Nonlinear positive feedback control method for insulation layer differential pressure of liquefied gas carrier liquid tank

Abstract

The application discloses a liquefied gas ship liquid cabin insulation layer pressure difference nonlinear positive feedback control method, including the following steps: step one, constructing a liquefied gas ship liquid cabin insulation layer pressure difference unstable system, and mapping the liquefied gas ship liquid cabin insulation layer pressure difference unstable system into a liquefied gas ship liquid cabin insulation layer pressure difference stable system through a mirror image mapping method; step two, designing a robust controller based on a closed-loop gain shaping algorithm; step three, designing a nonlinear function, obtaining the output of the robust controller, and constraining the robust controller through the nonlinear function and the output of the robust controller; step four, obtaining transfer functions under positive feedback states and negative feedback states respectively, designing a positive feedback controller according to the relationship between the transfer functions under the positive feedback states and the transfer functions under the negative feedback states and the constrained robust controller, and controlling the liquefied gas ship liquid cabin insulation layer pressure difference stable system according to the positive feedback controller. The control precision and reliability of the liquefied gas ship insulation layer pressure difference are improved.

Description

Technical Field

[0001] This invention relates to the field of pressure differential control of the insulation layer of liquefied natural gas (LNG) tanks, and more particularly to a nonlinear positive feedback control method for pressure differential of the insulation layer of LNG tanks. Background Technology

[0002] Liquefied natural gas (LNG) carriers are specialized vessels used to transport cryogenic (-163°C) liquefied natural gas (LNG). Membrane-type LNG carriers have two insulation layers, primary and secondary, to maintain the cryogenic temperature within the cargo tanks. To prevent LNG from leaking into the insulation layer space, nitrogen gas is injected into the primary and secondary insulation layers to maintain an inert state. This inert state effectively prevents explosions and ensures ship safety. However, nitrogen is expensive, and effectively controlling nitrogen loss and conserving nitrogen resources is a crucial issue. One effective method is to control the pressure difference within the insulation layer space. Currently, linear negative feedback is mainly used for pressure difference control, but this method has low precision.

[0003] Conventional feedback control involves filtering the error between the output and the setpoint and then directly feeding it back to the controller. Essentially, it's linear negative feedback control, and control system design focuses on improving the control law itself to enhance system performance. With advancements in computer science, mathematics, and control theory, the design level of control laws has continuously improved, but it's gradually approaching saturation. Further improvements to the control law can only slightly increase system performance, and the control laws themselves and their design processes are becoming increasingly complex. This has given us the opportunity to refocus on the feedback signal. If we can transform linear feedback into nonlinear feedback, ultimately improving system performance, this is the fundamental reason why nonlinear feedback algorithms emerged in 2011 and matured into theory by 2020. The concepts of positive and negative feedback arose simultaneously, but because negative feedback has a clear physical meaning, it's conventionally used in control systems. Positive feedback has applications in economics, education, optimization algorithms, and power generation, but its application in ship control is rarely reported. Summary of the Invention

[0004] This invention provides a nonlinear positive feedback control method for the pressure difference of the insulation layer of the liquid tank in a liquefied gas carrier, in order to overcome the above-mentioned technical problems.

[0005] A nonlinear positive feedback control method for the pressure difference of the insulation layer in the liquid tank of an LPG carrier includes,

[0006] Step 1: Construct an unstable pressure differential system for the insulation layer of the liquefied gas tanker. Use a mirror mapping method to map this unstable system to a stable system.

[0007] Step 2: Design a robust controller based on a closed-loop gain shaping algorithm.

[0008] Step 3: Design a nonlinear function to obtain the output of the robust controller. Then, use the nonlinear function and the robust controller's output to constrain the robust controller.

[0009] Step 4: Obtain the transfer functions of the liquefied gas tank insulation layer pressure difference stabilization system under positive feedback and negative feedback states respectively. Based on the relationship between the transfer functions under positive feedback and negative feedback states and the constrained robust controller, design a positive feedback controller and control the liquefied gas tank insulation layer pressure difference stabilization system according to the positive feedback controller.

[0010] Preferably, the method of mapping the unstable pressure difference system of the liquefied gas tank insulation layer to a stable pressure difference system of the liquefied gas tank insulation layer using the mirror mapping method involves constructing the unstable pressure difference system of the liquefied gas tank insulation layer according to formula (1) and mapping the unstable pressure difference system of the liquefied gas tank insulation layer to a stable pressure difference system of the liquefied gas tank insulation layer according to formula (2).

[0011]

[0012]

[0013] Where K0 and T0 are the proportionality constant and time constant, respectively, G0(s) is the unstable system of the liquid tank insulation layer of the liquefied gas carrier, G(s) is the stable system of the liquid tank insulation layer of the liquefied gas carrier, and s is time.

[0014] Preferably, the robust controller design based on the closed-loop gain shaping algorithm includes obtaining the robust controller according to formula (3).

[0015]

[0016] Where T1 is the time constant, which is approximately equal to the reciprocal of the bandwidth frequency in the liquefied gas tank insulation layer pressure difference stabilization system, and K is the robust controller.

[0017] Preferably, the nonlinear function is an S-function, which is expressed according to formula (4).

[0018] S=(1-exp(-1.5u′)) / (1+exp(-1.5u′)) (4)

[0019] Where u′ is the output of the robust controller.

[0020] Preferably, the constraint on the robust controller by the nonlinear function and the output of the robust controller is to constrain the robust controller according to formula (5).

[0021]

[0022] Where e is the error and u is the product of u' and K.

[0023] This invention provides a nonlinear positive feedback control method for the pressure difference of the insulation layer of a liquefied gas tanker. The method obtains a stable system of the pressure difference of the insulation layer of the liquefied gas tanker through a mirror mapping method, designs a robust controller based on a closed-loop gain shaping algorithm, and constrains the robust controller through a nonlinear function. The stable system is then controlled based on the constrained output, thereby improving the control accuracy of the pressure difference of the insulation layer of the liquefied gas tanker. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 This is a flowchart of the method of the present invention;

[0026] Figure 2 This is an overall structural diagram of the liquid tank insulation layer pressure control system of the present invention;

[0027] Figure 3 This is a simulation block diagram of the control system of the present invention;

[0028] Figure 4 This is a diagram showing the system output results of the present invention without system perturbation;

[0029] Figure 5a This is the output result of the controller in the presence of model perturbation according to the present invention;

[0030] Figure 5b This is a diagram showing the output of the system in the presence of model perturbation according to the present invention. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0032] Figure 1 This is a flowchart of the method of the present invention, as shown below. Figure 1 As shown, the method in this embodiment may include:

[0033] Step 1: Construct an unstable pressure differential system for the insulation layer of the liquefied gas tanker. Use a mirror mapping method to map this unstable system to a stable system.

[0034] Step 2: Design a robust controller based on a closed-loop gain shaping algorithm.

[0035] Step 3: Design a nonlinear function to obtain the output of the robust controller. Then, use the nonlinear function and the robust controller's output to constrain the robust controller.

[0036] Step 4: Obtain the transfer functions of the liquefied gas tank insulation layer pressure difference stabilization system under positive feedback and negative feedback states respectively. Based on the relationship between the transfer functions under positive feedback and negative feedback states and the robust controller, design a positive feedback controller and control the liquefied gas tank insulation layer pressure difference stabilization system according to the positive feedback controller.

[0037] Based on the above scheme, a stable system for the pressure difference of the insulation layer of the liquefied gas tanker is obtained by mirror mapping method. A robust controller is designed based on closed-loop gain shaping algorithm, and the robust controller is constrained by nonlinear function. The stable system is controlled according to the constrained output, which improves the control accuracy and reliability of the insulation layer difference of the liquefied gas tanker.

[0038] A mathematical model for controlling the pressure in the insulation layer of an LNG carrier is established. To maintain a certain pressure in the insulation layer of the liquid tank, a large amount of nitrogen is required. The pressure is automatically controlled by the liquid tank nitrogen system, as shown in Equation (1). Equation 1 is the mathematical model, which establishes the mathematical relationship between the insulation layer pressure difference and the air intake flow rate.

[0039]

[0040] In the formula, P e The pressure difference between the primary and secondary insulation layers The density of nitrogen gas (kg / m³) 3 ), g is the acceleration due to gravity, F r κ is the damping force under non-ideal conditions, and u is the intake flow rate. κ is a constant determined by the properties of the insulating layer material. The forces acting on the intake flow are mainly viscous force, inertial force, buoyancy, and gravity. u is the intake flow rate. The ratio of inertial force to viscous force is the Reynolds number. Since the characteristic parameter of a circular intake is the intake diameter d, the Reynolds number can be expressed in the form of equation (2).

[0041]

[0042] In the formula, u0 is the initial intake flow rate, and v is the kinematic viscosity coefficient. The ratio of inertial force to buoyancy is the Froude number, as shown in formula (3).

[0043]

[0044] In the formula, ρ0 is the initial density of the intake air, ρ a This refers to air density.

[0045] Fluid dynamics can be used to establish corresponding liquid tank gas mass transfer prediction models and gas emission models. The construction of the two prediction models here is not the research of this invention, but existing research results, and is only mentioned here. For details, please refer to the literature Liu K, Chen LX, Cai GP. An Experimental Study of Delayed Positive Feedback Control for a Flexible Plate[J]. International Journal of Acoustics and Vibration, 2012, 17(4): 171-180.

[0046] Step 1: Construct an unstable system of pressure difference in the insulation layer of an LPG tank. Then, use a mirror mapping method to map this unstable system into a stable system. The mirror mapping is explained as follows: For an unstable system with one or more poles located in the right half-plane, replace its unstable poles with their corresponding mirror poles (i.e., stable poles that are symmetric about the imaginary axis and located in the left half-plane of the complex plane). Define the resulting stable object as its mirror mapping process. In other words, it mirrors the unstable poles of the transfer function to map them into a stable system.

[0047] The method of mapping the unstable pressure difference system of the liquefied gas tank insulation layer to a stable pressure difference system of the liquefied gas tank insulation layer using the mirror mapping method is to construct the unstable pressure difference system of the liquefied gas tank insulation layer according to formula (4). The unstable system does not consider the time delay element. Formula (4) is an unstable controlled object because it has a pole s = T0 in the right half plane. Its mirror mapping object is G(s). The unstable pressure difference system of the liquefied gas tank insulation layer is mapped to a stable pressure difference system of the liquefied gas tank insulation layer according to formula (5).

[0048]

[0049]

[0050] Where K0 and T0 are the proportionality constant and time constant, respectively, G0(s) is the unstable system of the liquid tank insulation layer of the liquefied gas carrier, G(s) is the stable system of the liquid tank insulation layer of the liquefied gas carrier, and s is time.

[0051] After linearization near the equilibrium point, the mathematical model of the pressure-to-flow rate transfer function can be expressed as equation (6). The mathematical model previously shown in equation (4) is itself a nonlinear model. Here, linearization is performed near the equilibrium point of the nonlinear system, a common approach in control theory for nonlinear systems. The pressure P at the equilibrium point... e0 =2.0 mbar, initial flow rate u0 = 42 m 3 / h. For a certain LNG carrier, the parameters are K0 = 3.25, T0 = 0.78, τ = 0.25s.

[0052]

[0053] In the formula, K0 and T0 are the proportional constant and time constant, respectively, and τ is the time delay coefficient.

[0054] Step 2: Design a robust controller based on the closed-loop gain shaping algorithm. The robust controller is designed using the closed-loop gain shaping algorithm to reduce the model perturbation effect caused by pure time delay. The design of the robust controller based on the closed-loop gain shaping algorithm includes obtaining the robust controller according to formula (7).

[0055]

[0056] Where T1 is the time constant, which is approximately equal to the reciprocal of the bandwidth frequency in the liquefied gas tank insulation layer pressure difference stabilization system, and K is the robust controller.

[0057] Specifically, a robust controller K is designed using a first-order closed-loop gain shaping algorithm. The closed-loop transfer function of the system can be replaced by a pre-designed first-order inertial system.

[0058]

[0059] in, In the formula, T1 is the time constant of the closed-loop system, and its value is approximately equal to the reciprocal of the bandwidth frequency of the closed-loop system (T1 = 0.2s in the final simulation experiment of this embodiment). Substituting equation (7) into equation (8), then

[0060]

[0061] Because the closed-loop gain shaping algorithm is a robust control algorithm, it is essentially equivalent to a robust PD controller. PD controllers are common controllers in traditional PID control, referring to controllers that achieve control through proportional and derivative elements.

[0062] Step 3: Design a nonlinear function to obtain the output of the robust controller, and constrain the robust controller using the nonlinear function and the output of the robust controller. The nonlinear function is an S-function, and the amplitude of the controller output is reduced using the nonlinear modification technique of the S-function. The S-function is expressed according to formula (10).

[0063] S=(1-exp(-1.5u′)) / (1+exp(-1.5u′)) (10)

[0064] Where u′ is the output of the robust controller.

[0065] The constraint on the robust controller by the nonlinear function and the output of the robust controller is to constrain the robust controller according to formula (11).

[0066]

[0067] Where e is the error and u is the product of u′ and K.

[0068] Step 4: Obtain the transfer functions of the liquefied gas carrier's tank insulation layer pressure difference stabilization system under both positive and negative feedback states. Based on the relationship between the transfer functions under positive and negative feedback states and the constrained robust controller, design a positive feedback controller, where K″ = -K′. Control the liquefied gas carrier's tank insulation layer pressure difference stabilization system using the positive feedback controller. This approach demonstrates the feasibility of using a positive feedback system to replace a negative feedback system. By verifying the equivalence of positive and negative feedback control, a redundant or backup system can be formed in case of emergencies such as reversed feedback signals in the control system, improving the system's reliability and resilience.

[0069] By finding the transfer function of the closed-loop control system, we can know that...

[0070]

[0071] The left side of equation (12) is the transfer function of the negative feedback control system, and the right side is the transfer function of the positive feedback control system. When the positive feedback controller K″=-K′, the output of the positive feedback system differs from the output of the negative feedback system by a negative sign. Through the analysis of equation (12), theoretically, any system that can be controlled by negative feedback has an equivalent positive feedback control system. This can be initially understood as using the opposite control law to cancel the output effect, and finally modulating out the inverse signal of the input signal.

[0072] Equivalent transformation of positive and negative feedback: By finding the transfer function of the closed-loop control system, it can be seen that this explains the mathematical equivalence of positive and negative feedback control. It is a theoretical explanation. This embodiment verifies the feasibility of using positive feedback control to replace negative feedback.

[0073] The overall structure of the liquid tank insulation layer pressure control system is as follows: Figure 2 As shown, the control system includes a control unit, a nitrogen generator, a control regulating valve, an insulation layer, a safety valve, an isolation valve, and a vent mast.

[0074] The simulation experiment was conducted using Matlab, and the simulation block diagram is as follows: Figure 3 As shown. From Figure 4 As can be seen from Figure 5, the control law designed in this invention has no overshoot, the settling time is 3s, and it can quickly track the system input under positive feedback. As can be seen from Figure 5, after adding model perturbation, the system exhibits a 30% overshoot, but it can still quickly and accurately track the system input, indicating that the system has good robustness. If the performance index of the system output square plus the controller output square is used to evaluate the system performance, as shown in Equation (13), the comparison of time-domain response performance indexes is shown in Table 1, and the curves of controller output and system output are as follows. Figure 5a , Figure 5b As shown by the dashed line.

[0075] J=∫(P e 2 +u 2 )dt (13)

[0076] Table 1 Comparison of Time-Domain Response Performance Indicators

[0077]

[0078] The negative feedback control being compared was calculated from the literature Pressure control of insulation space forliquefied natural gas carrier with nonlinear feedback technique. Journal of Marine Science and Engineering. 2018, 6(4): 133.

[0079] Through the above simulation experiments, the beneficial effects of this invention are as follows: It uses a mirror mapping method to map the unstable system of the LNG ship's liquid tank insulation layer pressure difference into a stable system; then, it uses a closed-loop gain shaping algorithm to design a robust controller to reduce the model perturbation effect caused by pure time delay; next, it uses the nonlinear modification technique of the S-function to reduce the amplitude of the controller output; and finally, it uses positive feedback to achieve control of the entire control system. Theoretical analysis and simulation results show that positive feedback control can achieve the same control effect as negative feedback control, and the algorithm proposed in this invention outperforms previously published negative feedback control methods. This preliminarily demonstrates the feasibility and effectiveness of positive feedback control in ship control systems.

[0080] Its initial application scenario is that when the feedback signal of the ship control system is reversed, an emergency occurs. The program can be directly designed into a control scheme for positive feedback, forming a redundant or backup system in case of failure, thereby improving the reliability or resilience of the system.

[0081] Overall beneficial effects:

[0082] This invention provides a nonlinear positive feedback control method for the pressure difference of the insulation layer in liquefied gas tanks of liquefied gas carriers. A stable system of the pressure difference in the insulation layer of liquefied gas tanks is obtained through a mirror mapping method. A robust controller is designed based on a closed-loop gain shaping algorithm, and the robust controller is constrained by a nonlinear function. The stable system is then controlled based on the constrained output, improving the control accuracy of the pressure difference in the insulation layer of liquefied gas carriers. This invention preliminarily demonstrates the feasibility and effectiveness of positive feedback control in ship control systems, and provides guidance for further theoretical analysis and practical engineering applications of positive feedback control.

[0083] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A nonlinear positive feedback control method for the pressure difference of the insulation layer in a liquefied gas tank of an LPG carrier, characterized in that, include, Step 1: Construct an unstable pressure differential system for the insulation layer of the liquefied gas tanker. Use a mirror mapping method to map this unstable system to a stable system. Step 2: Design a robust controller based on a closed-loop gain shaping algorithm. Step 3: Design a nonlinear function to obtain the output of the robust controller. Then, use the nonlinear function and the robust controller's output to constrain the robust controller. Step 4: Obtain the transfer functions of the liquefied gas tank insulation layer pressure difference stabilization system under positive feedback and negative feedback states respectively. Based on the relationship between the transfer functions under positive feedback and negative feedback states and the constrained robust controller, design a positive feedback controller and control the liquefied gas tank insulation layer pressure difference stabilization system according to the positive feedback controller.

2. The nonlinear positive feedback control method for the pressure difference of the insulation layer of a liquefied gas tanker according to claim 1, characterized in that, The method of mapping the unstable pressure difference system of the liquefied gas tank insulation layer to a stable pressure difference system of the liquefied gas tank using the mirror mapping method involves constructing the unstable pressure difference system of the liquefied gas tank insulation layer according to formula (1) and mapping the unstable pressure difference system of the liquefied gas tank insulation layer to a stable pressure difference system according to formula (2). Where K0 and T0 are the proportionality constant and time constant, respectively, G0(s) is the unstable system of the liquid tank insulation layer of the liquefied gas carrier, G(s) is the stable system of the liquid tank insulation layer of the liquefied gas carrier, and s is time.

3. The nonlinear positive feedback control method for the pressure difference of the insulation layer of a liquefied gas tanker according to claim 2, characterized in that, The robust controller design based on the closed-loop gain shaping algorithm includes obtaining the robust controller according to formula (3). Where T1 is the time constant, which is approximately equal to the reciprocal of the bandwidth frequency in the liquefied gas tank insulation layer pressure difference stabilization system, and K is the robust controller.

4. The nonlinear positive feedback control method for the pressure difference of the insulation layer of a liquefied gas tanker according to claim 3, characterized in that, The nonlinear function is an S-function, which is expressed according to formula (4). S = (1-exp(-1.5u')) / (1+ exp(-1.5u')) (4) Where u' is the output of the robust controller.

5. The nonlinear positive feedback control method for the pressure difference of the insulation layer of a liquefied gas tanker according to claim 4, characterized in that, The constraint on the robust controller by the nonlinear function and the output of the robust controller is to constrain the robust controller according to formula (5). Where e is the error and u is the product of u' and K.

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