**3.2 Modelling and adaptive process control for train controller agent interfacing with rail vehicle actuator agent**

The two communication modes (direct and indirect communication) facilitate the communications between the rail vehicle actuator agent and the train controller agent. Direct communication mode can be accomplish through a direct information exchange between agents through the agent communication language (ACL). The inter-agent communications utilised in the same layer, while the indirect communication mode (LAN, wireless, GPS/GPRS, Bluetooth, etc.) is used for enabling the information exchange between agents in different layers.

#### **Figure 4.**

*Fuzzy-PID controller simulation structure for FeedForward, FeedBack, SetPoint and PIDINPUT.*

*Agent-Based Control System as a Tool towards Industry 4.0: Directed Communication Graph… DOI: http://dx.doi.org/10.5772/intechopen.87180*

*The resultant equation for* Train controller agent *is the dynamic mass regarded as G*2.

$$\mathcal{G}\_2 = \mathcal{M}\_{dynamic} = \frac{m\_g^2}{\left(\mathbf{1} - \mathbf{y}\right)^2} J\_m + \frac{\mathbf{1}}{\left(\mathbf{1} + \mathbf{y}\right)^2 r\_0^2} J\_w + \mathcal{M}\_{\text{stc}} \tag{16}$$

*ng* is the gear ratio, n is the gear efficiency, *r*<sup>0</sup> is the nominal rolling radius of the wheel, *Jm* is the total motor *Kgm*<sup>2</sup> implies as *Jm* <sup>¼</sup> <sup>1</sup> <sup>2</sup> *Mr*ð Þ *rr* <sup>2</sup> *l, Mr* is the motor mass, *rr* is the radius of rotor shaft, l is the total of the traction system set, *Jw* is the total sum of the right and left wheel inertia and implies as *Jw* <sup>¼</sup> *Mwr*<sup>2</sup> <sup>0</sup>*nm*

$$\mathbf{M}\_{\text{stc}} = \mathbf{M}\_{\text{pass}} + \mathbf{M}\_{\text{vb}} + \text{nm}(\mathbf{2M}\_{\text{av}} + \mathbf{M}\_{\text{x}} + \mathbf{M}\_{\text{br}}) + (\mathbf{M}\_{\text{b1}} + \mathbf{M}\_{\text{b2}} + \mathbf{M}\_{\text{b3}}) + \left(\mathbf{M}\_{\text{motor}} + \mathbf{M}\_{\text{g}}\right) \tag{17}$$

*Mpass* is the passenger mass, *Mw* is the mass of the single wheel, *Mx* is the axle mass, *Mbr* is the mass of the brake system, *Mb*1, *Mb*2, *Mb*<sup>3</sup> are bogie masses, *Mmotor* is the total mass of the traction motor. *Mg* is denoted the gearbox mass.

Rolling resistance created by the movement of rotating parts of the train, originated from the frictional torques such as rotor, bearing torques, axles, brake pads, gear teeth friction, etc. The mathematical expression of the rolling resistance shown in Eq. (18).

$$F\_{\text{Rolling}} = K\_0 + K\_1 \mathbf{V} \tag{18}$$

where

In deriving a Takagi-Sugeno fuzzy system, it is assume that the bounded domain

*x*2 

1 *x*\_ 2  þ

0 *Z*3 

<sup>¼</sup> <sup>0</sup> *<sup>Z</sup>*<sup>1</sup> 1 �*Z*<sup>2</sup> *x*<sup>1</sup>

*U* (14)

þ

0 *Z*3 

*U*

(15)

*x*2 

*X* is define by *x*<sup>1</sup> ∈½ � �10*;* 10 and *x*<sup>2</sup> ∈½ � �10*;* 10 where *x*<sup>1</sup> *and x*<sup>2</sup> is the T-S fuzzy system behaviour as exact duplicates in the equation in the domain. Then, the min *Z*<sup>1</sup> ¼ *b*1*<sup>m</sup>* ¼ �10*,* max *Z*<sup>1</sup> ¼ *b*1*<sup>m</sup>* ¼ 10*,* min *Z*<sup>2</sup> ¼ *b*2*<sup>m</sup>* ¼ 0*,* max *Z*<sup>2</sup> ¼ *b*2*<sup>m</sup>* ¼ 20*,*

min *Z*<sup>3</sup> ¼ *b*3*<sup>m</sup>* ¼ 1*,* max *Z*<sup>3</sup> ¼ *b*3*<sup>m</sup>* ¼ 10*,*for *Z*1*, Z*2*,* and *Z*3*,* 11 yields

<sup>¼</sup> <sup>0</sup> *<sup>Z</sup>*<sup>1</sup> 1 �*Z*<sup>2</sup> *x*<sup>1</sup>

1 *Tis x*\_

This section presents a simulation example to show an application of the proposed fuzzy-PI-D controller spreadsheet rules for the membership fuzzy and simulation structure containing Input interfaces; rule block and output interface and its

The two communication modes (direct and indirect communication) facilitate the communications between the rail vehicle actuator agent and the train controller agent. Direct communication mode can be accomplish through a direct information exchange between agents through the agent communication language (ACL). The inter-agent communications utilised in the same layer, while the indirect communication mode (LAN, wireless, GPS/GPRS, Bluetooth, etc.) is used for enabling the

**3.2 Modelling and adaptive process control for train controller agent**

*Fuzzy-PID controller simulation structure for FeedForward, FeedBack, SetPoint and PIDINPUT.*

Then the above Eqs. (12) and (13) rewritten as:

*x*\_ 1 *x*\_ 2 

<sup>¼</sup> *Kp* <sup>1</sup> <sup>þ</sup>

*3.1.1 Simulation results for fuzzy-PI-D controller*

**interfacing with rail vehicle actuator agent**

information exchange between agents in different layers.

satisfactory performance (**Figure 4**).

**Figure 4.**

**234**

*G*<sup>1</sup> ¼ *G*PI�<sup>D</sup> *Gff* þ *Gfb*

*Control Theory in Engineering*

$$K\_0 = M\_{\text{stc}} a\_{\text{Rolling}} + \text{n.m.b}\_{\text{Rolling}}$$

*K*<sup>1</sup> ¼ *Mstc, CRolling , aRolling, bRolling , CRolling* are running parameters, respectively.

The movement of the railway vehicle takes place against the airflow, and the force that the air applies to the train affects the longitudinal movement of the train. The aerodynamic force is due to the common effects of the pressure difference between the front and the rear of the train. Air separation results in vortex formation behind the vehicle and the surface roughness of the vehicle body related with the skin friction. The parametric relationship of the aerodynamic resistance force shown in the Eq. (19).

$$\mathcal{G}\_3 = F\_{aero} = \frac{1}{2} \rho\_{air} \mathcal{C}\_d A\_v V^2 = K\_2 V^2 \tag{19}$$

where, *ρair* is the air density (kg m3 ), *Cd* is an aerodynamic drag coefficient, Av is the frontal section of the train. These parameters represent a single parameter known as *K*2. A gradient force acts on the opposite direction to the movement of the train moving upwards on a road with slope. The gradient force is constant under the constant slope condition. Eq. (20) represents the mathematical form of the gradient force.

$$\mathbf{G\_4} = \mathbf{F\_{gradient}} = +/ - \mathbf{G\_2g} \left( a \tan \left( \mathbf{Q\_g} \right) \right) \tag{20}$$

g is the gravitational constant, *Qg* is the gradient.

Recall Eq. (5)*, C s*ð Þ *R s*ð Þ <sup>¼</sup> *<sup>G</sup>*2*G*3*G*4*G*1ð Þ *Gff* <sup>þ</sup>*Gfb* <sup>1</sup>þ*G*2*G*3*G*4*G*<sup>1</sup> as Train controller Agent equation is thus

*C s*ð Þ *R s*ð Þ *nn*<sup>2</sup> *g* ð Þ <sup>1</sup>�*<sup>y</sup>* <sup>2</sup> *Jm* <sup>þ</sup> <sup>1</sup> ð Þ <sup>1</sup>þ*<sup>y</sup>* <sup>2</sup> *r*2 0 *Jw* <sup>þ</sup> *Mstc* <sup>∗</sup> <sup>1</sup> <sup>2</sup> *<sup>ρ</sup>airCdAvV*<sup>2</sup> <sup>¼</sup> <sup>∗</sup> *nn*<sup>2</sup> *g* ð Þ <sup>1</sup>�*<sup>y</sup>* <sup>2</sup> *Jm* <sup>þ</sup> <sup>1</sup> ð Þ <sup>1</sup>þ*<sup>y</sup>* <sup>2</sup> *r*2 0 *Jw* þ *Mstc*g *a* tan *Qg* <sup>∗</sup> *Kp* <sup>1</sup> <sup>þ</sup> <sup>1</sup> *Tis x*\_ 1 *x*\_ 2 <sup>¼</sup> <sup>0</sup> *<sup>Z</sup>*<sup>1</sup> 1 �*Z*<sup>2</sup> *x*<sup>1</sup> *x*2 <sup>þ</sup> <sup>0</sup> *Z*3 *<sup>U</sup>* <sup>1</sup> <sup>þ</sup> *nn*<sup>2</sup> *g* ð Þ <sup>1</sup>�*<sup>y</sup>* <sup>2</sup> *Jm* <sup>þ</sup> <sup>1</sup> ð Þ <sup>1</sup>þ*<sup>y</sup>* <sup>2</sup> *r*2 0 *Jw* <sup>þ</sup> *Mstc* <sup>∗</sup> <sup>1</sup> <sup>2</sup> *<sup>ρ</sup>airCdAvV*<sup>2</sup> <sup>¼</sup> <sup>∗</sup> *nn*<sup>2</sup> *g* ð Þ <sup>1</sup>�*<sup>y</sup>* <sup>2</sup> *Jm* <sup>þ</sup> <sup>1</sup> ð Þ <sup>1</sup>þ*<sup>y</sup>* <sup>2</sup> *r*2 0 *Jw* þ *Mstc*g *a* tan *Qg* <sup>∗</sup>*Kp* <sup>1</sup> <sup>þ</sup> <sup>1</sup> *Tis x*\_ 1 *x*\_ 2 <sup>¼</sup> <sup>0</sup> *<sup>Z</sup>*<sup>1</sup> 1 �*Z*<sup>2</sup> *x*<sup>1</sup> *x*2 <sup>þ</sup> <sup>0</sup> *Z*3 *<sup>U</sup>* (21)

these units get the information from their own resources and control the system autonomously according to their control designs. These agents also transmit their information to some parts of the overall communication system. Therefore, the railway vehicle system is controlled and managed through their participation. The directed communication can be accomplished through a direct information

*Agent-Based Control System as a Tool towards Industry 4.0: Directed Communication Graph…*

exchange between agents is based on the agent communication language (ACL) and utilised for the inter-agent communications in the same layer. The indirect communication mode (LAN, wireless, GPS/GPRS, Bluetooth, etc.) is used for enabling

The results of the directed communication graph from Laplacian perspective prompted the adoption of the theory for the information consensus network. Con-

consensus through local communication with the neighboring controller agent on a graph *G* ¼ ð*V,E*), the asymptotically converging to a one-dimensional space agree-

The space agreement can be express as *<sup>x</sup>* <sup>¼</sup> *<sup>α</sup>***<sup>1</sup>** where **<sup>1</sup>** <sup>¼</sup> ð Þ <sup>1</sup>*;* …*;* <sup>1</sup> *<sup>T</sup>* and *<sup>α</sup>* <sup>∈</sup>*<sup>R</sup>* is the collective decision of the group of controller agents. Let *A* ¼ ½ � *aij* be the adjacency matrix of directed communication graph for *G*. The set of neighbours of an

The railway vehicle agent *i* communicates with the train controller agent *j* if *j* is a neighbour of *i or aij* ð Þ 6¼ 0 *,* the set of all nodes and their neighbor's defines the edge

A dynamic directed communication graph [47] *G t*ðÞ¼ ð Þ *V; E t*ð Þ is a graph in which the set of edges *E t*ð Þ and the adjacency matrix *A t*ð Þ are time varying. Clearly, the set of neighbours *Ni* of every agent in a dynamic directed communication graph for the Vehicle Actuator Agent is a time-varying [40] set shown as the linear

A distributed consensus algorithm guarantees convergence to a collective deci-

*<sup>i</sup> x*\_ ð Þ ð Þ <sup>1</sup> ¼ ð Þ 0 *:* In particular, applying this condition twice at times

sion via local inter-agent interactions. Assuming that the graph is undirected, ð Þ *aij* ¼ *aji for all i; j :*it follows that the sum of the state of all nodes is an invariant

> <sup>∝</sup> <sup>¼</sup> <sup>1</sup> *n* X *i*

*x*\_

<sup>1</sup> ¼ *ui*, in reaching a

<sup>1</sup> ¼ *ui* (22)

*Ni* ¼ f g *j*∈*V* : *aij* 6¼ 0 *; V* ¼ f g 1*;* …*; n* (23)

*E* ¼ f g ð Þ *i; j* ∈*V* � *V* : *aij* 6¼ 0 (24)

*aij xj*ð Þ�*<sup>t</sup> xi*ð Þ*<sup>t</sup>* � � � (25)

ð Þ ð Þ *xi*ð Þ 0 (26)

the information exchange between agents in different layers.

sidering a network of agents in **Figure 1** with dynamics *x*\_

ment can be characterize by the following equation:

*x*\_

*t* ¼ 0 and *t* ¼ ∞ gives the following result:

<sup>1</sup> ðÞ¼ *<sup>t</sup>* <sup>X</sup> *j* ∈ *Ni*

**communication graph system**

*DOI: http://dx.doi.org/10.5772/intechopen.87180*

agent *i* is *Ni* and defined by:

set of the graph as:

system;

quantity, or P

**237**

**3.3 Mathematical modelling of the Laplacian matrix for the directed**
