GB2618860A - Path tracking method for air cushion vehicle - Google Patents
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
- G05D1/02—Control of position or course in two dimensions
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
- G05D1/10—Simultaneous control of position or course in three dimensions
- G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft
Abstract
A path tracking method for an air cushion vehicle. The method comprises: establishing a track direction mathematical model and a longitudinal speed control mathematical model for an air cushion vehicle; designing an SFLOS curve path guidance algorithm, so as to obtain a path parameter update rate and an expected track angle; separately designing expanded state observers to observe external uncertain interference; designing, by using an integral barrier Lyapunov function, a bow steering torque control law to constrain a slew rate, such that the slew rate is within a safe limit, and the actual track angle of the air cushion vehicle tracks the expected track angle; and designing, by using a symmetrical logarithmic barrier Lyapunov function, a longitudinal thrust control law to constrain a sideslip angle, such that the sideslip angle is within a safe limit, and the actual longitudinal speed of the air cushion vehicle tracks an expected longitudinal speed. Therefore, an air cushion vehicle tracks an expected path while ensuring that a slew rate and a sideslip angle are within respective safe limits.
Description
SPECIFICATION
Air Cushion Hovercraft Path Following Method
FIELD OF THE INVENTION
[0001] The invention relates to an air cushion hovercraft path following method, in particular to the air cushion hovercraft path following method with sideslip angle and turning rate constraints, and belongs to the technical field of control.
BACKGROUND OF THE RELATED TECHNOLOGY
[0002] The air cushion hovercraft is a kind of special ship that relies on a cushion system to sail on water in a cushioned status. In the high-speed sailing process of the air cushion hovercraft, especially in the turning process, accidents such as sideslip, drift and even capsizing due to instability are prone to occur if the ship is inappropriately operated. Thus, during the motion control research of the air cushion hovercraft, it is extremely necessary to take the sailing safety of the air cushion hovercraft into consideration, and the consideration is also necessary during the path following research of the air cushion hovercraft.
[0003] For path following of the air cushion hovercraft, the main factors that may influence sailing safety are the turning rate and the sideslip angle. The turning rate in the turning process of an air cushion hovercraft in high-speed sailing is prone to exceed the safe limits, and furthermore, the sideslip angle in the turning process of the air cushion hovercraft may exceed the safe limits due to the excessive large turning rate, so a control method should be used to restrict the turning rate and the sideslip angle to their respective safe limits.
SUMMARY OF THE INVENTION
[0004] Aiming at the above-mentioned existing technology, the invention shall solve the technical problem by providing an air cushion hovercraft path following method with sideslip angle and turning rate constraints based on an SFLOS guidance algorithm, which can follow a straight path and a curve path and can restrict the turning rate and the sideslip angle to their respective safe limits by the constraint control method.
[0005] In order to solve the above-mentioned technical problem, the air cushion hovercraft path following method comprises the following steps that: [0006] Step 1: a four-degree-of-freedom motion mathematical model of an air cushion hovercraft is established, and a track control mathematical model and a longitudinal velocity control mathematical model of the air cushion hovercraft are determined on the basis of the four-freedom-degree motion mathematical model; [0007] Step 2: an SFLOS curve path guidance algorithm is designed to obtain a path parameter updating rate e and a desired track angle
SPECIFICATION
[0008] Step 3: according to the track control mathematical model and the longitudinal velocity control mathematical model in Step 1, extended state observers are designed respectively to observe uncertainties of external disturbance; [0009] Step 4: integral barrier Lyapunov functions are introduced to design a coursing changing moment control law to constrain a turning rate in path following control and keep the turning rate within safe limits in the path following process, and an actual track angle of the air cushion hovercraft can follow the desired track angle wild; [0010] Step 5: symmetric and logarithmic barrier Lyapunov functions are introduced to design a longitudinal thrust control law to constrain a sideslip angle in path following control and keep the sideslip angle within safe limits in the path following process, and an actual longitudinal velocity of the air cushion hovercraft can follow a desired longitudinal velocity.
[0011] The air cushion hovercraft path following method ilirther comprises that: [0012] 1. the track control mathematical model and the longitudinal velocity control mathematical model of the air cushion hovercraft in Step I are as follows: [0015] wherein, w" is the actual track angle, 0 is the sideslip angle and is assumed to be a measurable quantity, di is a component of the external uncertainty disturbance on the course changing degree of freedom, Dr is dynamic uncertainties on the course changing degree of freedom, di is a component of the external uncertainty disturbance on the surge degree of freedom, and Dll is dynamic uncertainties on the surge degree of freedom; r is a course changing angular velocity/ turning rate of the air cushion hovercraft in a ship coordinate system; p represents a heeling angle of the air cushion hovercraft in a North East coordinate system; TR is the course changing moment generated by an air tudder; tp is the longitudinal thrust generated by an air propeller; v represents the transverse velocity of the air cushion hovercraft in the ship coordinate system; and Ma) represents a resultant force on the yaw degree of freedom with TR and removed, and Fn represents a resultant force on the surge degree of freedom with TR and TR removed.
SPECIFICATION
[0016] 2. the path parameter updating rate and the desired track angle 11) ].'d in Step 2 meet the conditions that: [0017] [0018] wherein, Igo is a rotation angle when the North East coordinate system is converted into the SF coordinate system, and we = arctan2 (y Po, x Po), xo and yo are coordinates of an arbitrary point on the desired path P(0) and meet the condition of - wherein and kx is a design parameter greater than zero; A is a front view distance parameter greater than zero along the tangential direction of the set path at P(0), and the specific form of A is as follows: [0019] [0020] wherein p, AlllaX and Amin are design parameters greater than zero, Amax > Amin, and the convergence rate of A can be regulated by regulating p. [0021] 3. The extended state observers in Step 3 are specifically: [0022] for the track control mathematic model, the extended state observer is specifically: [0024] wherein, ; is an observation value of ID,, is an observation error of iv", r is an observation value of r, is an observation value of Dr, 2,11 and k12 and k13 are design parameters that are greater than zero, and fal(e,a,6) is a continuous nonlinear power function with the following form [0026] e is v. '6 is a design parameter greater than zero and represents the length of a linear segment of fal(e,a,6) near the origin, a is a design parameter greater than zero and smaller than one, and sgn( ) is a sign function; [0027] for the longitudinal velocity control mathematic model, the extended state observer is specifically: [0025]
SPECIFICATION
[0029] wherein, is an observation value of u, eu is an observation error of u, is an observation value of Du, 2,01 and 2.37 are design parameters that are greater than zero, and e is eu.
[0030] 4. The course changing moment control law in Step 4 is specifically: [0031]Ip [0032] wherein, TR is the course changing moment generated by an air rudder, MA), represents a resultant force on yaw degree of freedom with TR removed, I, is the rotational inertia of the z-axis, D, is the dynamic uncertainties on course changing degree of freedom, is an observation value of Dr, Nand K3 are constants that are greater than zero, re is the turning rate deviation and meets the condition that re = r -rd, rd is a desired turning rate, and r is the course changing angular velocity/ turning rate, rma, is the safe limits of the turning rate r, and pi (re,rd) meets the condition that: [0033] [0034] 5. The longitudinal thrust control law in Step 5 is specifically: [0035] [0036] wherein, Ty is the longitudinal thrust generated by the air propeller, RD represents the resultant force on surge degree of freedom with Tp removed, D, is the dynamic uncertainties on the surge degree of freedom, D, is the observation value of Du, A.;:, and 92 are constants that are greater than zero, m is the mass of the air cushion hovercraft, v represents the transverse velocity of the air cushion hovercraft in the ship coordinate system, and r represents the course changing angular velocity/turning rate of the air cushion hovercraft in the ship coordinate system; and is the first derivative of the desired longitudinal velocity ud, sui is the selected linear sliding mode surface and meets the condition that sit 1 = Xrne, wherein X7 is the sliding mode surface gain and is greater than zero, lue and umm is the smallest velocity.
U -Ud
SPECIFICATION
[0037] The air cushion hovercraft path following method has the advantages that compared to the existing technology, the adopted SFLOS guidance algorithm can follow both straight path and curve path, and the problem that a conventional LOS guidance algorithm can only follow straight path is solved; a course changing moment controller with turning rate constraints and a longitudinal thrust controller with sideslip angle constraints based on the SFLOS guidance algorithm are applied to the path following process of the special object model of air cushion hovercraft, thus the problems that the turning rate and the sideslip angle are prone to exceed their respective safe limits in the path follow turning process of the air cushion hovercraft are solved, and the path following controller with turning rate constraints and sideslip angle constraints based on the SFLOS guidance algorithm can enable the longitudinal position error and the transverse position error in the path following process of the air cushion hovercraft to gradually converge to zero respectively.
BRIEF DESCRIPTION OF THE DRAWINGS
[0038] Fig.1 Schematic diagram of air cushion hovercraft path following with state constraints; [0039] Fig.2 Comparison diagram of air cushion hovercraft following desired path and actual motion path; [0040] Fig.3 Comparison diagram of longitudinal position error and transverse position error of air cushion hovercraft path following; [0041] Fig.4 Comparison diagram of sideslip angles during motion of the air cushion hovercraft when Pmax = 5.5 0; [0042] Fig.5 Comparison diagram of actual longitudinal velocity during motion of the air cushion hovercraft; [0043] Fig.6 Comparison diagram of track angles during motion of the air cushion hovercraft; [0044] Fig.7 Comparison diagram of actual turning rates during motion of the air cushion hovercraft when rmax = 1.2 'Is; [0045] Fig.8 Actual value and observation value of uncertainties of external disturbance.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0046] The air cushion hovercraft path following method shall be further illustrated with reference to the brief description of the drawings and the detailed description of the embodiments.
[0047] With reference to Fig.1 the embodiment of the invention specifically comprises the steps that:
SPECIFICATION
[0048] Step 1: an air cushion hovercraft four-degree-of-freedom motion mathematical model including an air cushion hovercraft four-degree-of-freedom kinematic mathematical model and an air cushion hovercraft four-degree-of-freedom dynamic mathematical model is established, and a track control mathematical model and a longitudinal velocity control mathematical model of the air cushion hovercraft are determined on the basis of the established model to prepare for deriving the longitudinal thrust control law and the course changing moment control law; [0049] Step t. t: an air cushion hovercraft four-degree-of-freedom motion mathematical model in the form of differential equations and including four degrees of freedom of surge, sway, heel and yaw is established as follows; [0050] [0051] wherein x, y, cp and p represent the north position, the east position, the heel angle and the heading angle respectively of the air cushion hovercraft in the North East coordinate system, while u, v, p and r represent the longitudinal velocity, the transverse velocity, the heeling angular velocity and the course changing angular velocity/turning rate respectively of the air cushion hovercraft in the ship coordinate system; wherein, [0052] [0053] [0054] wherein m is the mass of the air cushion hovercraft, F, F,, Mx and M, are the longitudinal resultant force, the transverse resultant force, the heeling resultant moment and the course changing resultant moment of the air cushion hovercraft respectively, I, and L are the rotational inertia of the air cushion hovercraft around the x-axis and the z-axis respectively, "LT is the longitudinal thrust generated by the air propeller and is the to-be-designed longitudinal thrust control law, and TR is the course changing moment generated by the air rudder and is the to-be-designed course changing moment control law; the subscripts a, m, h and R of each component force (moment) represent
SPECIFICATION
component force (moment) of aerodynamic force (moment), air momentum force (moment), hydrodynamic force (moment) and air rudder force (moment) on the four degrees of freedom of surge, sway, heel and yaw; F,D, En, MAD and Mai are the resultant force with tp and ni (if any) removed on the four degrees of freedom of surge, sway, heel and yaw; and the relationship between the sideslip angle (3 and the longitudinal and transverse velocity is as follows: [0056] Step 1.2: based on the established models above and considering the external uncertainty disturbance that the air cushion hovercraft is subjected to, the track control mathematical model and the longitudinal velocity control mathematical model of the air cushion hovercraft are as follows respectively: [0057] [0058] [0059] wherein, iff", is an actual track angle, 13 is a sideslip angle and is assumed to be a measurable quantity, di is a component of external uncertainty disturbance on the course changing degree of freedom, Dr is dynamic uncertainties on the course changing degree of freedom, di is a component of external uncertainty disturbance on the surge degree of freedom, and D" is dynamic uncertainties on the surge degree of freedom.
[0060] Step 2: an SFLOS curve path guidance algorithm is designed, the path parameter updating rate 0 and the desired track angle two are given, and the specific design process of the SFLOS guidance algorithm is as follows: [0061] Step 2.1: the track error is converted: the desired path P(0) of the air cushion hovercraft is defined as [xo,y0]T, wherein 0 is the path parameter. The position error vector in the SF coordinate system is [xe,y]', and the position error vector in the North East coordinate system is [x -xo, y -ye]i'. And the two vectors meet the following equation: [0062]
S
SPECIFICATION
[0063] wherein yo is the rotation angle when the North East coordinate system is converted into the SF coordinate system, and yo = arctan2 (y 'o, x 'o).
[0064] If the air cushion hovercraft can successfully follow the desired path, only a guidance law needs to be designed to ensure that [xe,ye]' gradually converge to zero.
[0065] Step 2.2: derive the track errors xe and ye in the SF coordinate system to obtain that: [0066] [0067] Step 2.3: Lyapunov functions are constructed as follows: [0068] [0069] de ve VE to obtain that: [0070] [0071] Step 2.4: in order to enable xe to gradually converge to zero, the path parameter updating rate can be designed as follows according to in Step 2.3: y, 43) [0072] [0073] wherein kx. is the design parameter that is greater than zero. Substitute the designed 0 into to obtain that: [0074] [0075] Step 2.5: in order to enable ye to gradually converge to zero, the track angle of the air cushion hovercraft is regarded as a virtual control quantity, and the virtual control law iirwo is designed as follows: [0076] [0077] wherein A is the front view distance parameter greater than zero along the tangential direction of the set path at target tracking point P(0).
[0078] Step 2.6: the dynamic front view distance parameter is designed as follows: [0079] 4-{ [0080] wherein p, A. and A. are design parameters that are greater than zero, and A. > Amin; and the convergence rate of A can be regulated by regulating p, A is taken as the time variable and can change adaptively, when the distance between the air cushion hovercraft and the desired path is comparatively large, ye is comparatively large, A is close to Ai., the value of A is small, the air
SPECIFICATION
cushion hovercraft can rapidly approach the desired path, and ye can rapidly decrease; when the air cushion hovercraft sails to the surrounding area of the desired path, ye is comparatively small, A is close to Ana, the value of A is large, the decreasing speed of ye is slow, and overshoot of ye can be avoided, [008]] Step 2.7: the track angle error is stabilized. The track error of the virtual control quantity 111wd is defined as follows: [00821 [0083] then: [0085] Step 2.8: substitute Wv into (3 -19) to obtain that: [0086] [0087] If the control law is designed to enable 45-to gradually converge to zero, that is, AIN iihNd can gradually converge to zero, then it can be obtained that: [0088] [0089] In conclusion, the specific expression of the SFLOS guidance algorithm is as follows: [0090] [0091] wherein 0 is the path parameter updating rate, tit"d is the desired track angle, U is the actual resultant velocity, ma) is the rotation angle when the North East coordinate system is converted to the SF coordinate system, and ye = arctan2 (y '0,x '0), xe and ye are the coordinates of an arbitrary path point on the desired path P(0) and meet the condition of the following expression: [0092] [0093] wherein kx is the design parameter that is greater than zero; and A is the front view distance parameter greater than zero along the tangential direction of the set path at P(0);
SPECIFICATION
[0094] Step 3: according to the track control mathematical model and the longitudinal velocity control mathematical model in Step 1.2, the extended state observers are designed respectively to observe the external uncertainty disturbance, and the uncertainties of the external disturbance is compensated during the subsequent design process of the course changing moment control law and the longitudinal thrust control law respectively.
[0095] Step 3.1: for the air cushion hovercraft track control mathematical model with Dr, the extended state observer is designed as follows: [0096] [0097] wherein, is an observation value of 4),,, is an observation error of Ili icz is an observation value of r, is an observation value of Dr. XII, k12 and)cu are design parameters that are greater than zero, and fal(e,a,S) is a continuous nonlinear power function with the following form: [0098] [0099] e is is a design parameter that is greater than zero and represents the length of a linear segment of fal(e,a,o) near the origin, a is a design parameter that is greater than zero and smaller than one, and sgn( * ) is a sign function; [0100] Step 3.2: for the air cushion hovercraft longitudinal velocity control mathematical model with Da, the extended state observer is designed as follows: [0101] [0102] wherein is an observation value of u, e is an observation error of u, , is an observation value of Du, k21 and X22 are design parameters that are greater than zero, and e here is eu.
[0103] Step 4 the course changing moment control law is designed based on integral barrier Lyapunov functions B3LF to constrain the turning rate in the path following process, the actual track angle of the air cushion hovercraft can be enabled to successfully follow the desired track angle
SPECIFICATION
generated by SFLOS guidance law, and the transverse position error of the air cushion hovercraft can be further enabled to gradually converge to zero; and the turning rate in the path following process of the air cushion hovercraft can be guaranteed to be within the safe limits of the turning rate.
[0104] Step 4.1: the track angle deviation is defined as follows: [0105] [0106] wherein iti,vd is the desired track angle; and based on the track control model of the air cushion hovercraft, it can be obtained that: [01071 [0108] Step 4.2: the second-order sliding mode surface is taken as follows: [0109] [0110] wherein xs is the sliding mode surface gain and is a constant greater than zero, and then [0111] [0112] Step 4.3: the constant-velocity reaching law is taken as follows: [0113] [0114] wherein K2 is a constant and is greater than zero, sgn( ) is a sign function, and then [0115] [0116] the virtual control law rd can be designed as follows: [01171 [0118] Step 4.4: due to that [0119] r = re+rd [0120] substitute rd into r, and then substitute r into to obtain that: c6seijK'sgat,c,, )dt [0121] [0122] Step 4.5: the turning rate deviation is defined as follows: [0123] rer -rd [0124] wherein rd is the desired turning rate, derive both sides of the above equation, and based on the track control model of the air cushion hovercraft in Step 1.3, it can be obtained that:
SPECIFICATION
[0125] [0126] IBLF is taken as: [0127] [0128] [0129] [0130] wherein rmax is the safe limits of the turning rate r, that is, < rmax Step 4.6: derive V3 to obtain that: [0131] [0132] wherein y is taken as an integral variable, and according to integration by parts and substituting with G = 7 re to obtain that: [0133] [0134] the course changing moment control law can be designed as follows: [0135] [0136] wherein " ] is the observation value of the external disturbance Dr, and K3 are constants greater than zero.
[0137] Step 4.7: stability analysis is carried out, and the Lyapunov function is taken as follows: [0138] [0139] derive both sides of the equation V2 to obtain: [0140] [0141] it can be obtained from the above equation that if re and can all gradually converge to zero, or re and can all gradually converge to a small neighborhood of zero, then [0142]
SPECIFICATION
[0143] then will gradually converge to zero, thus xif1/4, and will gradually converge to zero; be achieved, thus re will gradually converge to zero; the idea of exponential reaching law is applied to the design process of Tie, so the process that re converges to zero is smooth and basically without buffeting, then f. will converge to a small neighborhood of zero; and furthermore, holds permanently, then will gradually converge to zero, so and ft, will gradually converge to zero.
[0147] Step 5: symmetric and logarithmic barrier Lyapunov function LBLF is applied to constrain the sideslip angle in the path following process to design the longitudinal thrust control law, the actual longitudinal velocity of the air cushion hovercraft can be enabled to follow the desired longitudinal velocity, and the sideslip angle in the path following process of the air cushion hovercraft can be ensured to be within the safe limits of the sideslip angle. At the same time, the designed longitudinal thrust control law can ensure that the air cushion hovercraft can avoid the sailing range close to the resistance peak velocity, so as to avoid the unstable sailing state of the air cushion hovercraft, and the condition of stall in the turning process of the air cushion hovercraft can also be prevented.
[0148] Step 5.1: the sideslip angle constraints are converted into longitudinal velocity constraints. According to the relationship between the sideslip angle p and the longitudinal velocity and transverse velocity, it can be determined that: [0149] can K. thus, the gain is designed as ' [0144] substitute TR into to obtain that: sgni) [0145] [0146] wherein boundary value of l, that is, is the observation error of external disturbance ' is the
SPECIFICATION
[0150] suppose the sideslip angle meets the following condition that: [0151] [0152] wherein f3max is the safe limits of the sideslip angle. [0153] Step 5.2: according to [0154] [0155] it can be obtained that: [0156] [0157] Step 5.3: longitudinal velocity is planned based on the longitudinal velocity constraints and the desired velocity. Suppose the initial longitudinal velocity u(0) meets the following expression that: [0158] umin (0)<u(0)<2ud (0) -umin (0) [0159] wherein umm(0) is the initial value of the to-be-reached minimum velocity umm during sailing, the expression of umm(0) is as follows: [0160] [0161] sailing; [0162] the initial desired longitudinal velocity ud(0) meets the following expression that: [0163] ud (0)>umin (0) [0164] Step 5.4: the programming function of the longitudinal velocity is designed as follows: umin(0) is the initial value of the to-be-reached minimum velocity umin during [0165] [0166] wherein [0167] [0168] kn, ö and c11 min are constants greater than zero The time-varying ud is selected, and then appropriate parameters are selected to enable the expression ud > umin to hold permanently.
[0169] Step 5.5: the longitudinal thrust control law is designed based on the LBLF. The absolute value of the longitudinal velocity deviation is defined as follows:
SPECIFICATION
[0170] ue U -Ud I [0171] the correlated variables of the LBLF boundary function are defined as follows: [0172] [0173] suppose the absolute value of ue meets the following condition that: [0174] [0175] Step 5.6: the linear sliding mode surface is taken as follows: [0176] sui = 2Que [0177] wherein A.2 is the sliding mode surface gain and is greater than zero, then [0178] [0179] Step 5.7: the LBLF is taken as follows: [0180] [0181] let [0182] then the above expression can be rewritten as: [0183] derive the above expression and combine with the longitudinal velocity control mathematical model in Step 1.3 to obtain that: [0185] according to the above expression, the longitudinal thrust control law can be designed as follows: [0187] wherein is the observation value of D", and rp are constants greater than zero [0188] Step 5.8: stability analysis is carried out, substitute Tp into to obtain that:
SPECIFICATION
[0190] wherein is the boundary value of that is, e gain is taken as then and ue will gradually converge to zero, [0191] the expression of path following controller without state constraints based on the SFLOS guidance algorithm is given in comparison with the path following controller with the turning rate and sideslip angle constraints based on the SFLOS guidance algorithm, and its specific form is as follows: [0195] wherein si and su are second-order sliding mode surfaces; rd is the virtual control law, TR is the course changing moment control law, and -cp is the longitudinal thrust control law, and 2, K3, Ad and Kt are constants greater than zero [0196] The part of simulation drawings in the attached drawings mainly compares the simulation drawing of the air cushion hovercraft path following with the turning rate and the sideslip angle constraints based on the SFLOS guidance algorithm and the simulation drawing of the air cushion hovercraft path following without state constraints based on the SFLOS guidance algorithm.
SPECIFICATION
[0197] According to Fig.2, the air cushion hovercraft path following controller with the turning rate and the sideslip angle constraints and the air cushion hovercraft without state constraints (hereinafter referred to as "with state constraints" and "without state constraints") can both follow the desired sine curve path. According to Fiu.3, at around 371 seconds, the longitudinal position deviation of the one without state constraints is almost zero, and the absolute value of the longitudinal position deviation of the one with the state constraints is about 0.2 meters; and from 350 seconds to 450 seconds, the transverse position deviation of the one without state constraints is close to zero, and the transverse position deviation of the one with state constraints fluctuates relatively greatly, which means the following sine curve path without state constraints can achieve better effect. According to Fig.4, Fig.5 and Fig.7, the sideslip angle, actual longitudinal velocity and turning rate of the air cushion hovercraft with state constraints did not exceed their respective boundary values of rilmax -5.5 °, umin and rrna, = 1.2 °/s, while the sideslip angle, actual longitudinal velocity and turning rate of the air cushion hovercraft without state constraints exceeded their respective boundary values at about 70 seconds, which shows the effectiveness of the designed controller with state constraints. According to Fig.6, the track angle controller without state constraints and the track angle controller with state constraints can both follow the desired track angle generated by the SFLOS guidance algorithm respectively. According to Fig.8, the designed extended state observers can observe external interference of the component of external uncertainty disturbance on the surge degree of freedom and on the course changing degree of freedom well.
[0198] In Fig.5, the one with the sideslip angle and turning rate constraints and the one with sideslip angle and turning rate constraints limn, are set to one group, and the one without state constraints and the one without state constraints Limn, are set to one group; and according to Fig.5, the one with sideslip angle and turning rate constraints umin is smaller than the actual longitudinal velocity of the air cushion hovercraft with sideslip angle and turning rate constraints all the time, while the one without state constraints unth, significantly exceeded the actual longitudinal velocity of the air cushion hovercraft without state constraints at about 100 seconds.
Claims (6)
- CLAIMS1. An air cushion hovercraft path following method is characterized by comprising the following steps that: Step 1: a four-degree-of-freedom motion mathematical model of an air cushion hovercraft is established, and a track control mathematical model and a longitudinal velocity control mathematical model of the air cushion hovercraft are determined on the basis of the fourfreedom-degree motion mathematical model; Step 2: an SFLOS curve path guidance algorithm is designed to obtain a path parameter updating rate o and a desired track angle -kv,a; Step 3: according to the track control mathematical model and the longitudinal velocity control mathematical model in Step 1, extended state observers are designed respectively to observe uncertainties of external disturbance; Step 4: integral barrier Lyapunov functions are introduced to design a course changing moment control law to constrain a turning rate during path following control, thus the turning rate can be kept within safe limits in the path following process and an actual track angle of the air cushion hovercraft can be enabled to follow the desired track angle Twa; Step 5: symmetric and logarithmic barrier Lyapunov functions are introduced to design a longitudinal thrust control law to constrain a sideslip angle during path following control, the sideslip angle can be kept within safe limits in the path following process and an actual longitudinal velocity of the air cushion hovercraft can be enabled to follow a desired longitudinal velocity.
- 2. According to claim 1, the air cushion hovercraft path following safe control method is characterized in that the track control mathematical model and the longitudinal velocity control mathematical model of the air cushion hovercraft in Step 1 are as follows:CLAIMSwherein, w", is an actual track angle, 0 is a sideslip angle and is assumed to be a measurable quantity, di is a component of external uncertainty disturbance on course changing degree of freedom, 1:), is dynamic uncertainties on course changing degree of freedom, di is a component of external uncertainty disturbance on surge degree of freedom, and Do is dynamic uncertainties on surge degree of freedom; r is a course changing angular velocity/ turning rate of the air cushion hovercraft in a ship coordinate system; w represents the heeling angle of the air cushion hovercraft in a North East coordinate system; TR is the course changing moment generated by an air rudder; -rp is the longitudinal thnist generated by an air propeller; v represents the transverse velocity of the air cushion hovercraft in the ship coordinate system; and MA, represents a resultant force on yaw degree of freedom with fp and tp removed, and FxD represents a resultant force on surge degree of freedom with fp and tp removed.
- 3. According to claim 1 or claim 2, the air cushion hovercraft path following method is characterized in that the path parameter updating rate e) and the desired track angle in Step 2 meet the conditions that: wherein, wo is a rotation angle when the North East coordinate system is converted into the SF coordinate system, and wo =arctan2 (y '0, x '0), xo and yo are coordinates of an arbitrary point on the desired path P(0) and meet the condition of wherein, " and lc. is a design parameter that is greater than zero; A is a front view distance parameter greater than zero along the tangential direction of the set path at P(0), and the specific form of A is as follows: (4,:s wherein p. A. and Amm are design parameters that are greater than zero, A. > Amm, and the convergence rate of A can be regulated by regulating IA 4 According to claim 1 or claim 2, the air cushion hovercraft path following method is characterized in that extended state observers in Step 3 are specifically: for the track control mathematic model, the extended state observer is specifically:CLAIMSwherein is an observation value of ww, is an observation error of ww, is an observation value of r, is an observation value of Dr, XH and A47 and X13 are design parameters that are greater than zero, and fal(e,a,6) is a continuous nonlinear power function with the following form: e is 4,"5 is a design parameter that is greater than zero and represents the length of a linear segment of fal(e,a,6) near the origin, a is a design parameter that is greater than zero and smaller than one, and sgn( -) is a sign function; for the longitudinal velocity control mathematic model, the extended state observer is specifically: wherein, *U is an observation value of u, ee is an observation error of u, D is an observation value of Du, X11 and k22 are design parameters that are greater than zero, and e is ee 5. According to claim 1 or claim 2, the air cushion hovercraft path following method is characterized in that the course changing moment control law in Step 4 is specifically:
- Awherein, TR is the course changing moment generated by an air rudder, Mau represents a resultant force on yaw degree of freedom with TR removed, L is the rotational inertia of the z-axis, DE is the dynamic uncertainties on course changing degree of freedom, L is an observation value of Dr, and 1(3 are constants that are greater than zero, re is the turning rate deviation and meets the
- CLAIMScondition that re = r -rd, rd is a desired turning rate, and r is the course changing angular velocity/ turning rate, r",", is the safe limits of the turning rate r, and pi (re,rd) meets the condition that.
- 6. According to claim 1 or claim 2, the air cushion hovercraft path following method is characterized in that the longitudinal thrust control law in Step 5 is specifically: wherein, -re is the longitudinal thrust generated by the air propeller, Ficu represents the resultant force on surge degree of freedom with 're removed, Da is the dynamic uncertainties on the surge degree of freedom, is the observation value of D", and fl2 are constants that are greater than zero, m is the mass of the air cushion hovercraft, v represents the transverse velocity of the air cushion hovercraft in the ship coordinate system, and r represents the course changing angular velocity/ turning rate of the air cushion hovercraft in the ship coordinate system; and n',,r is the first derivative of the desired longitudinal velocity ud, 5"1 is the selected linear sliding mode surface and meets the condition that s" i = kale, wherein X2 is the sliding mode surface gain and is greater than zero, lue I = U -Ud and urn in is the smallest velocity.
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| PCT/CN2022/070350 WO2023050636A1 (en) | 2021-09-29 | 2022-01-14 | Path tracking method for air cushion vehicle |
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