CN116736709B - Dynamic compensation type active disturbance rejection heading control method for marine robot - Google Patents
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Abstract
A dynamic compensation type auto-disturbance rejection heading control method for a marine robot relates to the field of robot motion control. The invention aims to solve the problems that the existing bow control method cannot ensure stable bow control performance under different navigational speeds, so that the accuracy of bow control is poor and the problem that the solution of bow control parameters is complex. The invention comprises the following steps: inputting a desired heading angle phi d of the marine robot into a tracking differentiator to obtain a transition process v 1 of which the tracking differentiator is arranged for phi d; inputting an actual heading angle psi, a control rudder angle delta and an actual navigational speed U of the marine robot into a linear expansion state observer to obtain a disturbance compensation parameter b, a submerged heading z 1, a steering acceleration z 2 and a disturbance z 3 of a submerged heading system; inputting z 1、z2、z3、b、v1 into the self-adaptive state error feedback to obtain a required control rudder angle delta'; and d ', transmitting delta ' to a steering engine to obtain phi ', and re-inputting the linear expansion state observer if the error of phi ' and phi d is not within the preset error until the error of phi ' and phi d is within the preset error. The invention is used for controlling the bow of the marine robot.
Description
Technical Field
The invention relates to the field of robot motion control, in particular to a dynamic compensation type active disturbance rejection heading control method of a marine robot.
Background
Marine robots are very diverse, such as unmanned boats, wave gliders, underwater robots, etc. For the problem of controlling the heading motion of the marine robot, most of the heading control process is driven by a steering engine. For such heading control problems, there are already various control algorithms, such as classical PID control, active disturbance rejection control, sliding mode control, etc.
The invention with the publication number of CN 109828462A provides a self-adaptive heading controller and a control method for the wave glider under the variable navigational speed, and disturbance compensation parameters b in an extended state observer are obtained through a wave glider heading response model and a similar principle, however, the problem of complicated parameter solving process and poor heading control accuracy can be caused by utilizing the similar principle. The invention with publication number CN 114815595A discloses an electric steering engine control system and a control method based on ADRC active disturbance rejection control, and the method refers to a method for modifying a nonlinear PID by utilizing a differential tracker. However, marine robots such as wave gliders have special propulsion mechanisms, the navigational speed of which is not controllable, and this method can cause oscillation or divergence of the bow control, thus resulting in a problem of poor accuracy of the bow control. The invention with publication number CN 104267743B provides a ship-borne camera shooting stable platform control method adopting an active-disturbance-rejection control technology, however, the extended state observer designed by the method is only suitable for a camera shooting stable platform and is not suitable for a marine robot heading control method. In conclusion, the heading controller on the traditional aircraft cannot ensure that good heading control performance can be maintained under different navigational speeds, and even control oscillation or divergence can be caused, so that the problem of poor accuracy of the heading control is caused, and meanwhile, the problem of complex solving of the heading control parameters also exists.
Disclosure of Invention
The invention aims to solve the problems that the existing bow control method is poor in bow control accuracy and complex in bow control parameter solving, and provides a dynamic compensation type active disturbance rejection bow control method of a marine robot.
A dynamic compensation type active disturbance rejection heading control method of a marine robot comprises the following specific processes:
Step one, inputting a desired heading angle phi d of the marine robot into a tracking differentiator to obtain a transition process v 1 of the tracking differentiator, wherein the transition process v 1 is arranged for the desired heading angle phi d;
step two, initializing and controlling a rudder angle delta;
Step three, acquiring a current actual heading angle psi and a current actual navigational speed U of the marine robot, and inputting the psi, delta and U into a linear expansion state observer to acquire a disturbance compensation parameter b of the submerged bow system and three state variables in the submerged bow system;
three state variables in the submerged bow system are: submerged bow z 1, steering acceleration z 2, and disturbance z 3 of submerged bow system;
Step four, inputting the z 1、z2、z3、b、v1 obtained in the step one and the step three into adaptive state error feedback based on a criterion function to obtain a required control rudder angle delta';
And fifthly, issuing the required rudder angle delta ' instruction obtained in the step four to an operating device of a steering engine through a main control computer, so as to obtain an actual heading angle phi ' of the marine robot corresponding to the required rudder angle delta ', comparing the phi ' with an expected heading angle phi d, ending the heading control if the error of phi ' and phi d is within a preset error, assigning delta ' to delta and phi ' and returning to the step three until the error of phi ' and phi d is within the preset error if the error of phi ' and phi d is not within the preset error.
Further, the tracking differentiator in the first step is as follows:
Where v 1 (t) is the transition at time t where the tracking differentiator is arranged for the desired heading angle ψ d, v 1 (t+1) is the transition at time t+1 where the tracking differentiator is arranged for the desired heading angle ψ d, v 2 (t) is the differentiated signal of v 1 (t), ψ d (t) is the desired heading of the submerged body at time t, r is the speed factor, h is the sampling step size, fh is the intermediate variable, h 0 is the filter factor, fhan (·) is the fastest control integration function.
Further, the method comprises the steps of,
Wherein d, a are intermediate variables.
Further, the method comprises the steps of,
Wherein d 0、a0, y are intermediate variables.
Further, the method comprises the steps of,
Further, the linear expansion state machine in the third step is as follows:
Where β 01、β02、β03 is the gain factor of the linear extended state observer, z i,i＝1,2,3,zi is the state variable of the linear extended state observer, e 1、b0 is the intermediate variable, Is the derivative of v, v is the actual navigational speed after smoothing U, K Fal is the proportionality coefficient affecting v versus U tracking speed, fal () is a functional filter, delta Fal is a filter factor, a Fal is a filter design parameter, e Fal is an intermediate variable, disturbance compensation parameter b=b 0v2.
Further, e Fal = U-v.
Further, the method comprises the steps of,
Wherein C is the lift coefficient of the rudder plate, L is the distance from the rudder plate to the gravity center of the submerged body, I is the moment of inertia of the submerged body around the gravity axis, lambda 66 is the additional moment of inertia coefficient of the submerged body in the bow direction, rho is the sea water density, and S is the rudder plate area.
Further, β 01＝3ω,β02＝3ω2,β03＝ω3;
Where ω is the gain design parameter.
Further, the adaptive state error feedback based on the criterion function in the fourth step is as follows:
Where δ' is the desired rudder angle, δ 0 is the intermediate variable, Δt > 0 is the interval time, z i (t) is z i at time t, and λ is the weight coefficient.
The beneficial effects of the invention are as follows:
The invention provides a dynamic compensation type active disturbance rejection heading control method of a marine robot. The invention designs an improved extended state observer based on speed information to observe the state information and disturbance information of a heading system, and obtains disturbance compensation parameters b according to a relation formula of a submerged body turning bow acceleration motion response and a rudder angle on the submerged body bow swing degree of freedom according to a wave glider motion mathematical model, wherein each parameter can be conveniently obtained through hydrodynamic force simulation calculation, so that the solution of a bow control parameter is simpler. The invention further provides a navigational speed preprocessing method and adaptive state error feedback based on a criterion function, so that the parameters of the controller can be adaptively adjusted along with the change of navigational speed, the marine robot controllers at different navigational speeds have adaptive adjustment capability, and the marine robot can ensure stable heading control performance at different navigational speeds, thereby improving the accuracy of bow control.
Drawings
FIG. 1 is a schematic diagram of the structure of the present invention;
fig. 2 is a flow chart of the present invention.
Detailed Description
The wave glider is a special marine robot, which consists of a floating body, a submerged body and a mooring rope. Wherein the floating body and the submerged body are connected by a mooring line. Only the heading of the submerged body can be directly controlled by a steering engine on the submerged body. The heading and the integral heading control of the floating body are completed under the dragging drive of the submerged body. The wave glider is provided with a main control computer, a navigational speed sensor, a heading sensor, a steering engine and other devices. The wave glider comprises a wave glider, a steering engine, a main control computer, a submarine bow angle phi, a steering engine and a wave glider, wherein the navigational speed U of the wave glider is obtained by a navigational speed sensor, the submarine bow angle phi is obtained by a bow sensor, the main control computer obtains an expected steering angle phi d, then the rudder angle delta is obtained through calculation processing, and an instruction is issued to the steering engine to execute a steering instruction.
The wave glider captures the kinetic energy of wave heave in the ocean by utilizing a novel mechanical structure of the wave glider and converts the kinetic energy into thrust in the horizontal direction to realize self navigation. The problem of heading control of the wave glider submarine is basically similar to that of a marine robot, so that the problem of heading control of the submarine is researched by taking the wave glider as an object. For the wave glider, the wave glider provides thrust by means of wave energy, the navigational speed of the wave glider is different under different sea conditions and is greatly influenced by marine environment, if a heading controller on a traditional aircraft is still adopted, good heading control performance can not be ensured to be maintained under different navigational speeds, and even control oscillation or divergence can be caused. The invention is described below in connection with specific embodiments.
The first embodiment is as follows: as shown in fig. 1-2, the dynamic compensation type active-disturbance-rejection heading control method of the marine robot in the embodiment specifically comprises the following steps:
Step one, inputting a desired heading angle phi d of the marine robot into a tracking differentiator to obtain differential signals v 2 of transition processes v 1 and v 1 arranged for the desired heading angle phi d by the tracking differentiator;
The tracking differentiator is as follows:
wherein fhan (·) is called the fastest control synthesis function, which is defined as:
Wherein, psi d (t) is the expected heading of the submerged body at time t; r is called a speed factor, the larger the speed factor is tracked by the tracking differentiator, but the larger the speed factor is, the noise signal is tracked by the tracking differentiator, so that an unsmooth result is caused; h 0 is called a filter factor, the greater the filter strength, but the output signal lag will also increase; h is the sampling step, d 0、a0, a, y, fh are intermediate variables, v 1 (t) is the transition at time t where the tracking differentiator is arranged for the desired heading angle ψ d, v 2 (t) is the differentiated signal of v 1 (t), sign () is the sign function.
Setting a control rudder angle delta, and initializing delta to 0.
Step three, acquiring a current actual heading angle psi, a control rudder angle delta and a current actual navigational speed U of the marine robot, and inputting the psi, the delta and the U into an improved linear expansion state observer to obtain a navigational speed v after smoothing, disturbance compensation parameters b of a submerged bow and yaw system and three state variables in the submerged bow and yaw system, namely a submerged heading z 1, a steering acceleration z 2 and disturbance z 3 of the submerged bow and yaw system;
the improved linear extended state observer is obtained by:
Step three, smoothing the actual navigational speed U of the marine robot to obtain a smoothed actual navigational speed v:
Where a Fal is a filter design parameter, a constant between 0 and 1, K Fal is a scaling factor affecting v versus U tracking speed, delta Fal is a filter factor, Is the derivative of v, fal () is a function filter, e Fal is an intermediate variable;
step three, acquiring basic parameters of the marine robot, and constructing a submerged bow system by utilizing the basic parameters of the marine robot, wherein the basic parameters comprise the following steps:
The basic parameters of the marine robot include: rudder plate area S, rudder plate lift coefficient C, rudder plate distance L from the center of gravity of the robot, rotational inertia I of the robot around a concentric axis, and additional rotational inertia coefficient lambda 66 of the robot in the yaw direction;
According to a wave glider motion mathematical model, on the degree of freedom of the submarine bow, the relation between the submarine bow acceleration motion response and the rudder angle is as follows:
Wherein r 1 is the submarine bow angular velocity, delta is the rudder angle, ρ is the sea water density, S is the rudder plate area, U is the current actual navigational speed of the submarine, C is the lift coefficient of the rudder plate, L is the distance from the rudder plate to the center of gravity of the submarine, I is the rotational inertia of the submarine around the mandrel, lambda 66 is the additional rotational inertia coefficient of the submarine in the bow direction, w is the interference suffered by the system, and f (r 1, w) is the other partial functions in the system including the system interference.
Definition:
i.e. the disturbance compensation parameter is b=b 0v2.
The submerged bow system may be expressed as:
wherein b 0, y1 are intermediate variables;
Thirdly, constructing an improved linear expansion state observer by utilizing the smoothing process of the first step and the submerged bow system obtained in the second step:
Where β 01、β02、β03 is the gain coefficient of the linear extended state observer (β 01＝3ω,β02＝3ω2,β03＝ω3, where ω is the gain design parameter), z i (i=1, 2, 3) is the state variables of the linear extended state observer, and e1 is the intermediate variable.
Inputting the z 1、z2、z3、b、v、v1 obtained in the step three into adaptive state error feedback based on a criterion function to obtain a required control rudder angle delta';
The adaptive state error feedback based on the criterion function is obtained by the following steps:
Step four, utilizing an improved linear expansion state observer to obtain a second-order cascade controlled system:
Where x 1 = ψ is the actual heading angle and x 2＝r1 is the submerged body turning heading angular velocity;
step four, designing the following criterion function for x 1:
Wherein, The expected value of x 1 is represented, λ is the weight coefficient, and Δt > 0 is the interval time.
Thirdly, carrying out Taylor series expansion on the criterion function obtained in the fourth step, and then only keeping the criterion function until a second derivative term is reached, and solving a partial derivative of delta' in the function when the criterion function is aligned to obtain the criterion function when the partial derivative is zero;
The Taylor series expansion formula is:
Wherein R is a Taylor series expansion remainder;
And (3) only retaining to a second derivative term, and obtaining a partial derivative of delta' in the function when the partial derivative is zero, wherein the minimum value is as follows:
where z i (t) is z i at time t.
Fourth, disturbance compensation is carried out on the control quantity of the system, and the following formula is adopted:
And step four, obtaining self-adaptive state error feedback based on the criterion function by using the disturbance compensation obtained in the step four and the criterion function with zero partial derivative obtained in the step four, wherein the self-adaptive state error feedback is based on the criterion function and comprises the following formula:
And fifthly, issuing the required rudder angle delta ' instruction obtained in the step four to an operating device of a steering engine through a main control computer, so as to obtain an actual heading angle phi ' of the marine robot corresponding to the required rudder angle delta ', comparing the phi ' with an expected heading angle phi d, ending the heading control if the error of phi ' and phi d is within a preset error, assigning delta ' to delta and phi ' and returning to the step three until the error of phi ' and phi d is within the preset error if the error of phi ' and phi d is not within the preset error.
After the heading control is finished at the current moment, taking the control rudder angle and the expected heading angle at the current moment as initial values of the control rudder angle and the expected heading angle at the next moment, and performing heading angle control at the next moment.
As shown in FIG. 1, the dynamic compensation type auto-disturbance-rejection heading control method of the marine robot is structurally schematic. The improved active disturbance rejection controller comprises: tracking differentiators, improved linear extended state observers, and adaptive state error feedback based on criterion functions. Wherein the disturbance compensation parameter b in the improved linear extended state observer is a time-varying coefficient b=b 0v2 affected by the change in the speed of the submerged body; disturbance compensation is added in the improved nonlinear state error feedback of the second-order system, so that the controlled system is converted into a second-order cascade integration system, a corresponding criterion function is designed based on Taylor series expansion, and the adaptive state error feedback based on the criterion function is deduced.
Claims (8)
1. A dynamic compensation type auto-disturbance rejection heading control method of a marine robot is characterized by comprising the following specific processes:
Step one, inputting a desired heading angle phi d of the marine robot into a tracking differentiator to obtain a transition process v 1 of the tracking differentiator, wherein the transition process v 1 is arranged for the desired heading angle phi d;
step two, initializing and controlling a rudder angle delta;
Step three, acquiring a current actual heading angle psi and a current actual navigational speed U of the marine robot, and inputting the psi, delta and U into a linear expansion state observer to acquire a disturbance compensation parameter b of the submerged bow system and three state variables in the submerged bow system;
three state variables in the submerged bow system are: submerged bow z 1, steering acceleration z 2, and disturbance z 3 of submerged bow system;
and (3) the linear expansion state observer in the step three is as follows:
Where β 01、β02、β03 is the gain factor of the linear extended state observer, z i,i＝1,2,3,zi is the state variable of the linear extended state observer, e 1、b0 is the intermediate variable, V is the derivative of v, v is the actual navigational speed after smoothing, K Fal is the proportionality coefficient affecting v to the U tracking speed, fal () is a function filter, delta Fal is a filter factor, a Fal is a filter design parameter, e Fal is an intermediate variable, disturbance compensation parameter b=b 0v2;
Step four, inputting the z 1、z2、z3、b、v1 obtained in the step one and the step three into adaptive state error feedback based on a criterion function to obtain a required control rudder angle delta';
adaptive state error feedback based on criterion functions, as follows:
Wherein, delta' is the required rudder angle, delta 0 is an intermediate variable, delta t > 0 is the interval time, z i (t) is z i at the time t, and lambda is the weight coefficient;
And fifthly, issuing the required rudder angle delta ' instruction obtained in the step four to an operating device of a steering engine through a main control computer, so as to obtain an actual heading angle phi ' of the marine robot corresponding to the required rudder angle delta ', comparing the phi ' with an expected heading angle phi d, ending the heading control if the error of phi ' and phi d is within a preset error, assigning delta ' to delta and phi ' and returning to the step three until the error of phi ' and phi d is within the preset error if the error of phi ' and phi d is not within the preset error.
2. The dynamic compensation type active-disturbance-rejection heading control method of the marine robot according to claim 1, wherein the method comprises the following steps: the tracking differentiator in the first step is as follows:
Where v 1 (t) is the transition at time t where the tracking differentiator is arranged for the desired heading angle ψ d, v 1 (t+1) is the transition at time t+1 where the tracking differentiator is arranged for the desired heading angle ψ d, v 2 (t) is the differentiated signal of v 1 (t), ψ d (t) is the desired heading of the submerged body at time t, r is the speed factor, h is the sampling step size, fh is the intermediate variable, h 0 is the filter factor, fhan (·) is the fastest control integration function.
3. The dynamic compensation type active-disturbance-rejection heading control method of the marine robot according to claim 2, wherein the method comprises the following steps:
wherein d, a are intermediate variables.
4. A dynamic compensation type auto-disturbance rejection heading control method of a marine robot according to claim 3, characterized in that:
wherein d 0、a0, y are intermediate variables.
5. The dynamic compensation type auto-disturbance rejection heading control method of the marine robot according to claim 4, wherein the method comprises the following steps:
6. the dynamic compensation type auto-disturbance rejection heading control method of the marine robot according to claim 5, wherein the method comprises the following steps: e Fal = U-v.
7. The dynamic compensation type auto-disturbance rejection heading control method of the marine robot according to claim 6, wherein the method comprises the following steps:
Wherein C is the lift coefficient of the rudder plate, L is the distance from the rudder plate to the gravity center of the submerged body, I is the moment of inertia of the submerged body around the gravity axis, lambda 66 is the additional moment of inertia coefficient of the submerged body in the bow direction, rho is the sea water density, and S is the rudder plate area.
8. The dynamic compensation type auto-disturbance rejection heading control method of the marine robot according to claim 7, wherein the method comprises the following steps: beta 01＝3ω,β02＝3ω2,β03＝ω3;
Where ω is the gain design parameter.
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