Solution method for bow-swing attitude controller of underwater robot

Abstract

The present invention discloses a solution method for a bow roll attitude controller of an underwater robot. The bow roll direction model is taken as a control object, which is linearized to obtain the controlled object and uncertainty parameter bounds, and structural constraints for designing a robust controller are selected. Interval analysis theory is used to perform global optimization calculations, and finally the controller parameter results are obtained through convergence. The present invention adopts a fixed structural constraint robust control strategy to ensure that the control system is robust to model uncertainty and external interference, while effectively reducing the order of the controller to make it physically easier to implement. The interval analysis theory transforms the control solution into a global optimization calculation, which solves the problem of robust comprehensive solution that traditional methods cannot solve given controller structural constraints. The present invention also obtains a low-order robot bow roll attitude controller with both robustness and simplicity in the global optimization problem, which is more conducive to the controller engineering implementation.

Description

Technical Field

[0001] The invention relates to the technical field of underwater robot control, and in particular to a solution method for an underwater robot bow pitch attitude controller. Background Art

[0002] Underwater robots are key ocean exploration tools. With the growing demand for underwater exploration and operations, the scientific and industrial fields have put forward higher requirements for the attitude control technology of underwater robots. Especially in the research of advanced controllers under disturbance, the demand is more urgent. Improving the control performance of underwater robots can improve their stability and accuracy under disturbance. This type of technology can not only improve the motion performance of conventional submersibles, improve the comfort and operating accuracy of drivers, but also assist ROV (underwater robot) drivers to improve operating accuracy and efficiency, or optimize the control of AUV (untethered underwater robot), reduce unexpected motion, and thus reduce the computational difficulty of multi-sensor image stitching and reconstruction.

[0003] Due to the complexity and changeability of the marine environment, underwater robot design has become a typical multidisciplinary cross-research field. Especially in terms of related modeling and control design, due to the complexity of its scientific problems, the development of modeling and control technology is slightly insufficient. The shortcomings of existing control technology have affected the development of high-performance underwater robots. Therefore, the present invention starts with the problem of solving the bow swing attitude controller of the underwater robot and proposes an innovative solution to the underwater robot robust controller. Summary of the invention

[0004] In view of the problems in the prior art, the present invention proposes a solution method for the bow swing attitude controller of an underwater robot, which adopts a fixed structure constraint robust control strategy to ensure that the control system is robust to model uncertainty and external interference, while effectively reducing the order of the controller, making it physically easier to implement, and simplifying the implementation of the controller while ensuring the robustness of the system; the present invention adopts interval analysis theory to transform the control solution into a global optimization calculation, which solves the problem of robust comprehensive solution of given controller structure constraints that traditional linear matrix inequalities and Riccati methods cannot solve; the present invention can directly obtain a low-order robot bow swing attitude controller with both robustness and simplicity in the global optimization problem, which is more conducive to the engineering implementation of the controller.

[0005] The present invention proposes a method for solving a bow pitch attitude controller of an underwater robot, comprising:

[0006] S1, establish a multi-degree-of-freedom motion model for underwater robots; including:

[0007] ,

[0008] in, is the inertia matrix, is the additional mass matrix, is the damping matrix, is the restoring force of the underwater robot; the posture vector is the position and angle component of the robot in the earth coordinate system, and the velocity vector are the linear velocity and angular velocity components defined in the body coordinate system; is the thrust vector consisting of force and torque components; is the thrust vector generated by the external environment, is the thrust vector generated by the thruster; the posture vector and the velocity vector The transformation matrix between body coordinates and geodetic coordinates is: :

[0009] ;

[0010] Rotation matrix by linear velocity and angular velocity rotation matrix, which are defined as:

[0011] ,

[0012] ;

[0013] S2, estimate model parameters and extract the bow roll direction model as the control object; including:

[0014] Estimation of the inertia matrix of underwater robots using numerical calculation tools , additional mass matrix and the damping matrix , specifically including:

[0015] (1) Use mechanical design tools to confirm the center of gravity of the underwater robot , calculate the mass and inertia parameters ,definition is the centroid The vector between the origin of the body coordinates can be deduced as the rigid body inertia matrix :

[0016] ;

[0017] (2) Hydrodynamic effect Expressed as: - , for small zero-buoyancy underwater robots, the restoring force can be ignored Coriolis ; Use numerical calculation tools to cut the robot surface into triangular or quadrilateral micro-elements, and deduce the additional mass matrix of the underwater robot based on the slice calculation results ;

[0018] (3) Ignore damping terms higher than the second order, Linear Damping and quadratic damping Two parts , use computational fluid software ANSYS-CFX or STAR-CCM+ to calculate the multi-degree-of-freedom damping force and torque parameters of the underwater robot; extract the bow roll direction model:

[0019] ;

[0020] in, is the rigid body moment of inertia, is the additional moment of inertia, is the nonlinear damping system number, is the linear damping coefficient, is the yaw angular velocity, is the torque generated by the thruster;

[0021] S3, linearize the bow sway direction model and obtain the controlled object and uncertainty parameter bounds; including:

[0022] According to the hydrodynamic calculation results, Construct a compensating torque on ,have:

[0023] ;

[0024] In the formula, is the expected linear damping coefficient after nonlinear compensation, and are the linear and nonlinear damping coefficients estimated by the computational fluid software; the error between the damping parameter estimated by the fluid software and the actual damping result is ; The selection of must ensure that the thruster compensation output is as small as possible. , from which the controlled object is deduced to be:

[0025] ;

[0026] The controller is designed based on and its margin to reasonably set the uncertainty parameter boundaries;

[0027] S4, select the structural constraints for designing a robust controller; including:

[0028] use represents all feasible controllers that satisfy the structural constraints The robust controller is composed of All uncertain parameters should be Model All can meet the stability conditions:

[0029] ;

[0030] Interval analysis tools are used to solve the uncertain parameter set The worst case corresponds to Norm , and then obtain the structured controller that satisfies the robust constraints :

[0031] According to the above ideas, It is the target object that needs to be optimized and solved in the control synthesis process, and the constraints can be freely selected. , determine the control parameters And its action relationship, the controller is further expressed as ; Evaluation input To evaluate the output The transfer function matrix between them adds structural constraint information ,Right now ; It is the result of obtaining the gain extreme value in a certain input-to-output direction in the matrix transfer function element; structural constraints Through variable parameters Directly affects the performance of the closed-loop system , the system performance index also becomes A transfer function matrix in space that varies with parameters, whose transfer function The numerator and denominator polynomials in the equation will change with the parameter change:

[0032] ;

[0033] The MIMO system The norm is decomposed into An independent MISO system Norm to solve the constraints, considering The norm definitions are:

[0034] ;

[0035] Reconsider ,

[0036] The controller that stabilizes the closed-loop system is The following objectives need to be met:

[0037] ,

[0038] because, , the problem is simplified to:

[0039] ,

[0040] For standard linear systems, the Routh-Hurwitz stability criterion can be used to construct With parameters Inequality Therefore, the structural constraints The comprehensive problem of robust control is formulated as:

[0041] ;

[0042] S5, using interval analysis theory for global optimization calculation;

[0043] S6, the calculation converges and the controller parameter results are obtained.

[0044] In some embodiments of the present invention, step S4 specifically includes:

[0045] Considering the uncertain parameter set The worst-case norm under the action is expressed as According to the worst performance evaluation standard,

[0046] ;

[0047] Considering the uncertainty parameter vector of the underwater robot , then the problem of solving the structural constraint robust controller can be expressed as:

[0048] ;

[0049] in, is the robust stability constraint inequality derived from the Routh-Hurwitz criterion, is the set of all controllers that satisfy the structural constraints.

[0050] Compared with the prior art, the advantages and positive effects of the present invention are as follows: the solution method for the bow roll attitude controller of an underwater robot proposed in the present invention first establishes a multi-degree-of-freedom model of the underwater robot, estimates the model parameters using numerical calculation tools, extracts the bow roll direction model as the control object, linearizes the bow roll direction model, obtains the controlled object and the uncertainty parameter bound, selects the structural constraint conditions for designing a robust controller, uses interval analysis theory to perform global optimization calculations, and finally converges to obtain the controller parameter results; the present invention adopts a fixed structural constraint robust control strategy to ensure that the control system is robust to model uncertainty and external interference, while effectively reducing the order of the controller, making it physically easier to implement; the interval analysis theory adopted in the present invention transforms the control solution into a global optimization calculation, solving the problem of robust comprehensive solution that the traditional linear matrix inequality and Riccati method cannot solve the given controller structure constraints; the present invention can also directly obtain a low-order robot bow roll attitude controller with both robustness and simplicity in the global optimization problem, which is more conducive to the controller engineering implementation.

[0051] Other features and advantages of the present invention will become more apparent after reading the detailed description of the embodiments of the present invention in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0053] Figure 1 The steps of the comprehensive solution method for the robust controller proposed by the present invention are shown in FIG.

[0054] Figure 2 This is the block diagram of the controlled object after the uncertainty of the bow swing direction model;

[0055] Figure 3 is a schematic diagram of a robust control system;

[0056] Figure 4 PID structure Schematic diagram of the robust controller;

[0057] Figure 5 PID structure Robust controller step response results;

[0058] Figure 6 PID structure Robust controller controller output results;

[0059] Figure 7PID structure Sensitivity evaluation function of robust controller W1;

[0060] Figure 8 PID structure Robust controller W2 sensitivity evaluation function;

[0061] Fig. 9 PID structure under uncertain parameters Robust controller step response results;

[0062] Fig.10 PID structure under uncertain parameters The robust controller controls the output result;

[0063] Fig.11 Schematic diagram of the global solution of the interval optimization tool; (a) is the initialization diagram, (b) is the iterative operation diagram, and (c) is the operation convergence diagram. DETAILED DESCRIPTION

[0064] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0065] The present invention aims to propose a structural constraint H for the bow sway attitude control of an underwater robot. ∞ A comprehensive solution method for robust controllers, within the framework of robust control, selects a low-order fixed-structure constrained robust controller, and uses the minimax branch-and-bound method to solve the controller transformed into a non-convex optimization problem.

[0066] Specifically, Figure 1 The steps shown are used to describe in detail the design contents included in the present application.

[0067] S1: Establish a multi-degree-of-freedom motion model for underwater robots.

[0068] Establishing a multi-degree-of-freedom model for underwater robots ;

[0069] in, is the inertia matrix, is the additional mass matrix, is the damping matrix, It is the restoring force of the underwater robot. is the thrust vector generated by the external environment, is the thrust vector generated by the thruster.

[0070] Considering that the underwater robot has six degrees of freedom, including sway, swing, heave, pitch, roll, and bow pitch, the robot's six positions and angle components can be defined in the geodetic coordinates (NED-Frame) to form the pose vector , the linear velocity and angular velocity components are defined in body coordinates (B-frame) to form the velocity vector , define 6 force and torque components to form the thrust vector . Pose vector and the velocity vector The transformation matrix between body coordinates (B-frame) and earth coordinates (NED-frame) is: :

[0071] ;

[0072] Rotation matrix by linear velocity and angular velocity rotation matrix, which are defined as:

[0073] ,

[0074] .

[0075] S2: Estimate model parameters and extract the bow roll direction model as the control object.

[0076] Estimation of the inertia matrix of underwater robots using numerical calculation tools , additional mass matrix and the damping matrix , including:

[0077] (1) Use mechanical design tools to confirm the center of gravity of the underwater robot , calculate the mass and inertia parameters ,definition is the centroid The vector between the origin of the body coordinates (B-Frame) can be used to deduce the rigid body inertia matrix result:

[0078] ;

[0079] The present invention takes a small underwater robot as an example. The inertia matrix of the underwater robot is PRO / ENGINEERING calculation results (quality: , moment of inertia: ), as follows:

[0080] .

[0081] (2) Hydrodynamic effect It can be expressed as: - , for small zero-buoyancy underwater robots, the restoring force can be ignored Coriolis Here, numerical calculation tools can be used to cut the robot surface into triangular or quadrilateral micro-elements, and the additional mass matrix of the underwater robot can be deduced based on the slice calculation results. .

[0082] Taking a small underwater robot as an example, the additional mass matrix WAMIT hydrodynamic estimation results (quality: , moment of inertia: ), as follows:

[0083] .

[0084] (3) Ignore the damping terms higher than the second order, Linear Damping and quadratic damping Two parts , use computational fluid software ANSYS-CFX or STAR-CCM+ to calculate the multi-degree-of-freedom damping force and torque parameters of the underwater robot.

[0085] Taking a small underwater robot as an example, the damping matrix As shown below:

[0086] ;

[0087] The model for extracting the heading direction is:

[0088] ;

[0089] in, is the rigid body moment of inertia, is the additional moment of inertia, is the nonlinear damping system number, is the linear damping coefficient, is the yaw angular velocity, is the torque generated by the thruster.

[0090] Taking the small underwater robot used in the present invention as an example, the specific parameters are given as follows:

[0091] Table 1: Parameters of underwater robot bow rolling direction model

[0092]

[0093] S3: Linearize the bow roll direction model and obtain the controlled object and uncertainty parameter bounds.

[0094] According to the hydrodynamic calculation results, Construct a compensating torque on , then:

[0095] ;

[0096] In the formula, is the expected linear damping coefficient after nonlinear compensation, and are the linear and nonlinear damping coefficients estimated by the computational fluid software. The error between the damping parameter estimated by the fluid software and the actual damping result is . The selection of must ensure that the thruster compensation output is as small as possible. , from which the controlled object is deduced to be:

[0097] ;

[0098] Since computational fluid software can provide relatively accurate nonlinear damping parameters, the error of the above linear model is reasonable and accurate for robust control design, and the model can accurately describe the performance boundary of the control design. According to the analysis results in the previous article, the following parameters can be brought into the above controlled object model: ; ; ; ; ; , the linearized bow roll direction model after nonlinear damping treatment is obtained as:

[0099] .

[0100] Table 2: Nonlinear damping compensation results of underwater robot

[0101]

[0102] In addition to considering the linearization of the system, the power and hydrodynamic parameters of the underwater robot also have obvious uncertainty disturbances. For example, the damping and additional mass parameters in the four directions of longitudinal, transverse, vertical and bow swing have certain errors with the experimental data. Moreover, in the actual application of underwater robots, changes to the main body structure often occur, including: adding sensors, replacing thrusters, adding battery compartments, expanding manipulators, etc. Changes in the main body structure will also significantly cause the hydrodynamic parameters to float. Therefore, the above parameter changes have to be considered in the controller design. The bow swing direction model of the underwater robot is summarized as follows:

[0103] ;

[0104] in The uncertainty of the moment of inertia caused by the external ocean environment or the changes of the AUV body, is the estimated error caused by the linearization of the model. In order to illustrate the effect of the present invention, this paper compares a variety of different control schemes on the robot, among which The margin is set to 30%, The margin is set to 40%. Figure 2 Shown is the block diagram of the controlled object after the uncertainty of the bow roll direction model is separated.

[0105] S4: Select structural constraints for designing a robust controller.

[0106] are all feasible controllers that satisfy the structural constraints The robust controller is composed of All uncertain parameters should be Model All can meet the stability conditions:

[0107] .

[0108] Affected by the structural constraints, the controller does not meet the requirements of the LMI (Linear Matrix Inequality) and ARE (Riccati Equation) methods. Therefore, the present invention uses interval analysis tools to solve the problem in the uncertain parameter set. The worst case under the action (Worst-Case) corresponds to , and then obtain the structured controller that satisfies the robust constraints .

[0109] According to the above ideas, It is the target object that needs to be optimized and solved in the control synthesis process. The designer freely selects the constraints. , determine the control parameters And its action relationship, the controller is further expressed as Evaluation Input To evaluate the output The transfer function matrix between them adds structural constraint information ,Right now . It is the result of obtaining the gain extreme value in a certain input-to-output direction in the matrix transfer function element. Structural Constraints Will pass variable parameters Directly affects the performance of the closed-loop system , the system performance index also becomes A transfer function matrix in space that varies with parameters. Its transfer function The numerator and denominator polynomials in the equation will change with the parameter change:

[0110] .

[0111] The MIMO (Multiple Input Multiple Output) system The norm is decomposed into An independent MISO system Norm to solve the constraints, considering The norm definitions are:

[0112] ;

[0113] Reconsider ,

[0114] The controller that stabilizes the closed-loop system is The following objectives need to be met:

[0115] ;

[0116] because, , the problem is simplified to:

[0117] ;

[0118] For standard linear systems, the Routh-Hurwitz stability criterion can be used to construct With parameters Inequality Therefore, the structural constraint The comprehensive problem of robust control is formulated as:

[0119] ;

[0120] Considering the uncertain parameter set The worst-case norm under the action is expressed as According to the worst performance evaluation standard,

[0121] ;

[0122] Considering the uncertainty parameter vector of the underwater robot , then the problem of solving the structural constraint robust controller can be expressed as:

[0123] ;

[0124] in, is the robust stability constraint inequality derived from the Routh-Hurwitz criterion, is the set of all controllers that satisfy the structural constraints.

[0125] The control design for the bow directional model mainly considers good reference signal tracking performance, interference suppression, control rapidity, and robustness to uncertain factors. Since the PID controller has the characteristics of a simple control structure, few parameters, and easy discretization calculation, the present invention uses the PID structure to demonstrate the solution of the structural constraint robust controller of the bow directional model. It should be noted that the present invention is not limited to the PID structure, and simple, low-order robust controller structures implemented in non-full dimensions are all within the scope of the present invention.

[0126] Considering uncertainty SISO (Single Input Single Output) system , the system and PID controller The sensitivity function of the unit feedback system is summarized as:

[0127] ;

[0128] in There are three real number parameters to be adjusted and one low-pass filter coefficient. The controller structure is described as follows:

[0129] ;

[0130] The above system can be expressed as Figure 4 Control tracking problem shown.

[0131] Without considering the uncertainty of the controlled object, it is not difficult to obtain the nominal sensitivity function of the above SISO system as follows: ,correspond To each evaluation output The transfer function is:

[0132]

[0133] The corresponding structural optimization process The objective function is:

[0134]

[0135] The stability condition of the closed-loop system can be obtained by constructing the following closed-loop system characteristic polynomial and finding the sign change of the first column of the Routh table Determining stability:

[0136] ,

[0137] ;

[0138] in,

[0139]

[0140] According to the above formula, the PID structure constrained robust controller design problem becomes:

[0141] min k ∈ K [ sup ω >0, ( max i∈ 1,2,3 ( f 1 (k,ω) ,f 2 (k,ω), f 3 (k,ω) ) )] subject to , R 1 (k)>0 R 2 (k)>0 R 3 (k)>0 .

[0142] The controlled object is transformed into a transfer function:

[0143] ;

[0144] Among them, according to the underwater robot bow pitch power and hydrodynamic model, the second-order parameter true value of the above system is sorted out as p 1 ^ = I YRB + I YA τ i ∈[0.3,0.69] , the first-order coefficient p 2 ^ = D YLA +δ τ i ∈[1.26,2.34] .

[0145] Normally , is designed as a low-pass filter because the loop reflects the low-frequency reference input tracking capability of the error signal. The cutoff frequency of the weight function should be basically consistent with the cutoff frequency of the controlled object to avoid redundant bandwidth design resulting in a large gain compensation of the controller. In order to reduce the energy waste of the controller, the controller output signal path is designed is a smaller number.

[0146] ,

[0147] ;

[0148] Consider the above second-order system The stability constraints after forming a closed-loop system with the controller are summarized as follows:

[0149] ;

[0150] because ,

[0151] Therefore, we can deduce the characteristic polynomial :

[0152] ;

[0153] Then arrange the polynomial coefficients:

[0154] ,

[0155] ,

[0156] ,

[0157] ,

[0158] ,

[0159] The first column of coefficients is constructed from the Routh table as follows:

[0160] ,

[0161] ,

[0162] ,

[0163] ,

[0164] ;

[0165] in,

[0166] ,

[0167] ;

[0168] Combining the two weight function designs, assuming , the stability inequality is constructed based on the above parameters, and then the interval analysis method can be used for optimization and solution. After sorting out the above process, the PID structure constraint is obtained. The robust controller synthesis problem is:

[0169] .

[0170] The structural design and constraint condition design of control synthesis greatly affect the comprehensive results of the controller. In order to explain the effect and versatility of the present invention in detail, in addition to the above-mentioned standard PID controller design, controllers with different structures such as anti-saturation structure and minimum zero point are also compared. The detailed analysis is as follows:

[0171] In view of the possible thrust saturation problem in the previous controller design, the present invention amplifies the inertia link coefficient To the parameter vector In , we solved:

[0172] .

[0173] In addition, the closed-loop transfer function of the above bow swing direction model is sorted out have:

[0174] .

[0175] From the basics of control theory, we know that the poles of a closed-loop system determine the attenuation term of the closed-loop system output, while the zeros affect the amplitude of the oscillation. Therefore, reducing the zeros of a closed-loop system can reduce unnecessary control jitter and energy consumption. In order to minimize the zeros of the above closed-loop system, the following constraints can be added to the controller synthesis process:

[0176] ;

[0177] Considering that satisfying the above conditions at the same time may lead to an unsolvable optimization problem. Therefore, it is generally considered that any one of the above conditions is used to achieve the zero-point constraint. The comprehensive optimization problem of time control is solved. Therefore, the above minimum zero point control PID structure constraints are sorted out. The robust controller synthesis problem is:

[0178] Controller Structure: C( k ,s)= k p + k i s + k d s k f s+1 min k ∈ K [ sup ω >0, p ∈ P ( max i∈{1,⋯,q} ∑ j=1 n | T w j → z i ( k , p ,jω)| 2 )] subject to, ∀ p ∈ P , r n ( k , p )≤0,n∈{1,⋯,q} Minimal-Zero Constraint: k p k f + k d =0 .

[0179] S5: Use interval analysis theory to perform global optimization calculations.

[0180] Interval operations can directly solve the global optimal solution of the controller optimization problem. Different from the local optimization results, the global optimization results are generally small enough intervals containing the optimal solution, which can ensure that the optimal result exists only in the result interval. Specifically, the interval analysis method uses the upper and lower endpoints to represent the operation variables, such as the non-empty interval is defined as a real closed set consisting of continuous real elements ( subspace), satisfying the following definition:

[0181] ;

[0182] in, represents the lower endpoint of the interval, Represents the upper endpoint of the interval.

[0183] Unlike statistical mathematics, this theory can provide deterministic calculation results. The target result is completely contained in the upper and lower endpoints. Take binary operations as an example. ,in, represents the interval operator, Represent addition, subtraction, multiplication and division:

[0184] ,

[0185] ,

[0186] ,

[0187] ;

[0188] It is not difficult to see that the interval algorithm has a high degree of operational reliability, which can ensure that all real numbers in the upper and lower endpoints of the interval are completely contained in the interval during the operation, and can effectively handle fuzzy and incompletely described operation problems. The interval algorithm has obvious advantages in solving non-convex and non-smooth control optimization problems, and can conveniently carry out global optimization solutions. It avoids the problem that methods such as LMI and ARE can only produce local optimal results. The present invention mainly adopts the interval method to repeatedly branch and bound, and then completes the optimization calculation of the controller.

[0189] The controller synthesis problem is essentially a problem of solving conditional constraints. These constraints include mathematical indicators such as the stability of the controller and the performance of the controller. From the perspective of optimization, conditional constraint problems generally include: constraints composed of multiple system structures and system indicators , a finite number of variables to be solved and the variables to be solved Vector space generated by initial solution interval . When there exists a vector solution Make all constraints When both satisfy the condition, the vector A consistent or feasible solution to this conditional constraint problem is when the vector Make any constraint If it does not satisfy, then it is called vector This is a non-uniform or infeasible solution to the problem with this conditional constraint. From all feasible solution vectors The set of initial conditions is called The feasible set of .

[0190] The basic idea of ​​interval branch and bound is to split the solution space into several adjacent but non-intersecting smaller subsets, then cyclically calculate the interval operation value of the objective function, and gradually reduce the width of the feasible solution space based on logical reasoning. The comprehensive solution of the structural constraints of the robust controller can be simplified and summarized as a conditional constraint interval optimization problem with objective minimization:

[0191] ;

[0192] in, is a non-convex objective function, is the constraint condition described by the inequality. When considering controller design, the objective function is generally determined by the system performance, and the constraint conditions are generally the stability conditions and structural constraints of the system. If we define is the feasible solution space of the above optimization problem, then the global optimal solution of the conditional constraint problem can be defined , which is the minimum value, satisfies:

[0193] ;

[0194] In interval algebra, the specific calculation includes: extracting solution intervals, trimming empty sets, bounding calculations, determining solutions, interval branches, pushing, etc. According to the input objective function, constraints and initial space, the above steps will be iterated repeatedly to gradually approach the minimum width of the feasible solution interval. When the program completes the calculation, the global optimal solution of the optimization problem is will be included in A series of solutions are stored in the interval.

[0195] The input information of the solution algorithm includes:

[0196] (1) Maximum optimization problem defined by objectives and constraints;

[0197] (2) Hypercube to be solved ;

[0198] (3) Solving the termination condition (represents the minimum width of cube splitting) or the number of loop calculations.

[0199] The output of the algorithm is:

[0200] (1) The set result containing the optimal solution: ;

[0201] (2) Closed interval enclosing the target extreme value .

[0202] like Fig.11 The figure shows the global solution diagram of the interval optimization tool; the global interval optimization result is generally a sufficiently small interval containing the optimal solution. is the objective function, is the stability and performance constraint, then is the structural constraint objective function The global optimal solution of . The interval can ensure that the optimal result exists only between the upper and lower endpoints of the interval. The specific solution process is shown in the figure. In (a), according to the objective function and performance constraints Initialize the feasible solution space In (b), the interval operation is completed and the solution space is clipped, and the width of the interval containing the optimal solution is iteratively reduced. In (c), the objective function is obtained by iterative convergence. The optimal solution , satisfying the constraints .

[0203] S6, the calculation converges and the controller parameter results are obtained.

[0204] like Figure 3 The following is a specific embodiment of the robust controller, according to the above three different PID structure constraints The robust controller synthesis problem is solved by the MMIBBA (minimax interval branch and bound algorithm) in this paper, and the initial conditions for optimization are as follows:

[0205] (1) Arrange the bow swing model parameters to obtain the controlled object The uncertain parameter cube is: [0.3,0.69]×[1.26,2.34] ;

[0206] (2) Since the cut-off frequency of the system in this example is approximately , so the frequency of the controller optimization problem is chosen The interval is: [ 10 -3 , 10 3 ] ;

[0207] (3) Controller PID parameters The corresponding initial interval hypercube: K =[-5,5]×[-5,5]×[-5,5]×[-5,5] .

[0208] Based on the Ibex interval computing library, the above problems are organized into the MMIBBA program, which is run on a single core in a DELL R7910 server with 64GB ECC memory.

[0209] The program eventually converges and gives a reasonable interval that strictly wraps the target value. , controller performance is visible Figure 5-10 In the figure, PID refers to PID method, Anti-Windup PID refers to anti-saturation PID method, Minimal-Zero PID refers to the minimum zero point PID, Max Torque refers to the maximum pitch angle.

[0210] Three PID structure constraints The comprehensive results of the control parameters of the robust controller and the closed-loop response results of the controller are listed as follows:

[0211] Table 3: PID structure constraints Robust Controller Results

[0212]

[0213] Table 4: PID structure constraints Robust controller results and closed-loop step response analysis

[0214]

[0215] Obviously, the above three PID structure constraints Robust controllers all have robust stability. After the controller and the controlled object with uncertain parameters form a closed-loop system, the evaluation transfer function can meet all target constraints, and the system has good input signal tracking and disturbance suppression capabilities. After the anti-saturation parameter is added, the output of the controller is effectively limited and the peak value is reduced. The minimum zero PID structure proposed in this invention The robust controller can achieve fast and effective control with a small overshoot. Among all controllers, its output peak value is the smallest at 0.86. , and the adjustment speed is the fastest, the adjustment time only takes Therefore, the minimum zero point PID structure is adopted This new control scheme, the robust controller, not only ensures that the controller has a simple structure, robust stability and robust performance, but also significantly reduces the actual output energy required for the controller to complete the same action.

[0216] The above results prove that the structural constraint robust controller proposed in the present invention can significantly improve the motion control performance of the underwater robot, and the structural design and constraint condition design play a key role in improving the controller performance.

[0217] The above simulation test considers scenarios including:

[0218] Working condition 1: The model parameters of the underwater robot are nominal parameters.

[0219] Working condition 2: The parameter perturbation range of the underwater robot is (Moment of inertia and additional mass) 30%, (Damping compensation coefficient) 40%.

[0220] It should be noted that, in the specific implementation process, the above-mentioned control part can be implemented by a hardware processor executing computer execution instructions in software form stored in the memory, which will not be elaborated here, and the programs corresponding to the actions performed by the above-mentioned control circuit can be stored in the computer-readable storage medium of the system in software form, so that the processor can call and execute the operations corresponding to the above-mentioned modules.

[0221] The computer-readable storage medium mentioned above may include volatile memory, such as random access memory; may also include non-volatile memory, such as read-only memory, flash memory, hard disk or solid-state drive; may also include a combination of the above types of memory.

[0222] It should be pointed out that the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by ordinary technicians in this technical field within the essential scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A method for solving a bow pitch attitude controller for an underwater robot, characterized in that: include: S1, establish a multi-degree-of-freedom motion model for underwater robots; include: ， in, is the inertia matrix, is the additional mass matrix, is the damping matrix, It is the underwater robot's restoring force; is the thrust vector generated by the external environment, is the thrust vector generated by the thruster; the posture vector is the position and angle component of the robot in the earth coordinate system, and the velocity vector are the linear velocity and angular velocity components defined in the body coordinate system; is the thrust vector composed of force and torque components; the posture vector and the velocity vector The transformation matrix between body coordinates and geodetic coordinates is: : ； Rotation matrix by linear velocity and angular velocity rotation matrix, which are defined as: ， ； S2, estimate model parameters and extract the bow roll direction model as the control object; including: Estimation of the inertia matrix of underwater robots using numerical calculation tools , additional mass matrix and the damping matrix , specifically including: (1) Use mechanical design tools to confirm the center of gravity of the underwater robot , calculate the mass and inertia parameters ,definition is the centroid The vector between the origin of the body coordinates can be deduced as the rigid body inertia matrix : ； (2) Hydrodynamic effect Expressed as: , for small zero-buoyancy underwater robots, the restoring force can be ignored Coriolis ; Use numerical calculation tools to cut the robot surface into triangular or quadrilateral micro-elements, and deduce the additional mass matrix of the underwater robot based on the slice calculation results ; (3) Ignore damping terms higher than the second order, Linear Damping and quadratic damping Two parts , use computational fluid software ANSYS-CFX or STAR-CCM+ to calculate the multi-degree-of-freedom damping force and torque parameters of the underwater robot; extract the bow roll direction model: ； in, is the rigid body moment of inertia, is the additional moment of inertia, is the nonlinear damping system number, is the linear damping coefficient, is the yaw angular velocity, is the torque generated by the thruster; S3, linearize the bow sway direction model and obtain the controlled object and uncertainty parameter bounds; including: According to the hydrodynamic calculation results, Construct a compensating torque on ,have: ； In the formula, is the expected linear damping coefficient after nonlinear compensation, and are the linear and nonlinear damping coefficients estimated by the computational fluid software; the error between the damping parameter estimated by the fluid software and the actual damping result is ; The selection of must ensure that the thruster compensation output is as small as possible. , from which the controlled object is deduced to be: ； The controller is designed based on and its margin to reasonably set the uncertainty parameter boundaries; S4, select the structural constraints for designing a robust controller; including: use represents all feasible controllers that satisfy the structural constraints The robust controller is composed of All uncertain parameters should be Model All can meet the stability conditions: ； Interval analysis tools are used to solve the uncertain parameter set The worst case corresponds to Norm , and then obtain the structured controller that satisfies the robust constraints : According to the above ideas, It is the target object that needs to be optimized and solved in the control synthesis process, and the constraints can be freely selected. , determine the control parameters And its action relationship, the controller is further expressed as ; Evaluation input To evaluate the output The transfer function matrix between them adds structural constraint information ,Right now ; It is the result of obtaining the gain extreme value in a certain input-to-output direction in the matrix transfer function element; structural constraints Through variable parameters Directly affects the performance of the closed-loop system , the system performance index also becomes A transfer function matrix in space that varies with parameters, whose transfer function The numerator and denominator polynomials in the equation will change with the parameter change: ； The MIMO system The norm is decomposed into An independent MISO system Norm constraint Solve, considering The norm definitions are: ； Reconsider , The controller that stabilizes the closed-loop system is The following objectives need to be met: ， because, , the problem is simplified to: ， For standard linear systems, the Routh-Hurwitz stability criterion can be used to construct With parameters Inequality Therefore, the structural constraints The comprehensive problem of robust control is formulated as: ； S5, using interval analysis theory for global optimization calculation; S6, the calculation converges and the controller parameter results are obtained.

2. The method for solving the bow pitch attitude controller of an underwater robot according to claim 1, characterized in that: Step S4 specifically includes: Considering the uncertain parameter set The worst-case norm under the action is expressed as According to the worst performance evaluation standard, ； Considering the uncertainty parameter vector of the underwater robot , then the problem of solving the structural constraint robust controller can be expressed as: ； in, is the robust stability constraint inequality derived from the Routh-Hurwitz criterion, is the set of all controllers that satisfy the structural constraints.

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