CN107145074A - A kind of high-speed trimaran pitching stabilization control method based on sliding moding structure convergence law - Google Patents

Abstract

The invention provides a method for pitch reduction control of a high-speed trimaran based on sliding mode variable structure approach law. This method designs random wave models of different levels; uses the ANSYS platform to analyze and obtain the hydrodynamic coefficient of the trimaran, establishes the mathematical model of the longitudinal motion of the trimaran, and obtains the heave height and pitch angle in response to the longitudinal motion; Angle is the input, and a sliding mode variable structure control law based on reaching law is designed to obtain the change in the output flow angle; the longitudinal motion model of the T-shaped wing of the anti-rolling appendage and the wave control plate is established, and the change of the incoming flow angle of the anti-rolling appendage is The quantity is used as the input of the anti-rolling appendage control system, and the output is the longitudinal force and moment provided by the anti-rolling appendage for the trimaran, and the feedback acts on the longitudinal motion system of the high-speed trimaran. The method can be applied to the stability control of military and civilian multihull ships, and can effectively reduce the influence of waves on the motion stability of the trimaran and improve passenger comfort.

Description

A Pitching Control Method for High Speed Trimaran Based on Sliding Mode Variable Structure Approach Law

technical field

The invention belongs to the field of anti-rolling control of high-speed trimaran longitudinal motion, in particular to a method for anti-rolling control of high-speed trimaran based on sliding mode variable structure approach law.

Background technique

Both classical control theory and modern control theory require the controlled object to have a clear mathematical model, but the actual controlled object is not ideal. The system mechanism may be complex, large in scale, with many variables, variable and coupled parameters, or the system In the case of nonlinearity, uncertainty, time-varying, and hysteresis, traditional control theory is difficult to use mathematics to analyze and establish a mathematical model that conforms to the law of motion. Usually, linearization should be used for nonlinear modeling, lumped parameters should be used for distribution parameters, and constant coefficients should be used for time-varying coefficients. There may be great discrepancies between modeling and reality, so traditional control algorithms are difficult to work in actual control. The traditional control method such as PID controller is used in the trimaran longitudinal anti-rolling control system. Although the algorithm is simple, it is only suitable for the system with constant parameters of the controlled object and non-serious nonlinearity. Dynamic control is realized during navigation, and according to the experimental results, its control effect is far from meeting the requirements. The optimal control effect of the LQR control method depends on the selection of the weighting matrix Q and R, which will produce a large workload and a large error.

The advantage of the sliding mode variable structure control method is that it can be designed and has nothing to do with the object parameters and disturbances, and it can respond quickly, has strong anti-disturbance ability, and is simple in physical implementation. For the anti-rolling control of high-speed trimaran, the traditional PID control method can no longer satisfy the fast and nonlinear real-time control in complex and irregular sea conditions, and the sliding mode variable structure can better adapt to these conditions due to its above characteristics. However, there is no clear design for the application of the sliding mode method to the pitch reduction of emerging high-speed trimarans.

Contents of the invention

The object of the present invention is to provide a high-speed trimaran pitch reduction control method based on sliding mode variable structure approach law that can better improve the longitudinal motion stability of a high-speed, slender trimaran.

A kind of pitch reduction control method of a high-speed trimaran based on sliding mode variable structure approach law of the present invention comprises the following steps:

Step 1: Design random wave models of different levels according to the wave standard of the International Meteorological Bureau;

Step 2: Using the random wave model, use the ANSYS platform to analyze and obtain the hydrodynamic coefficient of the trimaran, and then establish a mathematical model of the longitudinal motion of the high-speed trimaran according to the hydrodynamic coefficient, and obtain the heave height and pitch angle of the longitudinal motion of the high-speed trimaran ;

Step 3: Using the longitudinal motion of the above-mentioned high-speed trimaran to respond to the heave height and pitch angle, design a sliding mode variable structure control law based on the reaching law, and obtain the change in the control output head angle;

Step 4: Establish the lift and moment calculation model of the T-shaped wing of the anti-rolling appendage and the wave suppression plate, and use the change of the oncoming angle of the anti-rolling appendage to obtain the longitudinal force and moment provided by the anti-rolling appendage for the trimaran, and the feedback acts on Longitudinal motion system of high-speed trimaran.

The random sea wave model described in step 1 is specifically:

(1) According to the different significant wave heights H and frequency bands corresponding to different levels of waves specified by the International Meteorological Organization, use MATLAB programming to realize the establishment of different levels of random wave models;

(2) The model is established based on the rational spectrum method, and the designed rational spectrum is defined as follows:

Among them, S _x (ω) is the power spectral density function of the involved real stationary random process X(t), P(ω) and Q(ω) are ω real coefficient polynomials and the order of the denominator must be higher than that of the numerator;

The final model of the wave is:

ε _i represents the phase angle of the ocean wave, which is considered as a random variable in the interval (0, 2π), that is, ε _i =rand(0,2π), the power spectrum of S(w _i ) ocean wave at the circular frequency w _i Density, N is the number of samples;

(3) The input of the wave module is the clock, and the output is used as the input of the following modules.

The trimaran longitudinal motion model described in step 2 is specifically:

(1) Using the ANSYS platform to analyze and obtain the hydrodynamic coefficient of the trimaran at different speeds;

(2) According to the speed of the trimaran in the sea, the wave model and the encounter frequency, the "ss2tf" function of the MATLAB platform is used to realize the specific decoupling and solution of the longitudinal motion model of the trimaran.

The sliding mode variable structure control law based on reaching law described in step three is specifically:

(1) Establish the variable structure control of the longitudinal motion control system of the trimaran:

The exponential reaching law is designed as:

in: is the exponent approach term;

Get variable structure control:

(2) Soften the control law:

Among them, ξ is a small integer selected independently;

The final sliding mode variable structure control law based on reaching law is:

Among them, the parameter ε determines the robust performance of the system, the larger the value, the better the robust performance; the parameter q determines the speed at which the control system gradually approaches the hyperplane, the larger the q, the faster the system approaches, and A and B are the system states Matrix, C is the control matrix to be sought, which can be obtained by using the MATLAB compilation platform and using the pole allocation method, and ξ is a small integer selected independently.

The lift and moment calculation model of the anti-roll T-wing attached to the body and the wave control plate described in step 4:

There is a nonlinear relationship between the amount of change in the incoming flow angle and the force provided for the longitudinal direction of the trimaran corresponding to this angle, and the moment corresponding to the force is obtained at the same time:

M _T/F = d _a F _T/F

In the formula: ρ is the seawater density, 1.025×10 ³ kg/m ³ ; A is the projected area of T-shaped wing or wave breaker, V is the speed of the ship; α is the change in the angle of attack of the anti-rolling appendage; C _L ( α) is the lift coefficient of the anti-rolling appendage, which can generally be regarded as a constant when the angle of attack α is small; d _a is the vertical distance between the installation position of the T-shaped wing and the center of gravity; F _t , F _f and M _t , M _f represent the lift and moment provided by the T-shaped wing and the breaker, respectively.

The control method designed by the invention is aimed at the longitudinal antirolling of the currently most commonly used high-speed trimaran when navigating in the sea, and obviously reduces the heave and pitch of the hull in motion. The sliding mode control method has been applied to the longitudinal anti-rolling function of the high-speed trimaran, which is suitable for the sea navigation environment with complex sea conditions and high speed, and can be applied to the stability control of military and civilian multi-hull ships, and can effectively reduce the The impact of waves on the motion stability of the trimaran improves the comfort of passengers.

Description of drawings

Fig. 1 (a) is the SSN5 level random ocean wave three-dimensional model that the International Meteorological Bureau of Design stipulates in the present invention;

Fig. 1 (b) is the SSN6 grade random ocean wave three-dimensional model that the International Meteorological Bureau of Design stipulates in the present invention;

Fig. 2 is the structural block diagram of the control system that the present invention designs;

Fig. 3 is a flowchart of the control method of the present invention;

Fig. 4 is a structural diagram of a trimaran longitudinal motion model of the present invention.

detailed description

The present invention will be described in detail below in conjunction with the accompanying drawings.

The flow chart of the high-speed trimaran pitch reduction control method based on the sliding mode variable structure approach law is shown in Figure 3, and the specific process is as follows:

(1) Establishment of random wave model:

Ocean waves can be considered to be composed of a series of cosine waves with different amplitudes, wavelengths, and initial phases. The instantaneous wave height of ocean waves can be expressed as:

Among them, H is the average tidal height of the sea surface, ζ _i is the amplitude of the component wave, _ki is the wave number, θ _i is the angle between the propagation direction of the component wave and the x-axis, ω _i is the angular frequency of the component wave, and ε _i is the component wave The phase angle of can be considered as a random variable in the interval (0,2π), x is the width of the instantaneous wave along the x-axis direction, and z is the height of the instantaneous wave along the z-axis direction.

In the experiment, the average sea level wave height H=0 and fixed, the wave model can be simplified as:

Discretization using the rational spectral method:

A rational spectrum is defined as follows:

Among them, S _x (ω) is the power spectral density function of the involved real stationary random process X(t), P(ω) and Q(ω) are polynomials with real coefficients of ω and the order of the denominator must be higher than that of the numerator.

The approximation spectrum form of the unreasonable ocean wave is as follows:

Let s=jω, then:

According to the parameter estimation theory, we know that:

S(ω _i )＝S _x (ω _i ) (6)

Wherein, i=1, 2,..., N, (N>2n) and S(ω) is the power spectral density of the ocean wave:

Among them, A=8.10×10 ^-3 g ² , is the significant wave height, and ω is the wave circular frequency.

Substituting the above formula into (2) to obtain the final model of the ocean wave is:

Among them, ε _i represents the phase angle of the ocean wave, which is considered as a random variable in the interval (0, 2π), that is, ε _i =rand(0,2π), S(w _i ) is the wave at the circular frequency w _i The power spectral density of , N is the number of samples.

Examples of 3D images of SSN5 and SSN6 stochastic wave models are shown in Fig. 1(a) and Fig. 1(b).

The input of the wave module is the clock, and the output is used as the input of the following modules.

(2) Trimaran longitudinal motion model design:

First, use the AQWA software module of the ANSYS Workbench platform to conduct experiments, adjust the draft by moving the model, and because the entity cannot be calculated in AQWA, the model is then shelled to obtain a shell whose outer surface thickness is set to 0; Carry out waterline cutting for the high-speed trimaran and construct the overall structure of the ship. Then set the radius of gyration after inserting the center of mass: K _xx =0.163m, K _yy =0.807m, K _zz =0.807m. Finally, set the circular frequency: the circular frequencies used in the experiment at a speed of 40 knots are: 0.42249rad/s, 0.56275rad/s, 0.69203rad/s, 0.81299rad/s, 0.92691rad/s, 1.03491rad/s, 1.18757rad /s, 1.42196rad/s, 1.63671rad/s. Find the generated .DAT file in the folder obtained by simulation, and get the hydrodynamic coefficients a _ii , b _ii , c _ii of the trimaran after being processed by Aqwa16.0.

It can be seen from Fig. 4 that the system design is divided into the wave-force conversion part and the force-angle conversion part, and the final output is the longitudinal heave height and pitch angle of the trimaran.

According to d'Alembert's theory, the coupled equation of pitch and heave of high-speed ship can be obtained:

The left side of the equation is the dynamic model of the ship, and the right side is the relationship between waves and forces. The motion model of the ship under the action of force can be deduced from the left side of the equation, and the force model of the ship under the action of waves can be deduced from the right side. In the formula, m ₃₃ is the mass of the ship, a _ij is the additional mass of seawater to the ship, x ₃ is the heave, b _ij is the damping coefficient, c _ij is the restitution coefficient, x ₅ is the pitching amount, m ₅₅ is the pitching inertia These hydrodynamic coefficients are simulated on the ANSYS platform according to the size parameters of different trimarans. F _t , F _f and M _t , M _f represent the lift and moment provided by the T-shaped wing and the wave suppressor, respectively, and F _wave and M _wave are the heave disturbance force and pitch disturbance moment of the waves acting on the trimaran, respectively.

When the trimaran is at different sailing speeds and different encounter frequencies, different wave-force and force-angle transfer function equations can be obtained according to equation (10). When the selected speed is 40 knots, the sea wave is SSN5, and the encounter frequency is 1.5rad/s, the transfer function equation that can be obtained is as follows:

Force-heave:

Moment-heave:

Force-Pitch:

Moment-Pitch:

(3) Design of sliding mode variable structure module

The state space equation of the longitudinal motion linear differential equation of the trimaran is expressed as:

In the formula: is the control vector, where x ₃ and is the heave displacement and heave velocity, x ₅ and are the pitch angle and pitch angular velocity.

Choose the linear switching function accordingly:

S(x)=Cx(t) (14)

Design sliding mode surface: According to the sliding mode variable structure control theory, there are:

s(x)=Cx=C ₁ x ₁ +C ₂ x ₂ ＝0 (15)

The above formula can be derived on the hyperplane:

The sliding equation of the system is obtained as:

Establish variable structure control for the longitudinal motion control system of the trimaran:

Using the most widely used exponential reaching law:

in: is an exponential approach term, then the system state space equation can be obtained:

After introducing the exponential reaching law, the sliding mode control law with the A, B, C, and D matrices in the state space equation of the longitudinal motion system as parameters can be obtained. Among them, the unknown item is only the C matrix, using the MATLAB compilation platform, and using the pole allocation method Find the C matrix;

Variable structure control is available:

Among them: the size of the parameter q determines the speed of approaching the switching hyperplane, the larger the value, the faster the speed, but if it is too large, it will cause shocks; the size of the parameter ε determines the robustness of the system, the larger the value The larger the value, the better the robustness, but the larger the chattering amplitude will be and affect the steady-state accuracy of the system.

Soften the control law to prevent chattering:

So the final sliding mode control law is:

The only thing that needs to be determined is the matrix C, and the calculation of C can be realized by using the pole configuration method through MATLAB programming. When the trimaran is at different speeds and the encounter frequency is different, different switching functions of the sliding mode variable structure will be obtained Matrix C.

Substituting these switching function matrices C into the sliding mode control law formula (23), the corresponding sliding mode variable structure trimaran longitudinal motion anti-rolling control method can be obtained, so as to realize the nonlinear dynamic control of trimaran longitudinal motion anti-rolling .

(4) Design of anti-rolling attachment control module

ANSYS 16.0 is used for parametric solution, and the speed is fixed at 40 knots/hour. In the experiment, both the T-shaped wing and the wave breaker use the change of the angle of attack as a parameter, and the input of the two is processed by the sliding mode controller. The adjustment angle obtained after the response, this angle is the difference between the required angle and the current on-flow angle, so the calculation models of the lift and moment changed by the angle change provided by the sliding mode control law are:

M _t/f = d _a F _t/f (25)

Where: ρ is the seawater density, 1.025×10 ³ kg/m ³ ; A is the surface area of the T-shaped wing, m ² ; V is the speed of the ship, m/s; : The effective oncoming attack angle of the T-shaped wing in the actual working condition is composed of three parts, the rotation angle of the T-shaped wing, the pitch angle of the ship, and the additional angle generated by the longitudinal motion, and the pitch angle of the high-speed ship has a significant effect on the T-shaped The anti-rolling effect of the wing has a weakening effect, and the additional angle has a strengthening effect on the anti-rolling effect of the T-shaped wing). C _L (α) is the lift coefficient, which can be regarded as a constant when the angle of attack α is small, and d _a is the vertical distance between the installation position of the anti-rolling appendage and the center of gravity. In SIMULINK, the realization of the above description only needs to be combined with simple logic operation modules to realize the above formula.

The adjustment force and moment provided by the anti-rolling appendage obtained above are fed back to the trimaran longitudinal motion control system and superimposed on the original force, so as to realize the realization of the anti-rolling closed-loop system.

(5) The specific steps to realize the longitudinal motion model of high-speed trimaran based on sliding mode in MATLAB:

See Figure 2 for the specific implementation. The speed of the high-speed trimaran is selected as 40 knots. When the SSN5 level wave ξ(t) is used as input, the heave force F ₃ and the pitch force F ₅ are obtained after processing by the wave-force/moment module, which is used as the trimaran Longitudinal motion model force - input of heave/pitch module, get heave x ₃ and pitch x ₅ and their change acceleration with These four quantities are used as the input of the sliding mode controller, and after processing based on the approach law sliding mode control method, the required change amount α of the T-shaped wing attached to the anti-rolling body and the oncoming attack angle of the wave control plate is obtained, and the change amount As input, the longitudinal forces and moments provided by the two anti-rolling appendages for the trimaran are F _t , F _f and M _t , M _f respectively after being passed through the motion module of the anti-rolling appendage, and they are used as feedback to act on the force -In front of the heave/pitch module, the longitudinal motion stability control of the high-speed trimaran is realized.

Claims (5)

1. a high-speed trimaran anti-pitch control method based on sliding mode variable structure approach law, is characterized in that: comprise the steps: Step 1: Design random wave models of different levels according to the wave standard of the International Meteorological Bureau; Step 2: Using the random wave model, use the ANSYS platform to analyze and obtain the hydrodynamic coefficient of the trimaran, and then establish a mathematical model of the longitudinal motion of the high-speed trimaran according to the hydrodynamic coefficient, and obtain the heave height and pitch angle of the longitudinal motion of the high-speed trimaran ; Step 3: Using the longitudinal motion of the above-mentioned high-speed trimaran to respond to the heave height and pitch angle, design a sliding mode variable structure control law based on the reaching law, and obtain the change in the control output head angle; Step 4: Establish the lift and moment calculation model of the T-shaped wing of the anti-rolling appendage and the wave suppression plate, and use the change of the oncoming angle of the anti-rolling appendage to obtain the longitudinal force and moment provided by the anti-rolling appendage for the trimaran, and the feedback acts on Longitudinal motion system of high-speed trimaran. 2. the high-speed trimaran anti-rolling control method based on sliding mode variable structure approach law according to claim 1, is characterized in that: The random sea wave model described in step 1 is specifically: (1) According to the different significant wave heights H and frequency bands corresponding to different levels of waves specified by the International Meteorological Organization, use MATLAB programming to realize the establishment of different levels of random wave models; (2) The model is established based on the rational spectrum method, and the designed rational spectrum is defined as follows: <mrow> <msub> <mi>S</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>P</mi> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>Q</mi> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> Among them, S _x (ω) is the power spectral density function of the involved real stationary random process X(t), P(ω) and Q(ω) are ω real coefficient polynomials and the order of the denominator must be higher than that of the numerator; The final model of the wave is: <mrow> <mi>&amp;zeta;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msqrt> <mrow> <mn>2</mn> <mi>S</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;omega;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>&amp;Delta;&amp;omega;</mi> <mi>i</mi> </msub> </mrow> </msqrt> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;omega;</mi> <mi>i</mi> </msub> <mi>t</mi> <mo>+</mo> <msub> <mi>&amp;epsiv;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> ε _i represents the phase angle of the ocean wave, which is considered as a random variable in the interval (0, 2π), that is, ε _i =rand(0,2π), the power spectrum of S(w _i ) ocean wave at the circular frequency w _i Density, N is the number of samples; (3) The input of the wave module is the clock, and the output is used as the input of the following modules. 3. the high-speed trimaran anti-rolling control method based on sliding mode variable structure approach law according to claim 1, is characterized in that: The trimaran longitudinal motion model described in step 2 is specifically: (1) Using the ANSYS platform to analyze and obtain the hydrodynamic coefficient of the trimaran at different speeds; (2) According to the speed of the trimaran in the sea, the wave model and the encounter frequency, the "ss2tf" function of the MATLAB platform is used to realize the specific decoupling and solution of the longitudinal motion model of the trimaran. 4. the high-speed trimaran anti-rolling control method based on sliding mode variable structure approach law according to claim 1, is characterized in that: The sliding mode variable structure control law based on reaching law described in step three is specifically: (1) Establish the variable structure control of the longitudinal motion control system of the trimaran: <mrow> <mi>u</mi> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msup> <mi>u</mi> <mo>+</mo> </msup> <mo>,</mo> <mi>s</mi> <mo>&gt;</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <msup> <mi>u</mi> <mo>-</mo> </msup> <mo>,</mo> <mi>s</mi> <mo>&lt;</mo> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> </mrow> The exponential reaching law is designed as: in: is the exponent approach term; Get variable structure control: (2) Soften the control law: <mrow> <mi>&amp;theta;</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mi>s</mi> <mrow> <mo>|</mo> <mi>s</mi> <mo>|</mo> <mo>+</mo> <mi>&amp;xi;</mi> </mrow> </mfrac> </mrow> Among them, ξ is a small integer selected independently; The final sliding mode variable structure control law based on reaching law is: Among them, the parameter ε determines the robust performance of the system, the larger the value, the better the robust performance; the parameter q determines the speed at which the control system gradually approaches the hyperplane, the larger the q, the faster the system approaches, and A and B are the system states Matrix, C is the control matrix to be sought, which can be obtained by using the MATLAB compilation platform and using the pole allocation method, and ξ is a small integer selected independently. 5. the high-speed trimaran anti-rolling control method based on sliding mode variable structure approach law according to claim 1, is characterized in that: The lift and moment calculation model of the anti-roll T-wing attached to the body and the wave control plate described in step 4: There is a nonlinear relationship between the amount of change in the incoming flow angle and the longitudinal force provided by the trimaran corresponding to this angle, and the moment corresponding to the force is obtained at the same time: M _T/F = d _a F _T/F In the formula: ρ is the seawater density, 1.025×10 ³ kg/m ³ ; A is the projected area of T-shaped wing or wave breaker, V is the speed of the ship; α is the change in the angle of attack of the anti-rolling appendage; C _L ( α) is the lift coefficient of the anti-rolling appendage, which can generally be regarded as a constant when the angle of attack α is small; d _a is the vertical distance between the installation position of the T-shaped wing and the center of gravity; F _t , F _f and M _t , M _f represent the lift and moment provided by the T-shaped wing and the breaker, respectively.