A new cooperative control solution of subway BAS: an improved fuzzy PID control algorithm

The general structure of the ISCS

As a comprehensive information platform, ISCS integrates the central-level functions of several subsystems such as signaling and automatic ticketing to master the operation of the whole line equipment and is also responsible for monitoring and dispatching the equipment within its assessment and maintenance personnel. The ISCS can monitor the operation status and fault situations of the equipment under the assessment of each station system of the whole line. Issues are instructed to each station to unify the command and coordinate the operation of each station.

The overall structure of the ISCS is designed based on the principles of two levels of management (central, station) and three levels of control (central, station, site), as shown in Fig. 1.

The ISCS is divided into three layers from the configuration of hardware equipment.

1) Central-level Integrated Supervisory Control System (CISCS).

2) Station-level Integrated Supervisory Control System (SISCS).

3) Site-level control equipment (integrated subsystem part).

The overview of the coordination control framework

BAS generally consists of the BAS equipment installed in the station’s electric control rooms and other related components such as vehicle sections and on-site BAS equipment. BAS equipment is composed of a redundant station controller (PLC controller), BAS bus network, remote IO, and IBP disk PLC.

The PLC near the station control room (end A) is the master controller and the PLC at the other end (end B) is the slave controller. The PLCs at the two ends are connected by redundant buses, and various types of RI/O, site devices with intelligent communication ports, and local site mini-controllers are connected to monitor and manage the electromechanical equipment (heating, ventilation, and air conditioning (HVAC), escalators, low-voltage lighting, water supply, and drainage) at the two ends of the station, respectively.

In the fire mode, the FAS sends a command to the BAS, and the BAS controller will start the relevant equipment in a disaster mode according to the predefined working conditions. Then, the station control room has an integrated backup panel (IBP) set up by the integrated monitoring system as an emergency backup control in a disaster mode. The BAS has a single PLC in the IBP panel, which requires high reliability and real-time operation of the BAS and requires the system response faster and more accurate as shown in Fig. 2.

The architecture of the framework of the coordination control

The BAS adopts a two-level management and three-level control architecture, i.e., two-level management at the control center and station (vehicle section and parking lot), and three-level control at the control center (vehicle section, station, and parking lot). The BAS is integrated into the comprehensive monitoring system at the station level, which realizes its functions at the central and station levels, respectively. The BAS comprises rooms such as control, monitoring equipment, station control, vehicle section, parking lot, and other on-site BAS equipment. The control structure of a BAS is shown in Fig. 3.

Two sets of redundant G5pro PLCs are installed in the loop control rooms at each end of the station, with the PLC near the station control room (end A) as the master controller and the PLC at the other end (B end) as the slave controller. The PLCs at both ends of the station are connected to the Ethernet ring network. All kinds of RI/O and field devices with intelligent communication ports are connected to monitor and manage the electromechanical equipment (ventilation and air conditioning, lighting, directional signs, escalators, elevators, human-proof doors (flood-proof doors) and water supply and drainage systems at both ends of the station. The architecture of the coordinated control framework of a BAS is shown in Fig. 4.

The BAS station is equipped with a special COM5004RTU communication module connected to the FAS station for communication. In the fire mode, the FAS sends a command to the BAS, and the BAS controller will switch to the disaster mode and activate the relevant equipment according to the predetermined working conditions. The station control room has an IBP set up by the integrated monitoring system as an emergency backup control in disaster mode. The BAS site-level monitoring system mainly includes a redundant GCU5001-S controller as the BAS redundant controller, and the site-level monitoring equipment is configured according to the installation of mechanical and electrical equipment. The G5pro series remote intelligent RI/O is equipped to communicate with the redundant GCU5001-S controller through the network.

The main PLC controller of the underground station is equipped with two redundant EtherNet/IP Ethernet communication interfaces (redundant COM5002TCP modules) to communicate with the redundant switches of the integrated monitoring system. The GCU5001-S PLC controllers at both ends of the station communicate with the Ethernet ring network by using fiber optic media. The GCU5001-S PLC controllers communicate with the G5pro series remote I/O modules. GCU5001-S PLC controller and G5pro series remote I/O, frequency converter, intelligent low-voltage, etc., are connected by a ring network. The BAS redundant GCU5001-S PLC controller is connected to the FAS via the RS485 bus. The IBP disk GCU5001-S PLC is connected to the master and slave GCU5001-S PLC controllers via the Ethernet ring network.

Fuzzy PID control algorithm

Fuzzy control is a nonlinear control method, which has the advantages of not requiring an exact mathematical functional model, high stability, strong robustness, and better control systems containing PLCs. Therefore, to achieve the coordinated control of a BAS, this article adopts the fuzzy PID control algorithm as the basic control algorithm of a BAS.

The system structure of the fuzzy PID controller is shown in Fig. 5. The system mainly consists of two parts: PID control and fuzzy control. $R_p$ denotes the preset coordinated control response effect, and $R_a$ represents the coordinated control response effect in actual action, and the error $\epsilon$ and the change error rate ${\epsilon }_c$ are used as the input signals of the fuzzy controller (Laib et al., 2022; Ahmadi Kamarposhti et al., 2022).

The PID controller output value is calculated by using Eq. (1) (Puviyarasi, Murukesh & Srividya, 2022).

(1) $u(t)=k_p[e(t)k_i{\int }_0^{t}e(t)dt+k_d\frac{dϵ(t)}{dt}]$where $u(t)$, $k_p$, $k_i$, and $k_d$ denote controller output value, proportionality, integration, and differentiation coefficients, respectively in Eq. (1).

When the BAS responds to the coordinated control command, it detects the response error $\epsilon$ and the change error rate ${\epsilon }_c$ in real-time and then finds the optimal solution for adjusting the PID control parameters of $\mathrm{△}{k}_p$, $\mathrm{△}{k}_i$, and $\mathrm{△}{k}_d$ according to the fuzzy rules in real-time. The system response is fast and smooth. The adjustment is shown in Eq. (2) (Wang, Lu & Wang, 2022).

(2) $$\{\begin{array}{c}{k}_p=k_{p1}+\mathrm{△}{k}_p\hfill \\ k_i=k_{i1}+\mathrm{△}{k}_i\hfill \\ k_d=k_{d1}+\mathrm{△}{k}_d\hfill \end{array}$$

In Eq. (2), $k_{p1}$, $k_{i1}$ and $k_{d1}$ are the initial values of the PID control parameters of $k_p$, $k_i$, and $k_d$, respectively. The theoretical domain of the input variables’ errors $\epsilon$ and change error rate ${\epsilon }_c$ is contained in [−6, 6], and the theoretical domain of the output variables adjusted by the PID control parameters of $\mathrm{△}{k}_p$ $\mathrm{△}{k}_d$ is contained in [−1, 1]. The fuzzy subsets are described in fuzzy language as positive big (PB), positive medium (PM), positive small (PS), zero (ZO), negative small (NS), negative medium (NM), and negative big (NB) to facilitate data processing. Each fuzzy subset uses the triangular affiliation function corresponding to each fuzzy subset.

To ensure the reliability and stability of the whole system, reasonable fuzzy rules are proposed as follows:

(1) When $\epsilon$ and ${\epsilon }_c$ are small or equal to 0, $k_p$ takes a large value, $k_i$ takes a large value, and $k_d$ takes a medium value.

(2) When $\epsilon$ and ${\epsilon }_c$ are large, $k_p$ takes a large value, $k_i$ takes a zero value, and $k_d$ takes a small value.

(3) When $\epsilon$ and ${\epsilon }_c$ are equal in size, $k_p$ takes a small value, $k_i$ takes a moderate value, and $k_d$ takes a moderate value.

According to the above fuzzy rules, the fuzzy control rules are established as shown in Table 1.

The improved seeker optimization algorithm (ISOA) optimized fuzzy PID controller

SOA is a new swarm intelligent evolutionary algorithm that can find the optimal solution to a target by simulating the human search behavior for both the position and direction in space (Xiangrui et al., 2022). In the conventional fuzzy PID control, the quantization and scaling factors must be set according to the expert’s experience and cannot be adjusted adaptively when they are set. Thus, poor settings of these parameters could lead to oscillation and overshoot of the system, which cannot adapt to the random errors and disturbances existing in the actual regulation and control, and the steady-state performance becomes poorer. To improve the performance of the fuzzy PID controller, the SOA is employed for both the input and output processes of the fuzzy controller.

The SOA provides a basic principle. Suppose that a population has S search individuals distributed in a D-dimensional space. Everyone is equipped with both position and direction information. Through multiple search updates, the individual obtains both the optimal position and direction in the space to attain the objective function’s optimal solution. The position of individual X_i is shown in Eq. (3) (Duan, Luo & Liu, 2022).

(3) $$X_i={\left[x_i,x_{i2},\cdots ,x_{in}\right]}^p$$

Each individual in the group possesses three search behaviors, which are co-altruistic behavior ${\overrightarrow{d}}_{i,\mathrm{c}\mathrm{o}\mathrm{a}}$, altruistic behavior ${\overrightarrow{d}}_{i,alt}$, and proactive behavior ${\overrightarrow{d}}_{i,pro}$.

(4) $$\{\begin{array}{c}{\overrightarrow{d}}_{i,\mathrm{c}\mathrm{o}\mathrm{a}}(t)={\overrightarrow{P}}_{i,\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}}-{\overrightarrow{x}}_i(t)\hfill \\ {\overrightarrow{d}}_{i,\mathrm{a}\mathrm{l}\mathrm{t}}(t)={\overrightarrow{g}}_{i,\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}}-{\overrightarrow{x}}_i(t)\hfill \\ {\overrightarrow{d}}_{i,\mathrm{p}\mathrm{r}\mathrm{o}}(t)={\overrightarrow{x}}_i\left(t_1\right)-{\overrightarrow{x}}_i\left(t_2\right)\hfill \end{array}.$$where ${\overrightarrow{x}}_i(t)$, ${\overrightarrow{P}}_{i,\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}}$, and ${\overrightarrow{g}}_{i,\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}}$ represents individual current best position, individual historical best position, and group best position in the neighborhood, respectively, and ${\overrightarrow{x}}_i\left(t_1\right),{\overrightarrow{x}}_i\left(t_2\right)$ are delineated as the current moment as the previous reference moment and best position of the two moments before the current moment are defined.

Once the three search behaviors of an individual are calculated, the position can be updated iteratively according to the individual’s final search direction. The iterative update of the position according to the final search direction of the individual is presented in Eq. (5) (Ning et al., 2021).

(5) $$\{\begin{array}{c}{\overrightarrow{d}}_{id}(t)=sign\left[\omega {\overrightarrow{d}}_{id,\mathrm{p}\mathrm{r}\mathrm{o}}+0.5{\overrightarrow{d}}_{id,\mathrm{e}\mathrm{g}\mathrm{o}}+0.5{\overrightarrow{d}}_{id,a\mathrm{l}\mathrm{t}}(t)\right]\hfill \\ \mathrm{\Delta }{x}_{id}(t+1)=a_{id}{d}_{id}(t)\hfill \\ x_{{}_{id}}(t+1)=x_{id}(t)+\mathrm{\Delta }{x}_{id}(t+1)\hfill \end{array}$$where $\omega$ representing inertia weight determines the direction of the individual’s self-interested movement at the next moment, ${\overrightarrow{d}}_{id}(t)$ shows the direction of the individual’s search at the next moment, $a_{id}$ represents the search step determined by the Gaussian affiliation function, and $x_{id}(t+1)$ denotes the location of the individual at the next moment.

To evaluate the merit of the solution in the search evolution process, the ITAE performance index is chosen as the minimum objective function, where the squared input term u²(t) is added to reduce the overshoot and oscillation of the system, and the specific fitness function is presented in Eq. (6).

(6) $F={\int }_0^{\mathrm{\infty }}({\omega }_1|e(t)|)+{\omega }_2{u}^2(t)dt$where ${\omega }_1$ and ${\omega }_2$ take 0.9 and 0.1, respectively.

In the SOA, inertia weights play an important role in the search direction of individuals. When the individual target values are not attained, the individual search ability becomes poor, and the inertia weight should be increased to improve the global search ability. When the individual search values are scattered, the weight should be reduced to speed up the convergence. However, the inertia weight ω is generally fixed in the standard SOA, and this strategy will not be able to cope with the random disturbance factors of the fuzzy control process. Therefore, this article improves the SOA by utilizing a weight factor with adaptive characteristics to search for the best. Equation (7) presents this.

(7) $$\omega =\{\begin{array}{c}{\omega }_{min}+{\displaystyle \frac{\left({\omega }_{max}-{\omega }_{min}\right)\cdot \left(f-f_{min}\right)}{f_{\mathrm{a}\mathrm{v}\mathrm{g}}-f_{min}},f\le f_{\mathrm{a}\mathrm{v}\mathrm{g}}}\hfill \\ {\omega }_{max}\hfill \end{array}$$where ${\omega }_{max}$ and ${\omega }_{min}$ show the maximum and minimum values of the inertia weights, respectively, f, $f_{min}$, and $f_{\mathrm{a}\mathrm{v}\mathrm{g}}$ designates the current target fitness value, the minimum value of fitness in the current group of individuals, and the mean value of fitness in the current group of individuals, respectively.

When the calculated fitness score is lower than the population mean, the adaptive weight $\omega$ is employed for iteration; otherwise ${\omega }_{max}$ is chosen as the individual iteration weights that can be adaptively adjusted according to the changes in the population fitness values. More up-to-date research is also available (Liu et al., 2023; Manuel, İnanç & Lüy, 2023; Zhang & Xiao, 2023).

Design of the ISOA-Fuzzy PID Controller

The structure of the ISOA-fuzzy PID control can be obtained from “The ISOA-optimized fuzzy PID controller”, as shown in Fig. 6.

Based on the above study, a BAS controller with the SOA-optimized fuzzy PID is designed, and the specific steps are presented as follows:

Step 1: Initialize the search population, set the SOA individual size N as 50, set the individual search space dimension D as 5, represent the quantization factor and scale factor of fuzzy control, set the individual search range as (0; Basnayake et al., 2017), set the maximum number of iterations M as 50, set the minimum fitness value f as 0.1, and set the inertia weights ${\omega }_{max}$ and ${\omega }_{min}$ as 0.9 and 0.1, respectively.

Step 2: Call the BAS fuzzy PID module to obtain the fitness value of each individual in the current iteration and determine whether the abort condition (the maximum number of iterations or the minimum fitness value) is satisfied.

Step 3: Calculate the maximum and mean values of the population fitness in the current iteration and assign adaptive inertia weights ω to each of the N individuals according to Eq. (4).

Step 4: Update both the orientation and position of individuals according to Eq. (5) and go back to Step 2.

The coordinated control flow of the BAS with the SOA-optimized fuzzy PID is shown in Fig. 7.