CN117519280A - Four-rotor unmanned aerial vehicle height control method based on pipeline model predictive control - Google Patents
Four-rotor unmanned aerial vehicle height control method based on pipeline model predictive control Download PDFInfo
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Abstract
The invention belongs to the field of control of four-rotor unmanned aerial vehicles, and provides a height control method of a four-rotor unmanned aerial vehicle based on pipeline model predictive control, which comprises the following steps: establishing a state space equation of the model; solving for H ∞ Robust observer gain; and solving the optimal control by adopting an output feedback pipeline model prediction control method. Aiming at the problems that the existing four-rotor unmanned aerial vehicle control algorithm does not completely consider the system disturbance and measurement noise and the safety flying height control under the condition that certain states of the system are not measurable, the four-rotor unmanned aerial vehicle height control method based on output feedback model predictive control is provided, and the system is characterized in that H is adopted ∞ Theory makes observer to interfere with and noiseThe method has robustness and improves the observation precision.
Description
Technical Field
The invention belongs to the field of control of four-rotor unmanned aerial vehicles, and relates to a four-rotor height control method based on pipeline model predictive control.
Background
With the development of society and the progress of technology, unmanned plane technology is rapidly developed and is increasingly widely applied. In recent years, unmanned aerial vehicles have been widely used in industries such as agriculture, fire protection, military, education and the like due to the advantages of small body structure, simple operation, multiple applicable scenes and the like. The complex and changeable working environment has higher requirements on the robustness of the control system of the four-rotor unmanned aerial vehicle.
The four-rotor unmanned aerial vehicle is a complex multi-degree-of-freedom under-actuated control object, has the characteristics of complex modeling, multi-degree-of-freedom nonlinear characteristics, strong coupling, environmental disturbance and the like, and makes the design of a control algorithm of the four-rotor unmanned aerial vehicle have higher difficulty. The four-rotor unmanned aerial vehicle height control algorithm commonly used at present comprises a classical proportional-integral-derivative (PID) control algorithm, a linear quadratic regulator (Linear Quadratic Regulator, LQR) control algorithm, a model predictive control (Model Predictive Control, MPC) algorithm, a Back Stepping method (Sliding Mode Control, SMC) algorithm and the like. The PID control adjusts the deviation between the expected value and the actual output value of the system through proportional, integral and differential links, so that the deviation gradually tends to 0, and the controlled object is controlled. The LQR algorithm is based on a state space model, and an optimal control law is obtained by solving a system quadratic objective function. The mechanism of the MPC algorithm can be described as: at each sampling moment, according to the obtained current measurement information, solving a finite time domain open loop optimization problem on line, and acting the first element of the obtained control sequence on the controlled object. At the next sampling instant, the above process is repeated: the optimization problem is refreshed and solved again with new measurements. The backstepping method is one of nonlinear control algorithms commonly used, and is essentially a recursive algorithm, the control law is solved in several steps, lyapunov functions are respectively designed to calm each step, and the optimal control quantity is obtained after multi-step operation. The sliding mode control algorithm designs a switching hyperplane of the system according to the expected dynamic characteristic of the system, and the system state is converged from the outside of the hyperplane to the switching hyperplane through the sliding mode controller. Once the system reaches the switching hyperplane, the control function ensures that the system reaches the origin of the system along the switching hyperplane, and the process of sliding along the switching hyperplane to the origin is called sliding mode control.
Although the four-rotor unmanned aerial vehicle control algorithm is quite abundant at present, the various algorithms still have some defects. For example, in the "PID-based four-rotor aircraft control system research" article of Huang Yi et al, classical PID algorithms, while simple, have difficulty quantifying the effects of process disturbances and measurement noise present in the control system on the control process, often requiring empirical tuning. The control algorithm of the combination of the PID and LQR algorithms proposed in the article "four-rotor unmanned aerial vehicle control system based on PID and LQR" by Ma Min et al is not constrained, but can only pass post-processing, and also does not consider the effects of process disturbances and measurement noise. The four-rotor unmanned MPC algorithm proposed by Inna Sharf in "Aconstrained error-based MPC for path following of quadrotor with stability analysis" does not take into account the effects of measurement noise and some conditions of the system that are not measurable, although it takes into account the effects of process disturbances and constraints. Zhou Laihong et al, although the back-stepping method proposed in the article "four-rotor unmanned aerial vehicle trajectory tracking control based on the improved back-stepping method" is improved, the design process is still relatively complicated. The sliding mode control proposed in Cai Guang et al, "a fixed time quadrotor control method based on terminal sliding mode control," is prone to jitter.
Disclosure of Invention
Aiming at the problem that the existing four-rotor unmanned aerial vehicle control algorithm does not fully consider the influence of process interference and measurement noise on the flying height safety under the condition that certain states are not measurable, the invention provides a four-rotor height control method based on pipeline model predictive control.
In order to achieve the above purpose, the invention adopts the technical scheme that:
a four-rotor unmanned aerial vehicle height control method based on pipeline model predictive control comprises the following steps:
s1, establishing a height direction state space model of the four-rotor unmanned aerial vehicle:
s1.1, establishing a description of a nonlinear dynamics equation of the quadrotor unmanned aerial vehicle:
wherein phi is a roll angle, theta is a pitch angle, phi is a yaw angle, m is the mass of the four-rotor unmanned aerial vehicle, g represents the local gravitational acceleration, I x ，I y ，I z Respectively represent the rotational inertia of the unmanned aerial vehicle around X, Y and Z axes, C k Is the comprehensive lift coefficient omega of four rotors i Represents the angular velocity of the ith propeller, d is the half-axis length of the quadrotor, C M U is the back torque coefficient of the motor 1 、U 2 、U 3 、U 4 Respectively representing a vertical motion control amount, a roll control amount, a pitch control amount, and a yaw control amount;
s1.2, decoupling, linearizing and discretizing the nonlinear model, and separating a height direction model:
the continuous time actual system model considering the interference effect is:
wherein the state variable at time t isz (t) and->The position and the speed at the time t are respectively represented, and the control input at the time t is U (t) = [ mg-U) 1 cosφcosθ] T ，A z As a system matrix, B z Is a control matrix; w is the unknown but bounded process disturbance of the system existence, D w According to the actual situation; let-> State and control inputs representing a nominal system of the four-rotor unmanned aerial vehicle without disturbance and noise; discretizing the system to obtain a discrete time practical system in the height direction, wherein the discrete time practical system comprises the following steps:
wherein Δt represents the system sampling time;superscript n x ,n u ,n y Respectively the actual system state variables x z Control input u z Measuring output y z Are positive integers; v is measurement noise unknown but bounded by the system, < >>Superscript n v ，n w The dimensions of the measurement noise v and the process interference w are respectively represented and are positive integers; d (D) v Is an interference action matrix;
s2, using a Long Beige observer to the model obtained in the step S1 to obtain a dynamic error system:
the actual system design for discrete time is as follows Long Beige observer:
wherein,the state estimation quantity is L, and the observation gain matrix is needed to be designed;
the undisturbed nominal system of the discrete time actual system is set as follows:
wherein,is a state variable of the above nominal system, +.>For the control input of the above nominal system,a measurement output for the above nominal system;
order theThe error system of the actual value and the estimated value is expressed as:
wherein A is L Satisfy ρ (A) L )＜1；
Order theThe error system of the estimated value from the nominal value is expressed as:
wherein A is K Satisfy ρ (A) K ) < 1, K is control law matrix, let discrete timeControl input of real system (1)
S3, based on H ∞ Theoretical solution observer gain matrix L:
given a scalar γ > 0, let l=p -1 Y, whereinIs positive and->And satisfies the following linear matrix inequality:
wherein represents the transpose of the symmetrical position, I n Representing an n-dimensional array of units. The optimal matrix L is obtained by minimizing the parameter γ:
minγ 2
s.t.(5)
s3, predicting and solving optimal control based on an output feedback pipeline model:
let the robust positive invariant set of the error system of the actual value and the estimated value beThe robust positive invariant set of error system of estimated value and nominal value is +.>Let->
Constraint exists in a discrete time real system (1)Let the non-disturbance nominal system satisfy:
wherein X is f For terminal constraints, N is the prediction time domain,for the state constraint of a discrete-time real system, +.>Constraint for control input of discrete-time real system, < ->For state constraints of the nominal system, +.>Control input constraints for a nominal system; optimal control is obtained by solving the following optimization problem>
s.t.(6)
Wherein Q, R, P Z Is a matrix with a positive corresponding dimension,state indicating the i-th moment of the nominal system, +.>Control input representing the i-th moment of the nominal system, is->Indicating the state of the nominal system at time N.
The invention has the beneficial effects that: aiming at the problems that the existing four-rotor unmanned aerial vehicle control algorithm does not completely consider the system disturbance and measurement noise and the safety flying height control under the condition that certain states of the system are not measurable, the four-rotor unmanned aerial vehicle height control method based on output feedback model predictive control is provided, and the system is characterized in that H is adopted ∞ The theory makes the observer have robustness to interference and noise, improves the observation precision.
Drawings
FIG. 1 is a flow chart of overall control of a rotary-wing drone;
fig. 2 is a schematic structural diagram of an example X-type quad-rotor unmanned helicopter;
FIG. 3 is a schematic illustration of an example quad-rotor unmanned helicopter flight position;
FIG. 4 is a schematic diagram of an example quad-rotor unmanned helicopter observation error;
FIG. 5 is an example four rotor output feedback duct model predictive control schematic;
fig. 6 is a brief introduction to this patent embodiment.
Detailed Description
The following describes the embodiments of the present invention further with reference to the drawings and technical schemes.
A four-rotor unmanned aerial vehicle height control method based on pipeline model predictive control is shown in figure 1;
s1, establishing a height direction state space model of the four-rotor unmanned aerial vehicle:
s1.1, establishing a description of a nonlinear dynamics equation of the quadrotor unmanned aerial vehicle:
wherein phi is a roll angle, theta is a pitch angle, phi is a yaw angle, m is the weight of the quadrotor unmanned aerial vehicle, g represents the gravitational acceleration, I x ，I y ，I z Respectively represent the rotational inertia of the unmanned aerial vehicle around X, Y and Z axes, C k Is the comprehensive lift coefficient omega of four rotors i Represents the angular velocity of the ith propeller, d is the half-axis length of the quadrotor, C M Is the motor anti-torsion coefficient. U (U) 1 ，U 2 ，U 3 ，U 4 Respectively representing the vertical motion control amount, the roll control amount, the pitch control amount, and the yaw control amount.
S1.2, decoupling, linearizing and discretizing the nonlinear model, and separating a height direction model:
the continuous time actual system model considering the interference effect is:
wherein the state variable at time t isz (t) and->The position and the speed at the time t are respectively represented, and the control input at the time t is U (t) = [ mg-U) 1 cosφcosθ] T ，A z As a system matrix, B z Is a control matrix. w is the unknown but bounded process disturbance of the system existence, D w Depending on the actual situation. Let-> Representing the state and control inputs of a nominal system of a four rotor unmanned aerial vehicle without disturbance and noise. Discretizing the system to obtain a state space equation in the height direction of the discrete-time actual system:
x z [(k+1)Δt]＝(I+A z Δt)x z (kΔt)+B z Δtu z (kΔt)+D w Δtw(kΔt)
y z (kΔt)＝C z x z (kΔt)+D v v(kΔt)
the above formula is simplified for simplicity to:
where Δt represents the system sampling time,superscript n x ,n u ,n y Respectively the actual system state variables x z Control input u z Measuring output y z Is a positive integer. v is measurement noise unknown but bounded by the system, < >>D v Depending on the actual situation. />Superscript n v ，n w The dimensions of the measurement noise v and the process disturbance w are respectively represented, and are positive integers.
S2, using a Long Beige observer to the model obtained in the step S1 to obtain a dynamic error system:
s2.1 some basic concepts are first introduced below:
given two sets S 1 And S is 2 Their Minkowski Sum (Minkowski Sum) is defined as:
an m-order centrosymmetric polyhedron (zootope),is a hypercube B m Affine transformation of (c):
wherein the method comprises the steps ofIs->Wherein n and m are positive integers, matrix +.>Called->And determines its shape and size. For convenience of presentation, the notation +.>
Given two centrosymmetric polyhedronsAnd->Their minkowski sum satisfies:
we give a central symmetrical polyhedronAnd a matrix->Then:
assuming that the initial state of the actual system (1) satisfies x z (0)∈<p 0 ,H 0 >And is also provided with
S2.2 for the actual system (1) the following Long Beige observer is designed:
wherein the method comprises the steps ofIs a state estimator, let ∈ ->L is the observation gain matrix that needs to be designed.
The undisturbed nominal system of the discrete time real system (1) is set as follows:
wherein the method comprises the steps ofIs a state variable of the above nominal system, +.>For the control input of the above nominal system,is the measured output of the nominal system.
Order theThe error system of the actual value and the estimated value can be expressed as:
wherein A is L Satisfy ρ (A) L ) < 1, letThen->Assuming that the robust positive invariant set of the error system (3) of the actual value and the estimated value is +.>And->
Order theThe error system of the estimated value from the nominal value can be expressed as:
wherein A is K Satisfy ρ (A) K ) < 1. To reduce the disturbance effect, a feedback term is introduced, and the control input of the discrete-time real system (1) is thatK is a control law matrix. Let->Then->Let the robust positive invariant of the error system (4) of the estimated value and the nominal value be +.>And->
S3, based on H ∞ Theoretical solution observer gain matrix L:
by means of a reachable set analysis of the error system (3) of actual and estimated values, a set ε (k) can be determined such thatBecause of->So x is z (k) Can be expressed as:
set X (k) is estimated with stateIs centered and the error reachable set ε (k) determines its size and shape, so to obtain a more accurate x z (k) The estimation should design an observer gain matrix L to reduce the effect of measurement noise and process disturbances on the estimation error. So will H ∞ The robust observer theory is introduced into the member estimation, and the actual value and the estimation are combinedThe error system (3) of the values rewrites:
wherein the method comprises the steps of
Given a scalar γ > 0, let l=p -1 Y, whereinIs positive and->And satisfies the following linear matrix inequality:
wherein represents the transpose of the symmetrical position, I n Representing an n-dimensional array of units.
Because L=P -1 Y, so y=pl, substituting it into (6) yields:
according to the schulk lemma, the above formula is equivalent to:
according to the bounded real theorem, inequality (7) has the solution equivalent that the system (5) is stable and from d (k) toTransfer function of->Satisfy->Since d (k) is bounded, +.>Is also bounded.
The optimal matrix L is obtained by minimizing the parameter γ:
minγ 2
s.t.(6)
s3, predicting and solving optimal control based on an output feedback model:
order the
Constraint exists in a discrete time real system (1)We can let the nominal system (2) satisfy:
wherein X is f For terminal constraints, N is the prediction time domain,for the state constraint of the discrete-time real system (1), ->Constraint for control input of a discrete-time real system (1), for example>Is a nominal systemStatus constraint of->Constraints are input for the control of the nominal system. Optimal control is obtained by solving the following optimization problem>
s.t.(8)
Wherein Q, R, P Z Is a matrix with a positive corresponding dimension,state indicating the i-th moment of the nominal system, +.>Control input representing the i-th moment of the nominal system, is->Indicating the state of the nominal system at time N. Then fromA system optimal control input may be obtained.
A set of experimental simulations is given below:
model parameters of the X-type four-rotor unmanned aerial vehicle adopted in the experiment are as follows: mass 1.4kg, velocity in height directionGravitational acceleration g=9.8 m/s 2 ，0N≤U 1 Less than or equal to 20N, sampling time delta t=0.05s, and the expected reference point is(i.e. hovering at 2 meters), reference input +.>Four rotor unmanned aerial vehicle system initial state is [ 00 ]] T The initial value of the observation system is [ 0.002.0.02 ]] T . Prediction time domain n=10. The disturbance and measurement noise matrix is set as follows:
order theLet->|v(k)|≤1。K,P z Are each found by the matlab LQR function.
From fig. 3 it can be seen that the position error of the quadrotor drone is approaching 0 very quickly. It can be seen from fig. 4 that the errors of the true and observed values of the system state remain unchangedInside. From fig. 5 it can be seen that +.>Always within the constraint of a real system, and meets the requirement of predictive control of an output feedback pipeline model. The invention realizes the four-rotor unmanned aerial vehicle height control method based on the pipeline model predictive control.
The examples described above represent only embodiments of the invention and are not to be understood as limiting the scope of the patent of the invention, it being pointed out that several variants and modifications may be made by those skilled in the art without departing from the concept of the invention, which fall within the scope of protection of the invention.
Claims (1)
1. The four-rotor unmanned aerial vehicle height control method based on the pipeline model predictive control is characterized by comprising the following steps:
s1, establishing a height direction state space model of the four-rotor unmanned aerial vehicle:
s1.1, establishing a description of a nonlinear dynamics equation of the quadrotor unmanned aerial vehicle:
wherein phi is a roll angle, theta is a pitch angle, phi is a yaw angle, m is the mass of the four-rotor unmanned aerial vehicle, g represents the local gravitational acceleration, and I x ，I y ，I z Respectively represent the rotational inertia of the unmanned aerial vehicle around X, Y and Z axes, C k Is the comprehensive lift coefficient omega of four rotors i Represents the angular velocity of the ith propeller, d is the half-axis length of the quadrotor, C M U is the back torque coefficient of the motor 1 、U 2 、U 3 、U 4 Respectively representing a vertical motion control amount, a roll control amount, a pitch control amount, and a yaw control amount;
s1.2, decoupling, linearizing and discretizing the nonlinear model, and separating a height direction model:
the continuous time actual system model considering the interference effect is:
wherein the state variable at time t isz (t) and->The position and the speed at the time t are respectively represented, and the control input at the time t is +.>A z As a system matrix, B z Is a control matrix; w is the unknown but bounded process disturbance of the system existence, D w According to the actual situation; let-> State and control inputs representing a nominal system of the four-rotor unmanned aerial vehicle without disturbance and noise; discretizing the system to obtain a discrete time practical system in the height direction, wherein the discrete time practical system comprises the following steps:
C＝[1 0]
wherein Δt represents the system sampling time;superscript n x ,n u ,n y Respectively the actual system state variables x z Control input u z Measuring output y z Are positive integers; v is measurement noise unknown but bounded by the system, < >>Superscript n v ，n w The dimensions of the measurement noise v and the process interference w are respectively represented and are positive integers; d (D) v Is an interference action matrix;
s2, using a Long Beige observer to the model obtained in the step S1 to obtain a dynamic error system:
the actual system design for discrete time is as follows Long Beige observer:
wherein,the state estimation quantity is L, and the observation gain matrix is needed to be designed;
the undisturbed nominal system of the discrete time actual system is set as follows:
wherein,is a state variable of the above nominal system, +.>For the control input of the above nominal system,a measurement output for the above nominal system;
order theThe error system of the actual value and the estimated value is expressed as:
wherein A is L Satisfy ρ (A) L )＜1；
Order theThen the estimated value and nominalThe error system of values is expressed as:
wherein A is K Satisfy ρ (A) K ) The < 1, K is a control law matrix, and the control input of the discrete time actual system (1) is made
S3, based on H ∞ Theoretical solution observer gain matrix L:
given a scalar γ > 0, let l=p -1 Y, whereinIs positive and->And satisfies the following linear matrix inequality:
wherein represents the transpose of the symmetrical position, I n A unit array representing n dimensions; the optimal matrix L is obtained by minimizing the parameter γ:
minγ 2
s.t.(5)
s3, predicting and solving optimal control based on an output feedback pipeline model:
let the robust positive invariant set of the error system of the actual value and the estimated value beThe robust positive invariant set of error system of estimated value and nominal value is +.>Let->
Constraint exists in a discrete time real system (1)Let the non-disturbance nominal system satisfy:
wherein X is f For terminal constraints, N is the prediction time domainFor the state constraint of a discrete-time real system, +.>Constraint for control input of discrete-time real system, < ->For state constraints of the nominal system, +.>Control input constraints for a nominal system; optimal control is obtained by solving the following optimization problem>
s.t.(6)
Wherein Q, R, P Z Is a matrix with a positive corresponding dimension,state indicating the i-th moment of the nominal system, +.>Control input representing the i-th moment of the nominal system, is->Indicating the state of the nominal system at time N.
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