Optimization of a fuzzy self-tuning PID control system for a marine low-flashpoint fuel supply system

2.1 System Configuration

The LPG fuel supply system considered here follows the structure shown in Figure 1, in which the fuel path from the storage tank through the service tank, double-walled piping, and fuel pumps to the engine is represented explicitly. The main equipment is summarized in Table 1.

Figure 1:

Schematic configuration of the LPG fuel supply system

Table 1:

Main components of the LPG fuel supply system

To satisfy the LPG supply conditions required by the MAN ME-LGI (Mechanically operated, Electronically controlled—Liquid Gas Injection) engine, a simple fuel line is insufficient; the system operates as a tightly coupled assembly of devices. LPG drawn from the storage tank is first pressurized by the LP pump and then raised to the engine demand pressure by the HP pump. Temperature is equally important: the LF heater warms the fuel to the required engine inlet temperature using glycol water, while a cooler and a glycol-water loop absorb heat when the temperature rises excessively. A recirculation line installed at the discharge of each pump returns part of the flow to the tank, maintaining constant pressure between the supply line and the storage tank, minimizing vapor generation, and accommodating sudden load changes or valve transients. Figure 2 presents the corresponding piping-and-instrumentation arrangement; Figure 3 shows the LFSS demonstration plant used to confirm that the simulated configuration reproduces an industrial installation.

Figure 2:

Piping-and-instrumentation diagram of the LPG fuel supply system

Figure 3:

LFSS demonstration equipment

2.2 Storage and Supply Conditions

The storage conditions of the LPG in the fuel tank are listed in Table 2, and the operating conditions of the fuel delivered to the engine are summarized in Table 3. Because the tank is an IMO-independent Type-C cylindrical pressure vessel storing the cargo at ambient temperature and elevated pressure, the LP pump must transfer saturated fuel from the tank while maintaining the net positive suction head (NPSH) required by the HP pump.

Table 2:

LPG fuel storage condition (design basis)

Table 3:

LPG fuel supply condition (design basis)

2.3 Process Flow and Operation

The process flow diagram of the fuel supply system is based on the general MAN supply process. The LP pump draws fuel from the storage tank and feeds the HP pump, ensuring sufficient NPSH to prevent cavitation. The HP pump then meets the engine pressure demand. When the engine load changes, the valve opening inside the fuel valve train (FVT) changes, the head loss varies, and the supply pressure fluctuates; a fixed pump speed cannot accommodate this, so a variable-frequency drive (VFD) regulates the pump speed and, where necessary, a recirculation valve is opened to relieve excess pressure.

Fuel returning from the engine is heated to about 30 °C, raising its vapor fraction, and may be contaminated with sealing oil or nitrogen from purging. It is therefore routed not directly back to the storage tank but through a catch tank that separates impurities and vapor. Gas from the catch tank is discharged to the vent mast through a knock-out (KO) drum that retains entrained droplets. Sections that can be isolated by valves are protected by pressure safety valves (PSVs) to prevent a temperature rise in trapped liquid from overpressurizing the line. The equipment specifications are derived from a heat balance calculation for this configuration.

3.1 Pump Head–Flow Characteristics

The basic performance of a pump is expressed by the relationship between the volumetric flow rate Q and the head H. At constant rotational speed, the discharge pressure decreases progressively as the flow increases, owing to internal friction, the energy-transfer limit of the impeller, and viscous losses. This behavior is approximated by Equation (1), in which H₀ is the shut-off (zero-flow) head and K is a loss coefficient determined by the pump geometry and the fluid:

The shaft power P required to transfer the fluid is governed by the fluid density ρ, the gravitational acceleration g, the flow Q, the head H, and the pump efficiency η, as in Equation (2). The efficiency reaches its best-efficiency point (BEP) at a particular flow and decreases on either side of it:

The combined operation of the LP and HP pumps is therefore coupled to the supply-pressure control and is adjusted dynamically to the engine flow demand. In the controller design, the pump characteristic curve determines the operating point, and the resulting flow and pressure errors serve as inputs to the fuzzy control algorithm.

3.2 Pressure Control of the Fuel Supply System

Because the stored LPG is saturated, vapor can form on discharge from the tank due to heat ingress or pressure loss in the piping. The present system uses an ambient-temperature, high-pressure Type-C tank, so the LP pump must transfer saturated fuel from the tank and provide the NPSH required by the HP pump. When the engine load varies, the engine control unit (ECU) adjusts the FVT opening to regulate the fuel flow. If the discharge pressure then falls below the saturation pressure, vapor forms, control of pressure and flow in the engine gas block becomes impossible, and an engine trip may occur. Keeping the supply pressure constant is thus essential.

To this end, the controller regulates the LP- and HP-pump speeds via the VFD to maintain the discharge pressure at the engine demand value. Because the pumps are high-speed rotating machines, motor inertia limits the immediacy of speed control; when the supply pressure exceeds the demand, the controller therefore opens the recirculation valve to divert part of the flow through a bypass line and depressurize the discharge. Pump-speed control and recirculation-valve control may act sequentially or simultaneously. Surplus fuel returned from the liquid-injection engine, mixed with vapor, lubricating oil, and nitrogen, is buffered in the catch tank for impurity separation and pressure stabilization before returning to the HP-pump suction; the catch-tank pressure is held above the LP-pump discharge pressure by nitrogen through a pressure-control valve, and a level-control valve opens only above a set liquid level.

3.3 PID Control

PID control, the most widely used linear technique, drives the output using the proportional, integral, and derivative terms of the error, as in Equation (3), where u(t) is the control output mapped to the VFD speed, e(t) is the time-varying error, and K_p, K_i, and K_d are the proportional, integral, and derivative gains:

In the LFSS, the pump discharge pressure is the controlled variable, and the error signal is converted into a VFD speed command. Although linear PID control is widespread, it adapts poorly to the nonlinearity of the pressure–flow relationship, can overshoot when the load changes abruptly, and may lose overall stability due to interactions among control loops.

3.4 Fuzzy Self-Tuning PID Control

A fuzzy control system is a rule-based controller that mathematically models human reasoning and achieves stable control without a quantitative system model, which is advantageous for fuel supply systems subject to frequent disturbances and difficult to linearize. In the proposed controller, the input signals—the pressure error e and its rate of change Δe—are first converted into linguistic variables through fuzzification; If–Then rules are then applied in the fuzzy-inference stage; and finally, the inferred fuzzy output is converted back into a real control value through defuzzification.

Each input variable is expressed by five linguistic values, Equation (4), and each output gain by four linguistic values, Equation (5):

Here, NB, NS, ZE, PS, and PB denote negative-big, negative-small, zero, positive-small, and positive-big, while S, M, B, and VB denote small, medium, big, and very-big. The variables are represented by triangular membership functions with overlapping intervals to permit continuous control (Figures 4 and 5). Mamdani inference is used, and the rules take the If–Then form of Equation (6):

Figure 4:

Membership functions for fuzzification of the input variables

Figure 5:

Membership functions for defuzzification of the PID gains

The rule bases are built from expert operating experience and are designed to tune the pump speed [14]. This self-tuning scheme overcomes the limitations of fixed-gain controllers by automatically adjusting gains to disturbances and changes in operating conditions. Because the inference yields multiple membership values μ, the centroid method, Equation (7), is used for defuzzification to obtain the crisp control value u*:

The process is regulated by independent single-loop controllers assigned to each physical quantity, to respect the distinct control characteristics of each variable and optimize stability and responsiveness. The fuzzy layer itself is a two-input, three-output gain-tuning mechanism whose inputs are the error and its rate of change and whose outputs are the three PID gains. The controller inputs are the error and its rate of change, and the simultaneous outputs are the three gains, listed in Table 4; the corresponding rule tables for K_ₚ, K_i, and K_d are given in Tables 5-7.

Table 4:

Configuration of the fuzzy controller

Table 5:

Fuzzy rule base for the proportional gain Kₚ

Table 6:

Fuzzy rule base for the integral gain Kᵢ

Table 7:

Fuzzy rule base for the derivative gain Kᵈ

Gaussian membership functions provide smooth output transitions; however, they require the specification of center and variance parameters and involve exponential computations. Trapezoidal membership functions can maintain a constant membership degree over a specified interval, but they may provide reduced resolution for small error variations near the setpoint. Accordingly, triangular membership functions were selected in this study in consideration of the simplicity of control-surface generation, the ease of parameter interpretation, and their suitability for implementation in industrial controllers.

The input variables were represented by five linguistic terms: NB, NS, ZE, PS, and PB. These terms were used to distinguish among a large negative error, a small negative error, a condition near the setpoint, a small positive error, and a large positive error.

Applying five membership functions to each of the two input variables results in a total of 25 fuzzy rules. This configuration provides finer state classification than the nine-rule structure obtained using three membership functions, while reducing the design and validation burden compared with the 49-rule structure required when seven membership functions are used. Therefore, five membership functions were selected as a compromise between control resolution and rule-base complexity. A comparable trade-off between rule-base size and control resolution has been reported in variable-universe fuzzy self-tuning PID studies [15].

The fuzzy rules were established according to the following principles.

First, when the absolute value of the pressure error is large, the proportional gain (Kₚ) is set to a high value to enable a rapid return to the target pressure.

Second, in the small-error region near the target pressure, the influence of the integral gain (Kᵢ) is increased to eliminate persistent steady-state error.

Third, when a large transient error occurs, (Kᵢ) is limited to prevent overshoot and integral windup caused by excessive accumulation of the integral term.

Fourth, in regions where the error change rate is large or its sign changes, the derivative gain (K_d) is set to suppress abrupt changes in the control output and reduce oscillations.

The pump-speed command increases as the pressure error grows (direct action): when the supply pressure is below the set point, the pump speed is raised. The valve-opening command, in contrast, must close the valve as the same error grows in order to reduce pressure loss (reverse action). For identical inputs, the pump and valve operate in opposite directions, so applying the same control logic to both would cause output interference and unstable responses. An opposite-action rule set is consequently defined independently for each actuator.

In a regulatory problem where a state must be held constant, evaluating the membership functions of all rules at every sampling instant greatly increases the computational load and degrades real-time responsiveness. To resolve this, control responses are derived in advance from the error and its rate of change and stored as a rule table (the control surfaces of Figure 6). During operation, the controller does not perform full fuzzy inference at each sampling step but instead reads the stored rule directly, minimizing the computational burden while enabling delay-free, real-time control suited to a fuel supply system.

Figure 6:

Fuzzy self-tuning control surfaces of the PID gains as functions of error and error change rate

The controller proposed in this study uses the pressure error (e) and the error change rate (Δe) as input variables to identify the current dynamic control state. The applicable gain values, including Kₚ, Kᵢ, K_d are retrieved from the control surfaces generated using fuzzy rules and membership functions and are then applied to the PID control block.

However, rather than repeatedly evaluating all fuzzy rules during operation, the proposed controller stores the precomputed fuzzy control surfaces in an Excel database and retrieves the corresponding gain values during each control cycle. Therefore, the proposed method can be more precisely classified as a precomputed lookup-table-based fuzzy gain-adjustment controller.

Compared with conventional lookup-table-based fuzzy PID controllers, the primary contribution of this study lies not in the fundamental control algorithm itself, but in its application to an Aspen HYSYS dynamic process model of a marine LPG fuel supply system. The study also analyzes the effects of control-surface resolution and PID gain search ranges and evaluates the applicability of the proposed controller to pressure regulation under varying engine-load conditions.

The fuzzy controller developed in this study does not employ an online fuzzy inference scheme in which the complete fuzzy rule base and defuzzification process are repeatedly evaluated at every sampling interval.

First, the control surfaces for Kₚ, Kᵢ, K_d are generated in advance in the VBA environment by performing fuzzification, rule evaluation, and defuzzification over the entire input ranges of the error and the rate of change of the error. The resulting control surfaces are then stored in an Excel database.

During operation, the pressure error and its rate of change calculated in HYSYS are transferred to Excel. The control gains corresponding to these input values are retrieved from the precomputed control surfaces and subsequently transmitted back to the PID block in HYSYS for application during the next sampling interval

Accordingly, the control architecture adopted in this study can be defined as a real-time gain-updating method based on precomputed fuzzy control surfaces. This approach reduces the repetitive computational burden associated with online fuzzy inference while allowing the controller gains to be adjusted according to the current operating condition without replacing the existing PID control block.

4.1 Main Equipment Specifications

The main equipment of the target fuel supply system and its principal design conditions are summarized in Table 8. The storage and catch tanks are IMO Type-C cylindrical pressure vessels; the LP and HP pumps are centrifugal machines whose speed is regulated by VFDs; the LF heater and cooler are indirect glycol-water shell-and-tube exchangers in which the glycol flows on the shell side and the fuel on the tube side, providing flame-free heat transfer appropriate to a low-flashpoint fuel; and the LF filter removes particles larger than 10 µm. Each pump is fitted with a disc-type non-return valve and a safety interlock that stops the pump on low power, abnormal suction pressure, or an emergency shutdown (ESD) signal.

Table 8:

Main components and design conditions of the LPG fuel supply system.

4.2 Closed-Loop Co-Simulation Platform

Traditional control-system development relies on open-loop testers or prototype hardware, which is costly, time-consuming, and difficult to reproduce under identical conditions. To overcome this, a virtual co-simulation platform was constructed instead of a physical rig (Figure 7). The process dynamics of the real equipment are reproduced by an Aspen HYSYS dynamic simulation, and the developed control system is coupled to it in real time so that control performance can be verified in a closed loop.

Figure 7:

Closed-loop co-simulation architecture (HYSYS–Excel–VBA)

The fuel supply process was modeled in Aspen HYSYS Dynamic Simulation using the physical parameters of Table 8 and the Peng–Robinson equation of state. The dynamic-mode configuration, including the controller settings and the actuator response characteristics, followed established practice for dynamic process simulation in Aspen HYSYS [16]. The fuzzy-inference system was implemented in Microsoft Visual Basic for Applications (VBA) 7.1, and its output was exchanged with the HYSYS database via an Excel database, allowing control variables to be passed in real time at each sampling step. The Excel layer performs two roles: it records the error and error change rate computed from the measured pressure, temperature, and flow received from HYSYS, and it looks up the corresponding gains from the rule table and returns them to HYSYS. The simulation conditions are summarized in Table 9, and the full HYSYS process model of the 200 kW LPG fuel supply unit—comprising a fuel-supply part, a nitrogen-supply part, and a heating-medium part, each with its own feedback loop—is shown in Figure 8.

Table 9:

Simulation environment settings.

Figure 8:

Aspen HYSYS dynamic process simulation of the 200 kW LPG fuel supply system

4.3 Parametric Case Studies

Three cases, summarized in Table 10, were used to examine how the resolution of the fuzzy control surface and the gain search range affect control performance. In all cases, the engine load was fixed at 50 %.

Table 10:

Definition of the simulation cases

In this study, Kₚ and Kᵢ were updated using the fuzzy control surfaces, while K_d was fixed at zero. The derivative gain was not adjusted during operation because of the possibility that rapid fluctuations in the fuel-supply pressure signal and numerical differentiation could induce oscillatory control behavior.

Case 1 used a 100 × 100 control surface with narrow gain ranges (Kₚ: 0–1, Kᵢ: 0–2). As shown in Figure 9(a), Kₚ rises sharply during the first second as the controller aggressively seeks the set point, oscillates slightly between 1 and 3 seconds as the fuzzy system reacts to the initial error, and then converges to about 0.9. The integral gain Kᵢ in Fig. 9(b) rises quickly and stabilizes near 1.7 after about three seconds without sustained oscillation, since the integral action mainly removes residual error and requires little correction once the transient has passed. The discharge pressure in Fig. 9(c) overshoots the target initially but becomes completely flat after about 5 s, confirming stable regulation within the narrow gain range.

Figure 9:

Case 1 results (resolution 100 × 100; Kₚ 0–1, Kᵢ 0–2)

Case 2 retained the 100 × 100 resolution but widened the ranges to Kₚ: 0–4 and Kᵢ: 0–500. The response became faster, but oscillation appeared in the high-gain region. As shown in Figure 10(a), the fourfold wider Kₚ range produces a much stronger initial reaction; the controller enters the high-gain region and exhibits an erratic, spiking pattern before converging as the error decreases. The greatly extended Kᵢ range in Figure 10(b) causes the integral term to be over-compensated in places, producing irregular oscillation, and the discharge pressure in Figure 10(c) shows repeated overshoot and undershoot. These results indicate that an excessively wide search range makes the controller over-sensitive and that gain-magnitude limits are necessary in practice.

Figure 10:

Case 2 results (resolution 100 × 100; Kₚ 0–4, Kᵢ 0–500)

Case 3 kept the wide ranges of Case 2 but lowered the resolution to 15 × 15. The fine controllability of the response curve decreased, and error oscillation appeared near the target value. As shown in Figure 11(a), low resolution produces a staircase pattern in Kₚ because the coarse fuzzy surface's input–output mapping is not smooth; a rough surface can cause abrupt changes in the output. The integral gain in Figure 11(b) is likewise more irregular and variable, and the discharge pressure in Figure 11(c) exhibits larger error and a longer settling time. These results clearly demonstrate that the surface resolution is an important design parameter, although—as the comparison with Case 1 shows—its effect on the steady-state error band is secondary to that of the search range.

Figure 11:

Case 3 results (resolution 15 × 15; Kₚ 0–4, Kᵢ 0–500)

4.4 Performance under variable engine load

Based on the case analysis, the baseline gains were fixed at Kₚ = 0.66 and Kᵢ = 1.32, and the engine load was varied in the sequence 100 % → 50 % → 10 % → 100 % (Figure 12(a)). The fuzzy controller compensated for load-induced pressure changes in real time and maintained a control accuracy of ±0.15 bar—substantially tighter than the ±1 bar acceptance band—even during transients (Figure 12(b)), corresponding to roughly an 85% improvement relative to the acceptance criterion. This confirms that fuzzy-PID control secures high adaptability and stability under nonlinear load variation. A residual steady-state error nevertheless appeared in the low-load region below 10 %, where fine pump and valve adjustments to move the pressure are difficult to implement; this should be addressed in future work through nonlinear compensation or adaptive-gain correction.

Figure 12:

Controller performance under a variable engine-load profile

Author Contributions

Conceptualization, C. H. Park and J. K. Lee; Methodology, C. H. Park and K. G. Kim; Software, C. H. Park; Formal Analysis, C. H. Park; Investigation, C. H. Park; Resources, S. M. Ji; Data Curation C. H. Park; Writing-Original Draft Preparation, C. H. Park; Writing-Review & Editing, Y. J. Cheon and S. M. Ji; Visualization, C. H. Park; Supervision, Y. J. Cheon and J. K. Lee; Project Administration, J. K. Lee; Funding Acquisition, J. K. Lee.