup>*22*<sup>r</sup>* <sup>+</sup> *<sup>u</sup>*<sup>2</sup>

x

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

105

(2)

**Figure 2.** Gain Scheduling control schematic
