Active compensation model-free self-adaptive control method for electrically-driven ship-borne captive balloon winch under wind wave disturbance

Abstract

The invention discloses an electrically-driven ship-borne captive balloon winch active compensation model-free self-adaptive control method under wind wave disturbance, which comprises the following four steps: step 1, calculating the length change of a mooring rope under wind disturbance, step 2, establishing a sea wave and mother ship heaving motion model, and step 3, calculating the heaving motion model. 3, designing an active compensation model-free self-adaptive control system of the electric drive winch; 4, modeling and simulating the active compensation model-free self-adaptive control system of the electric drive winch. The method has the beneficial effects that the length of the infinitesimal cable is iteratively calculated according to a real-time wind field model; the method comprises the following steps: establishing a sea wave heaving motion model through a sea wave spectrum; establishing a heaving motion transfer function between a mother ship and sea waves; calculating the heaving displacement of the mother ship; calculating the change speed of the tail end of a mooring rope under the disturbance of wind waves; the active compensation control of the winch under the wind wave disturbance is realized, and the method has the characteristics of high response speed, strong robustness, high precision, strong practicability and the like.

Description

Technical Field

[0001] The invention belongs to an active compensation control method for a shipborne tethered balloon winch, and specifically relates to an active compensation model-free adaptive control method for an electrically driven shipborne tethered balloon winch under wind and wave disturbance. Background Art

[0002] The ship-borne tethered balloon is a small or medium-sized tethered balloon system loaded on ships. It consists of a sphere, mission payload, tethering cable, mooring winch, control system and other main parts. It usually carries radar, communication, jamming, reconnaissance and other electronic equipment under the sphere. Due to its long airborne time, large coverage area, and continuous and uninterrupted operation, it is widely used in maritime security, territorial waters and border monitoring, and naval military monitoring. In comparison, the performance of tethered balloons in this field is slightly better than other equipment, and it has high military application value and significance.

[0003] Since the daily work of ship-borne tethered balloons requires long-term constant altitude air operation, in the harsh marine environment, tethered balloons are often affected by time-varying strong sea breezes and the rise and fall of waves, causing the tethered cables to be stretched under time-varying tension, and even fatigue fracture of cables up to several thousand meters, thereby affecting the stability and safety of the tethered objects, causing great damage and losses to production operations. The tethered cables are key components for controlling the launch, recovery, residence, and attitude adjustment of tethered balloons. They also provide energy for the spheres and sometimes provide information transmission channels between the balloons and ship systems. In addition, the interference of wind and waves may also cause the tethered balloons to deviate from their original stable air position. Since the balloon air operation needs to be stable at a certain height for a long time, when the wind and waves change greatly and are not controlled, the tethered balloons will lose their air ability. Usually, active compensation control is performed through the anchoring and retracting winch, so that the winch can remain relatively still or can greatly reduce the swaying and extension of the cable in high wind and wave disturbances, which will greatly improve the working conditions of the above-mentioned engineering applications and improve the safety, utilization and efficiency of production equipment. To address this problem, the present invention analyzes the change in cable length when wind force changes, combines the heave and sink motion of waves, comprehensively analyzes the impact of wind and wave disturbance on the retraction and release length of the winch cable, calculates the changing speed of the cable end, establishes an electric drive winch system model, and uses model-free adaptive control as the active compensation control strategy for tethered balloons. Active compensation for the winch is performed, which is of great significance to ensure that the tethered balloon can still maintain a stable altitude for airborne operations under wind and wave disturbances. Summary of the invention

[0004] In order to achieve the tethered balloon to maintain a stable altitude in the wind and wave disturbance, the present invention discloses an active compensation model-free adaptive control method for an electrically driven shipborne tethered balloon winch under wind and wave disturbance.

[0005] The technical solution adopted by the present invention is: a model-free adaptive control method for active compensation of an electrically driven shipborne tethered balloon winch under wind and wave disturbance, which consists of the following four steps: Step 1: Calculate the change in cable length under wind disturbance To calculate the cable length under wind disturbance, it is necessary to first establish a real-time wind field model during tethered balloon operation, and calculate the change in cable length under wind disturbance through the force and geometric relationship between the balloon and microelement cable.

[0006] (1) Establishment of real-time wind field model The real-time wind field model that characterizes the wind speed time domain function of the tethered balloon operation is: (1) In the formula, V P is the average wind speed, V G is the gust wind speed, V T is the turbulent wind speed, c is a constant, V Gmax is the maximum peak gust wind speed, V Tmax is the peak value of turbulent wind speed, ran (-1,1) is a random number between -1 and 1. ω n is the initial phase angle of the turbulent wind, ω n ∈[0,2 π ], t 0 , t 1 , t 2 They are the critical times of the three stages of the gust wind field.

[0007] (2) Calculation of cable length Keep the tethered balloon at a high altitude h Divide into n Equal parts, each part has a height of △ h , and then divide the cable into equal parts according to the height n Segment, that is n A microelement cable is constructed, and the microelementized cable unit is equivalent to a "spring-damper" unit.

[0008] by t Time to lower the cable and balloon connection point X 0 The state is the boundary condition, at time t The boundary equation of the tethered balloon in the steady state under the real-time wind field can be simplified to (2) (3) In the formula, a 1 Cable tension and x The angle of the axis, F 1 is the cable tension between the cable and the balloon, m is the mass of the balloon and the load, g is the acceleration due to gravity, ρ a is the air density at the current altitude of the balloon, ρ h The density of the helium in the balloon, V is the volume of the balloon, v t for t The wind speed at the moment, s b is the characteristic area of ​​the balloon, C L is the balloon aerodynamic lift coefficient, C D is the aerodynamic drag coefficient of the balloon.

[0009] Keep the tethered balloon at a high altitude h Divide into n Equal parts, each part has a height of △ h , and then divide the cable into equal parts according to the height n paragraph, select i Taking the microelement cable as the object, a microelement cable mechanical model is established, as follows: F i cos α i = F i+1 cos α i+1 (4) (5) (6) In the formula, F i For the i The tension of the microelement cable, a i For the i Microelement cable tension and x The angle of the axis, ρ 绳 is the linear density of the cable, l i For the i Microelement cable length,A is the cross-sectional area of ​​the cable, E is the elastic modulus of the cable, η is the cable damping coefficient.

[0010] Initialize the basic parameters of the wind field, balloon, cable and the air height, and transform the cable into microelement according to the equal height principle. n , t Time to lower the cable and balloon connection point X 0 The state is the boundary condition, calculated by equation (2) and equation (3) t The connection point at the moment X 0 Boundary condition parameters F 1 , a 1 ,from i =1, and then loop through equations (4), (5), and (6) to calculate l i , F i+1 , a i+1 ,Will F i+1 , a i+1 Substitute into the next loop until i = n , the tension at the end of the cable can be obtained F n , calculated according to formula (7) t The length of the cable to be released at any time is (7) Step 2: Establish the wave and mother ship heave motion model A mathematical model for characterizing the heave and sink motion of waves is established by using the wave spectrum, and a mathematical model for the heave and sink motion of the mother ship is established by establishing a transmission model between the waves and the mother ship.

[0011] (1) Select the wave spectrum The wave spectrum model is selected as PM spectrum, which has the advantages of reasonable reliability, simple form, easy understanding and use. The PM spectrum expression is (8) In the formula, ω is the angular frequency of the harmonic, a is a dimensionless constant, generally taken as 0.0081. g is the acceleration due to gravity, β =0.74; U 19.5is the wind speed at a height of 19.5m above the sea surface, in m / s; (2) Establishing a wave heave and sink motion model The motion of ocean waves is an extremely complex random process, which can be regarded as the superposition of an infinite number of chaotic component waves, which can be expressed by the wave spectrum. The amplitude, frequency, direction and phase of these component waves are all different, so random ocean waves can be regarded as the superposition of simple harmonic waves of different frequencies, and the function of ocean wave heave motion can be obtained as (9) (10) In the formula, S a ( t )for t The displacement of the wave movement at any moment, S ai For the i The peak value of the harmonics, ω i For the i The angular frequency of the harmonics, ε i For the i The phase angle of the harmonics, ε i The initial value is uniformly random between 0 and 2p, ω is the angular frequency increment.

[0012] (3) Establish a mathematical model of the mother ship's heave and sink motion When the mother ship is working, the influence on the electric winch cable is mainly the vertical heave motion. Ignoring the influence of other degrees of freedom, and ignoring the influence of factors such as the damping coefficient of the motion between the mother ship and the waves in the calculation, the heave motion transmission model between the mother ship and the waves can be obtained as follows: (11) In the formula, S ci The heave displacement of the mother ship i The peak value of the harmonics, ρ is the density of seawater, S is the contact area between the mother ship's waterline and the seawater, M For the mother ship quality, g is the acceleration due to gravity.

[0013] Then the displacement of the mother ship's heave motion can be expressed as (12) In the formula, S c ( t )for tThe mother ship's heave and sink movement displacement at each moment.

[0014] Step 3: Design of model-free adaptive control system for active compensation of electric winch The changing speed of the cable end is calculated as the expected input of the control system, an electric drive winch system model is built, and a model-free adaptive controller is designed to control the tethered balloon winch.

[0015] (1) Calculate the speed change at the end of the cable From formula (7) and formula (12), we can know t The total length of the cable under wind and wave disturbance can be expressed as L s ( t )= L ( t )+ S c ( t ) (13) The linear velocity at the end of the cable is (14) (2) Electric drive winch system model The mathematical model between the voltage signal at the input end of the inverter and the angular velocity of the reel is expressed as (15) (16) T = iT f (17) (18) (19) In the formula, u is the voltage of the inverter control signal, U 1 is the stator input voltage of the variable frequency motor, K 1 for U 1 and u The conversion coefficient, T is the motor electromagnetic torque, p is the number of motor pole pairs, R 2 is the phase resistance of the rotor winding, S′ is the slip rate, f is the frequency of the output power, R 1 is the phase resistance of the stator winding, X 1is the leakage reactance of each phase winding of the stator, X 2 is the leakage reactance of each phase winding of the rotor, i is the transmission ratio of the reduction gearbox, T f is the equivalent resistance torque of the load, J is the total moment of inertia of the rotating parts converted to the motor shaft, G d is the mass of the rotating part of the motor, D d is the rotation diameter of the rotating part, G 1 is the pinion weight, D 1 is the diameter of the pinion, G 2 is the weight of the large gear, D 2 is the diameter of the large gear, G g is the weight of the drum, D g is the roller diameter, ω is the angular velocity of the reel, r is the roller radius, η c is the transmission efficiency, g is the acceleration due to gravity, F n is the tension at the end of the cable.

[0016] (3) Model-free adaptive controller design According to the model-free adaptive control principle based on compact dynamic linearization, the model-free adaptive controller is designed as (20) (twenty one) In the formula, y ( k )∈ R , u ( k )∈ R They are k The output and input of the moment system; for k Pseudo partial derivative of the system output at time instant; y * ( k +1) k +1 The expected output value of the system at time λ >0 is the weight factor, which is used to limit the change of input quantity; ρ is the step size factor, ρ∈(0,1]; for The initial value of ε is a sufficiently small positive number; u ( k -1) u ( k -1) Change, △ u ( k -1)= u ( k -1)- u ( k -2); sign( * ) is a symbolic function used to determine * The positive and negative situation of △ y ( k -1) y ( k -1) Change, △ y ( k -1)= y ( k -1)- y ( k -2); μ is the penalty factor for the pseudo partial derivative estimate, μ >0; η is the step size factor of the pseudo partial derivative, η ∈(0, 1], making the control more flexible.

[0017] Step 4: Modeling and simulation of active compensation model-free adaptive control system for electric drive winch The controllers of the electric-driven winch system are respectively adopted as the model-free adaptive controller (MFAC) and the PID controller. The linear velocity of the cable end is taken as the expected output value of the system. The angular velocity of the drum is output by the speed encoder and converted into the linear velocity of the drum as the feedback input signal of the MFAC controller. The output signal is the voltage signal at the input end of the frequency converter. According to the above method, an active compensation model-free adaptive control system for the electric-driven shipborne tethered balloon winch under wind and wave disturbance is designed, and simulation and analysis are carried out. By calculating the absolute error, relative error, average error and average relative error between the system output and the expected output, the control effects of the two control methods are compared and analyzed. The calculation expression is: (twenty two) (twenty three) (twenty four) In the formula, e k for k The absolute error between the system output and the expected value at that moment, ea is the average error, ξ k for k The relative error between the system output and the expected value at a given moment.

[0018] The beneficial effects of the present invention are as follows: the present invention relates to an active compensation model-free adaptive control method for an electrically driven shipborne tethered balloon winch under wind and wave disturbances. According to a real-time wind field model, the tethered cable is micro-elemented, and the micro-element cable length is iteratively calculated; a wave heave motion model is established through a wave spectrum, a heave motion transfer function between a mother ship and the waves is established, and the heave displacement of the mother ship is calculated; the changing speed of the cable end under wind and wave disturbances is calculated, an electrically driven winch system model is established, the linear speed of the cable end is used as the expected output value of the control system, and a model-free adaptive controller is designed. The advantage of this method is that it only requires input and output data of the controlled system, and has high robustness and response speed; active compensation control of the winch is realized under wind and wave disturbances, ensuring that the tethered balloon can continue to operate at a stable altitude for a long time. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 Flow chart of the model-free adaptive control method for active compensation of an electrically driven shipborne tethered balloon winch under wind and wave disturbances of the present invention Figure 2 This is the wind field time domain diagram under the fourth wind speed of the present invention Figure 3 This is a schematic diagram of the structure of the "balloon-cable-mother ship" system of the present invention. Figure 4 This is the force analysis diagram of the ship-borne tethered balloon of the present invention. Figure 5 This is the force analysis diagram of the "spring-damper" unit of the present invention Figure 6 The frequency domain diagram of the PM spectrum of the present invention is Figure 7 This is the time domain diagram of the sea wave heave motion and the mother ship heave motion of the present invention Figure 8 The comparison diagram of the total length change of the cable under wind interference and wind and wave interference of the present invention is shown in FIG. Fig. 9 The present invention is a diagram of the speed change of the cable end under wind and wave interference. Fig.10 This is a control block diagram of the model-free adaptive control system for the electric-driven shipborne tethered balloon winch active compensation under wind and wave disturbances of the present invention. Fig.11 This is a comparison chart of the control effect of the present invention Fig.12 This is a comparison diagram of the control error of the present invention. DETAILED DESCRIPTION

[0020] The present invention will be further described below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0021] See attached figure, Figure 1 The present invention is a flow chart of the active compensation model-free adaptive control method of the electric-driven shipborne tethered balloon winch under wind and wave disturbance, which includes the following four steps: (1) calculating the change of cable length under wind disturbance, (2) establishing the wave and mother ship heave motion model, (3) designing the electric-driven winch active compensation model-free adaptive control system, (4) modeling and simulation of the electric-driven winch active compensation model-free adaptive control system; Step 1: Calculate the change in cable length under wind disturbance (1) Establishment of real-time wind field model Select level 4 wind speed for real-time wind field modeling. Under level 4 wind speed, the average wind speed is 5.5m / s and the peak gust speed is V Gmax 2m / s, peak turbulent wind speed V Tmax is 4m / s, t 0 =10s, t 1 =30s, t 2 =50s, ω n 6 / π , substituting into formula (1) we can get the real-time wind field model. Setting the simulation time to 1-50s, the simulation results are as follows Figure 2 The time domain diagram of the wind field under level 4 wind speed is shown.

[0022] (2) Calculation of cable length See attached figure, Figure 3 is a structural diagram of the balloon-cable system of the present invention. The tethered balloon system includes a balloon and a cable. Figure 4 This is the force analysis diagram of the ship-borne tethered balloon. Figure 5 The balloon is selected as a shipborne tethered balloon, and the cable is selected as a special optoelectronic composite cable for tethered balloons. The basic parameters of the tethered balloon are helium density ρ h =0.17kg / m 3 , Main airbag volume V =4504.1m 3 、Maximum cross-sectional area of ​​airship s b =183.8m 2 The mass of the balloon and the mass of the payload are 163.7kg and 500kg respectively, so the total mass of the balloon and the payload is m =663.7kg, acceleration due to gravity g =9.8m / s2 , Balloon aerodynamic lift coefficient C L =0.1, balloon aerodynamic drag coefficient C D =0.53; basic parameters related to cables are cable density ρ 绳 =134g / m, cable damping coefficient η =1.2, cable elastic modulus E =172GPa, cable diameter is D =15mm, so the cross-sectional area of ​​the cable A =0.001414m 2 The basic parameters of the tethered balloon environment are: the air density at an altitude of 500 meters is 1.19 kg / m 3 .

[0023] Balloon altitude h =500 meters is divided into n =50000 equal parts, each part has a height of △ h is 0.01 m, and then the cable is divided into 50,000 sections according to the height, and the differential cable unit is equivalent to the "spring-damper" unit; t Substitute the real-time wind speed, balloon basic parameters and environmental basic parameters at the moment into equations (2) to (3) to obtain the boundary equation of the tethered balloon; substitute the basic parameters of the cable into equations (4) to (6) to obtain the original length relationship of the cable; t At this moment, the cable is connected to the balloon. X 0 As the boundary condition, it is calculated by equation (2) and equation (3) t The connection point at the moment X 0 Boundary condition parameters F 1 , a 1 ,from i =1, and then loop through equations (4), (5), and (6) to calculate l i , F i+1 , a i+1 ,Will F i+1 , a i+1 Substitute into the next loop until i = n , the tension at the end of the cable can be obtained F n , and then calculate according to formula (7) t Cable length at all times.

[0024] Step 2: Establish the wave and mother ship heave motion model U 19.5 Take 10m / s and substitute it into equation (8) to obtain the frequency domain diagram of PM spectrum, as shown in Figure 6 As shown, set the frequency increment Δ ω =0.08rad / s, the simulation frequency band is set to 0.35-2.75rad / s, and the i The simple harmonic peak value corresponding to the angular frequency S ai ; Take the mother ship mass M =3·10 6 kg, density of seawater ρ =1030kg / m 3 , the contact area between the mother ship's waterline and the seawater S =330m 2 , the above parameters and S ai Substituting into equation (11), we can obtain the simple harmonic peak value corresponding to each angular frequency of the mother ship's heave motion: S ci ; Set simulation time t ∈(1,50), the simple harmonic peak value corresponding to each angular frequency S ai The simple harmonic peak value corresponding to each angular frequency of the mother ship S ci Substituting into equation (9) and equation (12), we can obtain the time domain function of the wave heave motion and the time domain function of the mother ship heave motion. Figure 7 Shown is a time domain diagram of the rising and falling motion of waves and the rising and falling motion of the mother ship.

[0025] Step 3: Design of model-free adaptive control system for active compensation of electric winch (1) Calculate the speed change at the end of the cable Will t Total length of the cable disturbed by the downwind at the moment L ( t ) and the mother ship heave displacement S c ( t ) into equation (13) and equation (14), we can get t The total length of the cable and the speed of the cable end under the wind and wave interference at the moment, such as Figure 8 The following is a comparison of the total length of the cable under wind disturbance and wind and wave disturbance. Fig. 9 The figure shows the changing velocity of the cable end under wind and wave disturbance.

[0026] (2) Electric drive winch system model Inverter input voltage frequency conversion coefficient K 1 =5.2, number of motor pole pairs p =6, stator winding phase resistance R 1 =0.355Ω, rotor winding phase resistance R 2 =0.24Ω, leakage reactance of each phase winding of the stator X 1 =1.265Ω, leakage reactance of each phase winding of the rotor X 2 =2.065Ω, slip rate S′ =0.02, gearbox transmission ratio i =8, the mass of the rotating part of the motor G d =500kg, rotating part rotation diameter D d =1560mm, pinion weight G 1 =51kg, pinion diameter D 1 =200mm, large gear mass G 2 =545.7kg, large gear diameter D 2 =1600mm, roll diameter D g =2176mm, drum and cable mass G g =10t, roller radius r =1600mm, transmission efficiency η c =0.95, substituting the winch related parameters into equations (15)-(19) can obtain the system transfer function between the voltage signal input at the input end of the inverter and the angular velocity of the drum.

[0027] (3) Model-free adaptive controller design Set weight factors based on experience λ =1, step factor ρ = 0.2, penalty factor for pseudo partial derivative estimation μ =2, step size factor of pseudo partial derivative η =1, substituting the parameters into equation (20) and equation (21) yields a model-free adaptive controller.

[0028] Step 4: Modeling and simulation of active compensation model-free adaptive control system for electric drive winch See the attached figure, Fig.10This is the control block diagram of the model-free adaptive control system for the active compensation of the electrically driven shipborne tethered balloon winch under wind and wave disturbance. The linear velocity of the cable end is taken as the expected output value of the system, and the angular velocity of the drum is output by the speed encoder and converted into the linear velocity of the drum as the feedback input signal of the MFAC controller. The output signal of the controller is the voltage signal at the input end of the frequency converter. The PID controller is used instead of the model-free adaptive controller (MFAC) for comparative analysis. The parameters of the PID controller are: K P =150, K I =10, K D =9; Fig.11 To compare the control effects, the system output value is substituted into equations (22) to (24) to calculate the absolute error, average error and relative error. Fig.12 This is a control error comparison chart, in which the maximum absolute error values ​​of MFAC and PID are 0.1019 and 0.4964, respectively, the maximum relative errors are 6.92% and 36.78%, respectively, and the average errors are 0.0250 and 0.1114, respectively. The results show that the maximum absolute error of the model-free adaptive controller (MFAC) is reduced by 79.49% compared with the PID controller, the maximum relative error is reduced by 81.19%, and the average error is reduced by 77.56%. It can be concluded that compared with PID control, model-free adaptive control (MFAC) can well reduce control lag and greatly improve control accuracy.

[0029] The beneficial effects of the present invention are as follows: the present invention relates to an active compensation model-free adaptive control method for an electrically driven shipborne tethered balloon winch under wind and wave disturbances. According to a real-time wind field model, the tethered cable is micro-elemented, and the micro-element cable length is iteratively calculated; a wave heave motion model is established through a wave spectrum, a heave motion transfer function between a mother ship and the waves is established, and the heave displacement of the mother ship is calculated; the changing speed of the cable end under wind and wave disturbances is calculated, an electrically driven winch system model is established, the linear speed of the cable end is used as the expected output value of the control system, and a model-free adaptive controller is designed. The advantage of this method is that it only requires input and output data of the controlled system, and has high robustness and response speed; active compensation control of the winch is realized under wind and wave disturbances, ensuring that the tethered balloon can continue to operate at a stable altitude for a long time.

[0030] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. The present invention discloses an active compensation model-free adaptive control method for an electrically driven shipborne moored balloon winch under wind and wave disturbance. According to a real-time wind field model, the moored cable is micro-elemented, and the micro-element cable length is iteratively calculated. A wave heave motion model is established through a wave spectrum, a heave motion transfer function between a mother ship and the waves is established, the heave displacement of the mother ship is calculated, and the changing speed of the cable end under wind and wave disturbance is calculated. An electrically driven winch system model is established, and a comparative analysis is performed using the maximum absolute error, average error, and maximum relative error between the control output and the expected output as performance indicators. The method is characterized in that: The linear velocity at the end of the cable is taken as the expected output value of the control system, and the controller is designed using the model-free adaptive control algorithm to realize the active compensation control of the winch under wind and wave disturbances. The following four steps are followed: Step 1: Calculate the change in cable length under wind disturbances. Step 2: Establish a model of wave and mother ship heave motion. Step 3: Design of the model-free adaptive control system for active compensation of the electric drive winch. Step 4: Modeling and simulation of the model-free adaptive control system for active compensation of the electric drive winch. Step 1: Calculate the change in cable length under wind disturbance To calculate the cable length under wind disturbance, it is necessary to first establish a real-time wind field model during the tethered balloon operation, and calculate the change in cable length under wind disturbance through the force and geometric relationship between the balloon and the microelement cable; (1) Establishment of real-time wind field model The real-time wind field model that characterizes the wind speed time domain function of the tethered balloon operation is: （1） In the formula, V P is the average wind speed, V G is the gust wind speed, V T is the turbulent wind speed, c is a constant, V Gmax is the maximum peak gust wind speed, V Tmax is the peak value of turbulent wind speed, ran (-1,1) is a random number between -1 and 1. ω n is the initial phase angle of the turbulent wind, ω n ∈[0,2 π ], t 0. t 1. t 2 are the critical times of the three stages of the gust wind field; (2) Calculation of cable length Keep the tethered balloon at a high altitude h Divide into n Equal parts, each part has a height of △ h , and then divide the cable into equal parts according to the height n Segment, that is n A microelement cable is created, and the microelement cable unit is equivalent to a "spring-damper" unit; by t Time to lower the cable and balloon connection point X The state of 0 is the boundary condition, and at time t The boundary equation of the tethered balloon in the steady state under the real-time wind field can be simplified to （2） （3） In the formula, a 1 Cable tension and x The angle of the axis, F 1 is the cable tension between the cable and the balloon, m is the mass of the balloon and the load, g is the acceleration due to gravity, ρ a is the air density at the current altitude of the balloon, ρ h The density of the helium in the balloon, V is the volume of the balloon, v t for t The wind speed at the moment, s b is the characteristic area of ​​the balloon, C L is the balloon aerodynamic lift coefficient, C D is the balloon aerodynamic drag coefficient; Keep the tethered balloon at a high altitude h Divide into n Equal parts, each part has a height of △ h , and then divide the cable into equal parts according to the height n paragraph, select i Taking the microelement cable as the object, a microelement cable mechanical model is established, as follows: F i cos α i = F i+1 cos α i+1 (4) （5） （6） In the formula, F i For the i The tension of the microelement cable, a i For the i Microelement cable tension and x The angle of the axis, ρ 绳 is the linear density of the cable, l i For the i Microelement cable length, A is the cross-sectional area of ​​the cable, E is the elastic modulus of the cable, η is the cable damping coefficient; Initialize the basic parameters of the wind field, balloon, cable and the air height, and transform the cable into microelement according to the equal height principle. n , t Time to lower the cable and balloon connection point X The state of 0 is the boundary condition, calculated by equation (2) and equation (3) t The connection point at the moment X 0 boundary condition parameters F 1. a 1. From i =1, and then loop through equations (4), (5), and (6) to calculate l i , F i+1 , a i+1 ,Will F i+1 , a i+1 Substitute into the next loop until i = n , the tension at the end of the cable can be obtained F n , calculated according to formula (7) t The length of the cable to be released at any time is （7） Step 2: Establish the wave and mother ship heave motion model A mathematical model for characterizing the heave and sink motion of waves is established by using the wave spectrum, and a mathematical model for the heave and sink motion of the mother ship is established by establishing a transmission model between the waves and the mother ship; (1) Select the wave spectrum The wave spectrum model is selected as PM spectrum, which has the advantages of reasonable reliability, simple form, easy understanding and use. The PM spectrum expression is （8） In the formula, ω is the angular frequency of the harmonic, a is a dimensionless constant, generally taken as 0.0081. g is the acceleration due to gravity, β =0.74; U 19.5 is the wind speed at a height of 19.5m above the sea surface, in m / s; (2) Establishing a wave heave and sink motion model The motion of ocean waves is an extremely complex random process, which can be regarded as the superposition of an infinite number of chaotic component waves, which can be expressed by the wave spectrum. The amplitude, frequency, direction and phase of these component waves are all different, so random ocean waves can be regarded as the superposition of simple harmonic waves of different frequencies, and the function of ocean wave heave motion can be obtained as （9） （10） In the formula, S a ( t )for t The displacement of the wave movement at any moment, S ai For the i The peak value of the harmonics, ω i For the i The angular frequency of the harmonics, ε i For the i The phase angle of the harmonics, ε i The initial value is uniformly random between 0 and 2p, ω is the angular frequency increment; (3) Establish a mathematical model of the mother ship's heave and sink motion When the mother ship is working, the influence on the electric winch cable is mainly the vertical heave motion. Ignoring the influence of other degrees of freedom, and ignoring the influence of factors such as the damping coefficient of the motion between the mother ship and the waves in the calculation, the heave motion transmission model between the mother ship and the waves can be obtained as follows: （11） In the formula, S ci The heave displacement of the mother ship i The peak value of the harmonics, ρ is the density of seawater, S is the contact area between the mother ship's waterline and the seawater, M The quality of the mother ship, g is the acceleration due to gravity; Then the displacement of the mother ship's heave motion can be expressed as （12） In the formula, S c ( t )for t The displacement of the mother ship at every moment; Step 3: Design of model-free adaptive control system for active compensation of electric winch Calculate the speed change of the cable end as the expected input of the control system, build an electric drive winch system model, and design a model-free adaptive controller to control the tethered balloon winch; (1) Calculate the speed change at the end of the cable From formula (7) and formula (12), we can know t The total length of the cable under wind and wave disturbance can be expressed as L s ( t )= L ( t )+ S c ( t ) （13） The linear velocity at the end of the cable is （14） (2) Electric drive winch system model The mathematical model between the voltage signal at the input end of the inverter and the angular velocity of the reel is expressed as （15） （16） T = iT f （17） （18） （19） In the formula, u is the voltage of the inverter control signal, U 1 is the stator input voltage of the variable frequency motor, K 1 for U 1 and u The conversion coefficient, T is the motor electromagnetic torque, p is the number of motor pole pairs, R 2 is the phase resistance of the rotor winding, S′ is the slip rate, f is the frequency of the output power, R 1 is the phase resistance of the stator winding, X 1 is the leakage reactance of each phase winding of the stator, X 2 is the leakage reactance of each phase winding of the rotor, i is the transmission ratio of the reduction gearbox, T f is the equivalent resistance torque of the load, J is the total moment of inertia of the rotating parts converted to the motor shaft, G d is the mass of the rotating part of the motor, D d is the rotation diameter of the rotating part, G 1 is the weight of the pinion, D 1 is the diameter of the pinion, G 2 is the weight of the large gear, D 2 is the diameter of the large gear, G g is the drum weight, D g is the roller diameter, ω is the angular velocity of the reel, r is the roller radius, η c is the transmission efficiency, g is the acceleration due to gravity, F n is the tension at the end of the cable; (3) Model-free adaptive controller design According to the model-free adaptive control principle based on compact dynamic linearization, the model-free adaptive controller is designed as （20） （21） In the formula, y ( k )∈ R , u ( k )∈ R They are k Output and input of the moment system; for k Pseudo partial derivative of the system output at time instant; y * ( k +1) k +1 The expected output value of the system at time λ >0 is the weight factor, which is used to limit the change of input quantity; ρ is the step size factor, ρ ∈(0,1]; for The initial value of ε is a sufficiently small positive number; △ u ( k -1) u ( k -1) Change, △ u ( k -1)= u ( k -1)- u ( k -2); sign( * ) is a symbolic function used to determine * The positive and negative situation of △ y ( k -1) y ( k -1) Change, △ y ( k -1)= y ( k -1)- y ( k -2); μ is the penalty factor for the pseudo partial derivative estimate, μ >0; η is the step size factor of the pseudo partial derivative, η ∈(0, 1], making the control more flexible; Step 4: Modeling and simulation of active compensation model-free adaptive control system for electric drive winch The controllers of the electric-driven winch system are respectively adopted as the model-free adaptive controller (MFAC) and the PID controller. The linear velocity of the cable end is taken as the expected output value of the system. The angular velocity of the drum is output by the speed encoder and converted into the linear velocity of the drum as the feedback input signal of the MFAC controller. The output signal is the voltage signal at the input end of the frequency converter. According to the above method, an active compensation model-free adaptive control system for the electric-driven shipborne tethered balloon winch under wind and wave disturbance is designed, and simulation and analysis are carried out. By calculating the absolute error, relative error, average error and average relative error between the system output and the expected output, the control effects of the two control methods are compared and analyzed. The calculation expression is: （22） （23） （24） In the formula, e k for k The absolute error between the system output and the expected value at that moment, e a is the average error, ξ k for k The relative error between the system output and the expected value at a given moment.

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