DESIGN METHOD FOR ACTIVE DISTURBANCE REJECTION ROLL CONTROLLER OF VEHICLE UNDER DISTURBANCE OF COMPLEX SEA CONDITIONS

Abstract

The present disclosure provides a design method for an active disturbance rejection roll controller of a vehicle under disturbance of complex sea conditions, including: step 1: establishing a vehicle roll attitude control model; step 2: designing an active disturbance rejection controller (ADRC) on the basis of the control model in step 1 and a pole placement method; and step 3: performing an active disturbance rejection roll control by using the active disturbance rejection controller in step 2. The present disclosure solves the problem of a stable control of the vehicle under the disturbance of the complex sea conditions.

Claims

1. A design method for an active disturbance rejection roll controller of a vehicle under disturbance of complex sea conditions, wherein an active disturbance rejection roll control method for the vehicle comprises: step 1: establishing a vehicle roll attitude control model; step 2: designing an active disturbance rejection controller (ADRC) on the basis of the control model in step 1 and a pole placement method; and step 3: performing an active disturbance rejection roll control by using the active disturbance rejection controller in step 2.

2. The design method for the active disturbance rejection roll controller of the vehicle under the disturbance of the complex sea conditions according to claim 1, wherein in step 1, according to a theorem of momentum and moment of momentum, an equation of the roll motion is obtained as follows: $\begin{array}{cc}\{\begin{array}{c}{J}_x{\stackrel{.}{w}}_x+\left(J_z-J_y\right)w_y{w}_x=A_{m_x}^{\beta }{v}^2\beta -A_{m_x}^{\delta }{v}^2{\delta }_d-A_{m_x}^w{v}^2{w}_x+A_{m_{\mathrm{xp}}}{v}^2-{\lambda }_{44}{\stackrel{.}{w}}_x-B\left(z_b\cos \phi +h\sin \phi \right)\cos \theta +M_d\\ \phi =w_x-\left(w_y\cos \phi -w_z\sin \phi \right)\tan \theta \\ \cos \Theta \sin \Phi =\cos \beta \cos \theta \sin \phi -\sin \alpha \sin \beta \cos \theta \cos \phi +\cos \alpha \sin \beta \sin \theta \end{array}& \left(1\right)\end{array}$ wherein, a simplifying assumption is made on the equation according to a typical trajectory, that is, the equation is simplified under three conditions of linearization, horizontal straight trajectory and axial symmetry of the vehicle, and the simplified equation of roll motion is as follows: $\begin{array}{cc}\left(J_x+{\lambda }_{44}\right)\frac{d{w}_x}{dt}+\frac{1}{2}\rho v^{2}SL{m}_x^{wx}{w}_{x_1}=\frac{1}{2}\rho v^{2}SL{m}_x^{{\delta }_d}{\delta }_d+M_d& \left(2\right)\end{array}$ where J.sub.x is a moment of inertia of the vehicle along an x axis, λ.sub.44 is additional mass of the vehicle along the x axis, P is density of an environment where the vehicle is located, v is a velocity of the vehicle, S is a characteristic area of the vehicle, L is a characteristic length of the vehicle, m.sub.x.sup.wx is a roll moment damping constant of the vehicle, w.sub.x is an angular velocity in roll of the vehicle, m.sub.x.sup.δ.sup.d is a relative derivative of a roll control moment of the vehicle, δ.sub.d is an equivalent roll rudder deflection angle of the vehicle, and M.sub.d is a disturbance moment caused by the complex sea conditions around the vehicle; and a transfer function of a roll angle to a roll rudder deflection angle is as follows: $\begin{array}{cc}{G}_{\phi }\left(s\right)=\frac{\frac{1}{2}\rho v^{2}SL{m}_x^{{\delta }_d}}{\left(J_x+{\lambda }_{44}\right)s-\frac{1}{2}\rho v^{2}SL{m}_x^{wx}}\frac{1}{s}& \left(3\right)\end{array}$

3. The design method for the active disturbance rejection roll controller of the vehicle under the disturbance of the complex sea conditions according to claim 1, wherein designing the active disturbance rejection controller in step 2 comprises: step 2.1: designing a linear extended state observer (LESO) without an object model; step 2.2: designing a linear state error feedback (LSEF) controller; step 2.3: performing a simulation analysis on the LESO in step 2.1 and the LSEF controller in step 2.2; and step 2.4: verifying performance of the active disturbance rejection controller (ADRC).

4. The design method for the active disturbance rejection roll controller of the vehicle under the disturbance of the complex sea conditions according to claim 3, wherein in step 2.1, with making y.fwdarw.φ and w representing total disturbance, a vehicle roll control system is described as follows:
ÿ−a.sub.1{dot over (y)}−a.sub.0y+w+bu   (4) wherein, y is a roll angle, {dot over (y)} is an angular velocity in roll, ÿ is an acceleration of the roll angle, u is an input of control quantity, b is a relative coefficient of control, a.sub.0 is a relative coefficient of the roll angle, and a.sub.1 is a relative coefficient of the angular velocity in roll; the total disturbance is set as follows:
f(y, {dot over (y)}, w, t)=−a.sub.1{dot over (y)}−a.sub.0y+w+(b−b.sub.0)u   (5) formula (5) is rewritten as follows:
ÿ=f+b.sub.0u   (6) by setting state variables as follows: x.sub.1=y, x.sub.2={dot over (y)}, and x.sub.3=f, a continuous extended state observer is obtained as follows:
{dot over (x)}=Ax+Bu+E{dot over (f)}  (7) wherein, $A=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 0& 0& 0\end{array}\right],B=\left[\begin{array}{c}0\\ b_0\\ 0\end{array}\right],\mathrm{and}E=\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right];$ a corresponding LESO is: $\begin{array}{cc}\{\begin{array}{c}\stackrel{.}{z}=\mathrm{Ax}+Bu+L\left(y-\hat{y}\right)\\ \hat{y}=Cz\end{array}& \left(8\right)\end{array}$ wherein, C=[1 0 0], and L=[L.sub.1L.sub.2 L.sub.3].sup.T is an error feedback control gain matrix of the observer; a characteristic equation of the formula is:
λ(s)=|sI−(A−LC)|  (9) after parameterization, a pole of the characteristic equation is designed as follows:
λ(s)=(s+w.sub.0)(s+k.sub.0w.sub.0)(s+k.sub.2w.sub.0)   (10) where w.sub.0 is a pole of a designed extended state observer, and k.sub.1 and k.sub.2 are pole placement coefficients of the extended state observer; and a gain matrix of the extended state observer is obtained as follows: $\begin{array}{cc}L=\left[\begin{array}{c}\left(k_1+k_2+1\right)w_0\\ \left(k_1+k_2+k_1{k}_2\right)w_0^2\\ \left(k_1{k}_2\right)w_0^3\end{array}\right]& \left(11\right)\end{array}$

5. The design method for the active disturbance rejection roll controller of the vehicle under the disturbance of the complex sea conditions according to claim 3, wherein in step 2.2, the LSEF adopts a controller of a linear proportional and derivative (PD) combination, z.sub.1.fwdarw.y, z.sub.2.fwdarw.{dot over (y)}; and a control law is:
u.sub.0=k.sub.p(z.sub.c−z.sub.1)−k.sub.dz.sub.2   (12) where, u.sub.0 is a final control output, z.sub.c is an expected roll angle, z.sub.1 is a roll angle of the vehicle in a current state, and z.sub.2 is an angular velocity in roll of the vehicle in the current state; a closed-loop transfer function is: $\begin{array}{cc}G\left(s\right)=\frac{k_p}{s^2+k_{d}s+k_p}& \left(13\right)\end{array}$ where k.sub.p and k.sub.d are controller parameters needing to be designed, and, by selecting the pole of the transfer function of the controller and placing the pole at different positions w.sub.c and k.sub.3w.sub.c, w.sub.c>1, k.sub.3>1, the controller parameters are obtained as follows:
k.sub.p=k.sub.3w.sub.c.sup.2
k.sub.d=(k.sub.3+1)w.sub.c   (14) after parametric design, six parameters to be adjusted in the ADRC are w.sub.0, w.sub.c, b.sub.0, k.sub.1, k.sub.2, k.sub.3, wherein w.sub.0 is the pole of the extended state observer, w.sub.c is a pole of the controller, b.sub.0 is a control coefficient, k.sub.1 and k.sub.2 are the pole placement coefficients of the extended state observer, and k.sub.3 is a pole placement coefficient of the controller.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0041] FIG. 1 is a schematic structural diagram of an ADRC in the present disclosure.

[0042] FIG. 2 is a schematic structural diagram of an extended state observer in the present disclosure.

[0043] FIG. 3 is a graph of ADRC output with an input signal as a unit step signal and an external disturbance as a constant disturbance in the present disclosure.

[0044] FIG. 4 is a graph of PID output with an input signal as a unit step signal and an external disturbance as a constant disturbance in the present disclosure.

[0045] FIG. 5 is a graph of ADRC rudder deflection angle with an input signal as a unit step signal and an external disturbance as a constant disturbance in the present disclosure.

[0046] FIG. 6 is a graph of PID rudder deflection angle with an input signal as a unit step signal and an external disturbance as a constant disturbance in the present disclosure.

[0047] FIG. 7 is a graph of ADRC output with an input signal as a unit step signal and an external disturbance as a periodic disturbance in the present disclosure.

[0048] FIG. 8 is a graph of PID output with an input signal as a unit step signal and an external disturbance as a periodic disturbance in the present disclosure.

[0049] FIG. 9 is a graph of ADRC rudder deflection angle with an input signal as a unit step signal and an external disturbance as a periodic disturbance in the present disclosure.

[0050] FIG. 10 is a graph of PID rudder deflection angle with an input signal as a unit step signal and an external disturbance as a periodic disturbance in the present disclosure.

[0051] FIG. 11 is a graph of ADRC output with an input signal as a square signal and an external disturbance as a periodic disturbance in the present disclosure.

[0052] FIG. 12 is a graph of PID output with an input signal as a square signal and an external disturbance as a periodic disturbance in the present disclosure.

[0053] FIG. 13 is a graph of ADRC rudder deflection angle with an input signal as a square signal and an external disturbance as a periodic disturbance in the present disclosure.

[0054] FIG. 14 is a graph of PID rudder deflection angle with an input signal as a square signal and an external disturbance as a periodic disturbance in the present disclosure.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0055] The technical solutions in the embodiments of the present disclosure are clearly and completely described below with reference to the accompanying drawings in the embodiments of the present disclosure. Apparently, the described embodiments are merely some rather than all of the embodiments of the present disclosure. On the basis of the embodiments of the present disclosure, all other embodiments derived by a person of ordinary skill in the art, without involving any creative effort, fall within the scope of protection of the present disclosure.

[0056] An active disturbance rejection roll control method for a vehicle under disturbance of complex sea conditions includes the following steps:

[0057] step 1: establishing a vehicle roll attitude control model;

[0058] step 2: designing an active disturbance rejection controller (ADRC) on the basis of the control model in step 1 and a pole placement method; and

[0059] step 3: performing an active disturbance rejection roll control by using the active disturbance rejection controller in step 2.

[0060] Furthermore, in step 1, according to a theorem of momentum and moment of momentum, an equation of the roll motion is obtained as follows:

[00008]$\begin{array}{cc}\{\begin{array}{c}{J}_x{\stackrel{.}{w}}_x+\left(J_z-J_y\right)w_y{w}_x=A_{m_x}^{\beta }{v}^2\beta -A_{m_x}^{\delta }{v}^2{\delta }_d-A_{m_x}^w{v}^2{w}_x+A_{m_{\mathrm{xp}}}{v}^2-{\lambda }_{44}{\stackrel{.}{w}}_x-B\left(z_b\cos \phi +h\sin \phi \right)\cos \theta +M_d\\ \phi =w_x-\left(w_y\cos \phi -w_z\sin \phi \right)\tan \theta \\ \cos \Theta \sin \Phi =\cos \beta \cos \theta \sin \phi -\sin \alpha \sin \beta \cos \theta \cos \phi +\cos \alpha \sin \beta \sin \theta \end{array}& \left(1\right)\end{array}$

[0061] where, a simplifying assumption is made on the equation according to a typical trajectory, that is, the equation is simplified under three conditions of linearization, horizontal straight trajectory and axial symmetry of the vehicle, and the simplified equation of the roll motion is as follows:

[00009]$\begin{array}{cc}\left(J_x+{\lambda }_{44}\right)\frac{d{w}_x}{dt}+\frac{1}{2}\rho v^{2}SL{m}_x^{wx}{w}_{x_1}=\frac{1}{2}\rho v^{2}SL{m}_x^{{\delta }_d}{\delta }_d+M_d& \left(2\right)\end{array}$

[0062] where, J.sub.x is a moment of inertia of the vehicle along an x axis, δ.sub.44 is additional mass of the vehicle along the x axis, P is density of an environment where the vehicle is located, v is a velocity of the vehicle, S is a characteristic area of the vehicle, L is a characteristic length of the vehicle, m.sub.x.sup.wx is roll moment damping constant of the vehicle, w.sub.x is an angular velocity in roll of the vehicle, m.sub.x.sup.δ.sup.d is a relative derivative of a roll control moment of the vehicle, δ.sub.d is an equivalent roll rudder deflection angle of the vehicle, and M.sub.d is a disturbance moment caused by the complex sea conditions around the vehicle.

[0063] To study an individual roll motion, the simplifying assumption is made according to the typical trajectory:

[0064] (1) the equation is linearized by a small-angle assumption;

[0065] (2) the horizontal straight trajectory is considered; and

[0066] (3) the vehicle is axisymmetric, a propeller is balanced, and a center of gravity is not shifted.

[0067] A transfer function of a roll angle to a roll rudder deflection angle is as follows:

[00010]$\begin{array}{cc}{G}_{\phi }\left(s\right)=\frac{\frac{1}{2}\rho v^{2}SL{m}_x^{{\delta }_d}}{\left(J_x+{\lambda }_{44}\right)s-\frac{1}{2}\rho v^{2}SL{m}_x^{wx}}\frac{1}{s}& \left(3\right)\end{array}$

[0068] Furthermore, the design of the active disturbance rejection controller in step 2 specifically includes the following steps:

[0069] step 2.1: designing a linear extended state observer (LESO) without an object model;

[0070] step 2.2: designing a linear state error feedback (LSEF) controller;

[0071] step 2.3: performing a simulation analysis on the LESO in step 2.1 and the LSEF controller in step 2.2; and

[0072] step 2.4: verifying performance of the active disturbance rejection controller (ADRC).

[0073] Furthermore, in step 2.1, with making y.fwdarw.φ and w representing total disturbance, a vehicle roll control system is described as follows:

ÿ−a.sub.1{dot over (y)}−a.sub.0y+w+bu   (4)

[0074] where, y is a roll angle, {dot over (y)}) is an angular velocity in roll, ÿ is an acceleration of the roll angle, u is an input of control quantity, b is a relative coefficient of control, a.sub.0 is a relative coefficient of the roll angle, and a.sub.1 is a relative coefficient of the angular velocity in roll.

[0075] The total disturbance is set as follows:

f(y, {dot over (y)}, w, t)=−a.sub.1{dot over (y)}−a.sub.0y+w+(b−b.sub.0)u   (5)

[0076] Formula (5) is rewritten as follows:

ÿ=f+b.sub.0u   (6)

[0077] By setting state variables as follows: x.sub.1=y, x.sub.2={dot over (y)}, and x.sub.3=f , a continuous extended state observer is obtained as follows:

{dot over (x)}=Ax+Bu+E{dot over (f)}  (7)

[00011]$A=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 0& 0& 0\end{array}\right],B=\left[\begin{array}{c}0\\ b_0\\ 0\end{array}\right],\mathrm{and}E=\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right].$

[0078] where,

[0079] The corresponding LESO is:

[00012]$\begin{array}{cc}\{\begin{array}{c}\stackrel{.}{z}=\mathrm{Ax}+Bu+L\left(y-\hat{y}\right)\\ \hat{y}=Cz\end{array}& \left(8\right)\end{array}$

[0080] where, C=[1 0 0], and L=[L.sub.1L.sub.2 L.sub.3].sup.T is an error feedback control gain matrix of the observer.

[0081] A characteristic equation of the formula is:

λ(s)=|sI−(A−LC)|  (9)

[0082] After parameterization, a pole of the characteristic equation is designed as follows:

λ(s)=(s+w.sub.0)(s+k.sub.0w.sub.0)(s+k.sub.2w.sub.0)   (10)

[0083] where, w.sub.0 is a pole of a designed extended state observer, and k.sub.1 and k.sub.2 are pole placement coefficients of the extended state observer; and

[0084] a gain matrix of the extended state observer is obtained as follows:

[00013]$\begin{array}{cc}L=\left[\begin{array}{c}\left(k_1+k_2+1\right)w_0\\ \left(k_1+k_2+k_1{k}_2\right)w_0^2\\ \left(k_1{k}_2\right)w_0^3\end{array}\right]& \left(11\right)\end{array}$

[0085] and derivative (PD) combination with the following form, z.sub.1.fwdarw.y, z.sub.2.fwdarw.{dot over (y)}; and the control law is:

u.sub.0=k.sub.p(z.sub.c−z.sub.1)−k.sub.dz.sub.2   (12)

[0086] where u.sub.0 is a final control output, z.sub.c is an expected roll angle, z.sub.1 is a roll angle of the vehicle in a current state, and z.sub.2 is an angular velocity in roll of the vehicle in the current state;

[0087] a closed-loop transfer function is:

[00014]$\begin{array}{cc}G\left(s\right)=\frac{k_p}{s^2+k_{d}s+k_p}& \left(13\right)\end{array}$

[0088] where k.sub.p and k.sub.d are controller parameters needing to be designed, and, by selecting the pole of the transfer function of the controller and placing the pole at different positions w.sub.c and k.sub.3w.sub.c w.sub.c>1, k.sub.3>1, the controller parameters are obtained as follows:

k.sub.p=k.sub.3w.sub.c.sup.2

k.sub.d=(k.sub.3+1)w.sub.c   (14)

[0089] After parametric design, the ADRC has six parameters to be adjusted, namely w.sub.0, w.sub.c, b.sub.0, k.sub.1, k.sub.2, k.sub.3, where w.sub.0 is the pole of the extended state observer, w.sub.c is a pole of the controller, b.sub.0 is a control coefficient, k.sub.1 and k.sub.2 are the pole placement coefficients of the extended state observer, and k.sub.3 is a pole placement coefficient of the controller.

[0090] The active disturbance rejection controller and the PID controller are respectively configured to perform simulation, and an amplitude of the roll angle is set to be ±20°.

[0091] An input signal is a unit step signal, and an external disturbance is a constant disturbance.

[0092] It can be seen from curves in FIG. 3 to FIG. 6 that an ADRC step response signal converges faster and has no constant error, while a PID converges for a longer time and finally has a constant error, but in general, a difference between control effects of the two is small under this operating condition.

[0093] The input signal is a unit step signal, and the external disturbance is a periodic disturbance.

[0094] It can be seen from curves in FIG. 7 to FIG. 10 that under the periodic disturbance, the ADRC step response signal converges faster, and final error convergence is smaller, while the PID controller has a larger tracking error.

[0095] The input signal is a square signal, and the external disturbance is the periodic disturbance.

[0096] It can be seen from curves in FIG. 11 to FIG. 14 that under the periodic disturbance, a tracking error of the ADRC with respect to a periodic square signal is smaller and finally converges, while the PID controller has a larger tracking error.