CN108776432B - Predictive control method of airport runway detection robot based on network - Google Patents

Predictive control method of airport runway detection robot based on network Download PDF

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CN108776432B
CN108776432B CN201810589307.8A CN201810589307A CN108776432B CN 108776432 B CN108776432 B CN 108776432B CN 201810589307 A CN201810589307 A CN 201810589307A CN 108776432 B CN108776432 B CN 108776432B
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airport runway
detection robot
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李芃
涂德志
张兰勇
张鑫
曹聪
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Harbin Engineering University
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Abstract

The invention discloses a network-based prediction control method for an airport runway detection robot, which is characterized in that a kinematics model of the airport runway detection robot is established for an airport runway detection robot network control system, the kinematics model is converted into a controlled autoregressive integral sliding model used in minimum variance control, then the model is converted into two independent single-input single-output linear models in the x direction and the y direction of the robot under a global coordinate system, and the airport runway detection robot is subjected to prediction control through an improved GPC algorithm. The method can effectively reduce the network delay and noise interference influence caused by remote network control in the movement process of the airport runway detection robot, and improves the resolving speed and robustness of the movement controller of the airport runway detection robot in the network environment.

Description

Airport runway detection robot prediction control method based on network
Technical Field
The invention relates to a robot prediction control method, in particular to an airport runway detection robot prediction control method based on a network, and belongs to the technical field of robot motion control in a network environment.
Background
With the development of the modern aviation industry, the safety problem of the airport runway is more and more emphasized as an important platform for the takeoff and landing of the airplane. Defects and foreign bodies on the runway of the airport pose a great threat to the taking-off and landing process of the airplane. Therefore, the safety detection of the airport runway has important practical significance for ensuring the smooth takeoff and landing of the airplane. The invention realizes the safety detection of the runway by remotely controlling the runway detection robot in the wireless network environment. The remote control center receives sensor signals through a network and transmits motion control signals to the robot, the problems of network random delay, packet loss and the like exist, the motion control performance of the system is affected, and the original control method cannot meet the requirements.
Since the generalized predictive control algorithm proposed by Clarke et al in the 20 th century has a good control effect and strong robustness, the generalized predictive control algorithm is widely applied in the actual production process, but the control algorithm needs to solve a nephogram (dip) equation on line and needs to perform inversion operation on a control matrix, so that the on-line calculation workload is large. Aiming at the defect of the generalized predictive control algorithm, a plurality of scholars at home and abroad research the generalized predictive control algorithm. A series of improved methods are proposed with the aim of reducing the amount of computation, among which the implicit GPC algorithm is used more. Although the method avoids solving the Diphantine equation, inversion is still required, and the robot cannot be quickly and effectively controlled in a remote real-time manner.
Disclosure of Invention
In view of the above-mentioned prior art, the technical problem to be solved by the present invention is to provide a network-based airport runway inspection robot predictive control method that can solve the problem of motion control of airport runway inspection robots in an environment with network delay and interference.
In order to solve the technical problem, the invention provides a network-based airport runway detection robot prediction control method, which comprises the following steps:
s1: performing kinematic modeling according to a Mecanum wheel (Mecanum wheel) kinematic chassis of the airport runway detection robot to obtain a kinematic model;
s2: converting a kinematic model of the airport runway detection robot into a controlled autoregressive integral sliding average model;
s3: respectively converting a controlled autoregressive integral sliding average model of the airport runway detection robot into a model in the x direction under a global coordinate system and a model in the y direction under the global coordinate system, and respectively carrying out generalized predictive control on the models;
s4: establishing an original controller performance index function by utilizing a generalized predictive control algorithm;
s5: reconstructing the performance index function on the basis of the original controller performance index function to obtain a reconstructed performance index function;
s6: obtaining the control quantity delta V in the x direction according to the reconstructed performance index functionx(k) And control quantity DeltaV in y directiony(k) The delta V is converted into the data through a wireless network modulex(k) And Δ Vy(k) Is transmitted to the airport runway detection robot from the upper computer,wherein:
Figure BDA0001690149490000021
the invention relates to a network-based airport runway detection robot prediction control method, which further comprises the following steps:
the kinematics model of the airport runway inspection robot in S1 satisfies:
Figure BDA0001690149490000022
wherein v isxDetecting x-direction speed, v, of robot under global coordinate system for airport runwayyThe speed of the airport runway detection robot in the y direction under the global coordinate system is defined, omega is the rotation angular speed of the airport runway detection robot, theta is the included angle between the airport runway detection robot and the x axis under the global coordinate system, R represents the radius of a Mecanum wheel, and l is the rotation angular speed of the airport runway detection robot under the global coordinate system1For each Mecanum wheel's distance, l, from the x-axis in the individual coordinate system2For each Mecanum wheel's distance, v, from the y-axis in the individual coordinate system1,v2,v3,v4The rotational speeds of the motors controlling the four mecanum wheels, respectively.
The controlled autoregressive integral moving average model in S2 satisfies:
Figure BDA0001690149490000023
wherein z is-1Is a one-step retrogradation operator, wherein, Deltax and Deltay are respectively the displacement variation of the runway detection robot in the x and y directions under the global coordinate system in the time T, d is time delay, and z is time delay-dIs an introduced delay factor.
The controlled autoregressive integral moving average model in the x direction in S3 satisfies:
(1-z-1)x＝Tz-dvx(k-1)
the controlled autoregressive integral moving average model in the y direction respectively meets the following conditions:
(1-z-1)y＝Tz-dvy(k-1)。
the performance index function in S4 satisfies:
Figure BDA0001690149490000031
where E is the mathematical expectation, Δ u is the control increment, and Δ u (t + j) is 0, j is Nu,...,N1Is represented in NuThe control quantity is not changed after the step. N is a radical of1、N2Minimum and maximum predicted time domain lengths, N, respectivelyuFor controlling the time domain length, lambda is a control weighting coefficient, y (k + j) is an output predicted value of the step j of the system, and yr(k + j) is the expected value of the object output.
The performance indicator function reconstructed in S5 satisfies:
Figure BDA0001690149490000032
where P is the maximum number of predicted steps, giIs the sampled value of the first i term of the step response of the device.
Obtaining the control quantity Δ V in the x direction according to the reconstructed performance index function in S6x(k) And control quantity DeltaV in y directiony(k) The method specifically comprises the following steps:
taking the reconstructed performance index function as an objective function and converting the objective function into a vector form, namely:
J＝E{[Y(k+1)-Yr(k+1)]T[Y(k+1)-Yr(k+1)]+λΔU(k)TGΔU(k)}
obtaining a control quantity delta u (k) according to the formula, and obtaining a control quantity delta V in the x direction according to the control quantity delta u (k)x(k) And a control amount Δ V in the y directiony(k) Wherein Δ u (k) satisfies:
Δu(k)＝qT[Yr(k+1)-E(z-1)Δu(k-1)-S(z-1)y(k)]
the invention has the beneficial effects that: the invention introduces and improves the traditional General Predictive Control (GPC) algorithm to solve the remote motion Control problem of the airport runway detection robot in the environment of network delay and noise interference. The method can effectively reduce the network delay and noise interference influence caused by remote network control in the movement process of the airport runway detection robot, and improves the resolving speed and robustness of the movement controller of the airport runway detection robot in the network environment. Compared with the prior art, the method considers that the network delay and the noise interference influence of the controlled object can be solved under the network control environment, so that the airport runway detection robot obtains a stable motion control signal. Compared with the traditional GPC controller, the improved GPC controller has the characteristics of simple structure, high resolving speed of a control algorithm, strong robustness and the like.
Drawings
Fig. 1 is a schematic diagram of a network-based airport runway detection robot forecasting method according to the present invention.
Fig. 2 is a relation diagram of a body coordinate system and a global coordinate system of the airport runway detection robot.
Fig. 3 is a schematic diagram of a kinematic chassis kinematic model of an airport runway inspection robot.
Detailed Description
The following describes embodiments of the present invention with reference to the drawings.
The invention designs a network control system for an airport runway detection robot, establishes an airport runway detection robot kinematic Model, converts the Model into a Controlled Autoregressive Integrated Moving Average Model (CARIMA) used in minimum variance control, converts the Model into two independent single-input single-output linear models in the x direction and the y direction of the robot under a global coordinate system, and performs prediction control on the airport runway detection robot by an improved GPC algorithm.
As shown in fig. 1, the invention designs a network-based airport runway detection robot predictive control method, which comprises the following steps:
airport runway detection robot existenceUnder the condition of external noise xi (k) interference, the motion state of the robot is transmitted to a remote control center through a network by a sensor, and due to network transmission, a forward channel delay tau is causedcaThe remote control center obtains a control signal u (k) through calculation, and then transmits the control signal to the driver through the network, and the reverse channel delay tau is generated due to the network transmissionscThe total delay is recorded as d ═ tausc+τcaAnd finally, the driver drives the Mecanum wheels to enable the airport runway detection robot to work.
The moving chassis of the airport runway detection robot is composed of four Mecanum wheels, and kinematic modeling is carried out according to the moving chassis of the Mecanum wheels of the airport runway detection robot.
As shown in fig. 2, a robot body coordinate system is established on a robot chassis, a global coordinate system is established on a robot motion environment, the coordinate systems are rectangular coordinate systems, an included angle θ between the robot and an x axis is formed in the global coordinate system, and a conversion relationship between the robot body coordinate system and the global coordinate system is as follows:
Figure BDA0001690149490000041
as shown in fig. 3, the speed v of the robot in the x direction under the global coordinate system isxY-direction velocity vyThe rotation angular speed is omega, the radius of the Mecanum wheels is R, and the distance between each Mecanum wheel and the x axis of the individual coordinate system is l1And a distance l from the y-axis2The rotating speeds of four Mecanum wheels of the chassis are v respectively1,v2,v3,v4The kinematic equation of the airport runway detection robot is as follows:
Figure BDA0001690149490000051
model-based modeling of parameters vx vy ω]TConverted into motor rotating speed [ v ] for controlling four Mecanum wheels1 v2 v3v4]TAnd the motion control of the mobile robot is realized.
The GPC uses a Controlled Autoregressive Integrated Moving Average (cari) Model used in minimum variance control, described below:
A(z-1)y(k)＝B(z-1)u(k-1)+C(z-1)ξ(k)/Δ
wherein:
Figure BDA0001690149490000052
Figure BDA0001690149490000053
Figure BDA0001690149490000054
Δ＝1-z-1
z-1is a step back operator, y (k) is the actual output of the system, u (k) is the system control quantity, xi (k) is the noise sequence, { ai},{biAnd { c }andiIs the polynomial coefficient corresponding to each of A, B and C, na、nbAnd ncAre the corresponding respective orders, and Δ is the difference operator.
V in the course of detecting robot movement on airport runwayx、vyThe position of the robot trolley on the plane can be controlled, and omega controls the front orientation of the robot trolley. Because the robot can move on the plane of the robot at any angle and any speed, omega is independent of the position variation of the robot and can be implemented by a separate control strategy, the calculation of omega can be independent of vx,vyThe method is divided into independent operations and comprises the following specific steps:
obtaining a CARIMA model of the robot in the x direction and the y direction under a global coordinate system according to the kinematics principle of the robot:
(1-z-1)x＝Tz-dvx(k-1)
(1-z-1)y＝Tz-dvy(k-1)
wherein T is the time taken for the robot to move in the x and y directions, and z-dIs an introduced delay factor.
Introduce the expression of the lost graph:
1＝Rj(z-1)A(z-1)Δ+z-jSj(z-1)
Rj(z-1)B(z-1)＝Gj(z-1)+z-jEj(z-1)
wherein:
Figure BDA0001690149490000061
Figure BDA0001690149490000062
Gj(z-1)＝g0+g1z-1+…+gjz-j+1
Figure BDA0001690149490000063
degA＝na
degB＝nb
the conventional controller performance index function is
Figure BDA0001690149490000064
Where E is the mathematical expectation, Δ u is the control increment, and Δ u (k + j) is 0, j is Nu,...,N1Is represented in NuThe control quantity is not changed after the step. N is a radical of1、N2Minimum and maximum predicted time domain lengths, N, respectivelyuFor controlling the time domain length, lambda is a control weighting coefficient, y (k + j) is an output predicted value of the step j of the system, and yr(k + j) is the expected value of the object output.
The method is improved on the basis of the traditional controller performance index function, and the performance index function is reconstructed as follows:
Figure BDA0001690149490000065
where P is the maximum predicted step number, j is 1.., P, i is 0.., j-1, Δ u is the control increment, y (k + j) is the predicted output value of the system j step, and y (k + j) is the predicted output value of the system j steprIs a given value, λ is a control weighting coefficient, giIs the sampled value of the i item before the step response of the device, and the delta u is the control increment.
Writing the objective function in vector form:
J＝E{[Y(k+1)-Yr(k+1)]T[Y(k+1)-Yr(k+1)]+λΔU(k)TGΔU(k)}
wherein:
Y(k+1)＝[y(k+1),y(k+2),...,y(k+P)]T
Yr(k+1)＝[yr(k+1),yr(k+2),...,yr(k+P)]T
Figure BDA0001690149490000071
ΔU(k)＝[Δu(k),Δu(k+1),...,Δu(k+P-1)]T
the partial derivative of the objective function at Δ U can be obtained:
Figure BDA0001690149490000072
let the above equation be 0, the corresponding control law can be obtained as follows:
ΔU(k)＝(G+λI)-1[Yr(k+1)-E(z-1)Δu(k-1)-S(z-1)y(k)]
thus, the new control rates are:
Δu(k)＝qT[Yr(k+1)-E(z-1)Δu(k-1)-S(z-1)y(k)]
wherein:
qT＝(1,0,…,0)(G+λI)-1
E(z-1)＝[E1(z-1),E2(z-1),…,Ep(z-1)]T
S(z-1)＝[S1(z-1),S2(z-1),…,Sp(z-1)]T
Figure BDA0001690149490000081
and obtaining the control rate required by the robot in the x direction and the y direction according to the delta u (k).
Figure BDA0001690149490000082
Figure BDA0001690149490000083
In the remote control center upper computer, a control signal is transmitted to the robot through a network, so that the robot can perform track tracking control motion in a network environment.
The specific implementation mode of the invention also comprises:
the method comprises the following steps of establishing a kinematic model of a motion chassis according to the fact that the motion chassis of the airport runway detection robot is composed of four Mecanum wheels, and comprises the following specific steps:
establishing a robot body coordinate system on a robot chassis, and establishing a global coordinate system on a robot motion environment;
v. thexFor the moving speed, v, of the robot in the x direction under the global coordinate systemyThe motion speed of the robot in the y direction under the global coordinate system is shown, and omega is the machineThe angular speed of rotation of the human, R represents the radius of the Mecanum wheel, theta is the included angle between the robot and the x axis under the global coordinate system, and l1For the distance between each Mecanum wheel and the x-axis of the individual coordinate system, l2For the distance, v, between each Mecanum wheel and the y-axis of the individual coordinate system1,v2,v3,v4In order to control the motor rotating speeds of the four Mecanum wheels, the kinematic equation of the airport runway detection robot is as follows:
Figure BDA0001690149490000084
the model may relate the parameters vx vy ω]TConverted into motor rotating speed [ v ] for controlling four Mecanum wheels1 v2 v3v4]TBased on the model, the mobile robot can be subjected to motion control.
During the movement of the mobile robot, vx、vyThe position of the robot trolley on the plane can be controlled, and omega controls the front orientation of the robot trolley.
Because the mobile robot can move on the plane of the robot at any angle and any speed, omega is independent of the position variation of the robot and can be implemented by a separate control strategy, the calculation of omega can be independent of vx,vySeparate independent operations.
Establishing a CARIMA model of the robot in the x direction and the y direction under a global coordinate system:
(1-z-1)x＝Tz-dvx(k-1)
(1-z-1)y＝Tz-dvy(k-1)
wherein z is-1Is a one-step backward operator, T is the time for the robot to move in the x and y directions, d is the time delay, z-dFor the introduced delay factor, GPC control is performed separately for both directions.
The performance indicator function is reconstructed on the basis of the performance indicator function of the traditional GPC controller.
Furthermore, the control rates required by the robot in the x direction and the y direction under the global coordinate system are respectively obtained.
In the remote control center upper computer, a robot sensor feedback signal is received through a network, robot motion control quantity is obtained through calculation, and a control signal is transmitted to the robot through the network.
The embodiments of the present invention have been described in detail with reference to the drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the gist of the present invention.

Claims (5)

1.一种基于网络的机场跑道检测机器人预测控制方法，其特征在于：包括以下步骤：1. a network-based airport runway detection robot predictive control method is characterized in that: comprise the following steps: S1：根据机场跑道检测机器人的麦克纳姆轮运动底盘进行运动学建模，获得运动学模型；S1: Carry out kinematic modeling based on the Mecanum wheel motion chassis of the airport runway detection robot to obtain the kinematic model; S2：将机场跑道检测机器人的运动学模型转化为受控自回归积分滑动平均模型；S2: Convert the kinematic model of the airport runway detection robot into a controlled autoregressive integral moving average model; S3：将机场跑道检测机器人的受控自回归积分滑动平均模型分别转化得到全局坐标系下x方向的模型和全局坐标系下y方向的模型，且对其分别进行广义预测控制；S3: Transform the controlled autoregressive integral moving average model of the airport runway detection robot to obtain the model in the x-direction under the global coordinate system and the model in the y-direction under the global coordinate system, and perform generalized predictive control on them respectively; S4：利用广义预测控制算法建立原始控制器性能指标函数；S4: Use the generalized predictive control algorithm to establish the original controller performance index function; S4所述性能指标函数满足：The performance index function described in S4 satisfies:
Figure FDA0003187845890000011
Figure FDA0003187845890000011
 其中E为数学期望，Δu为控制增量，Δu(k)为k时刻的控制增量，且Δu(k+j)＝0，j＝Nu,...,N2，表示在Nu步后控制量不再变化，N1、N2分别为最小、最大预测时域长度，Nu为控制时域长度，λ为控制加权系数，y(k+j)为系统第j步的输出预测值，yr(k+j)为对象第j步的输出期望值；where E is the mathematical expectation, Δu is the control increment, Δu(k) is the control increment at time k, and Δu(k+j)=0, j=N u ,...,N 2 , indicating that at N u The control quantity does not change after the step, N 1 and N 2 are the minimum and maximum prediction time domain lengths respectively, Nu is the control time domain length, λ is the control weighting coefficient, and y( k +j) is the output of the jth step of the system Predicted value, y r (k+j) is the expected output value of the object at the jth step; S5：在原始控制器性能指标函数的基础上将性能指标函数重新构建，获得重建的性能指标函数；S5: Reconstruct the performance index function on the basis of the original controller performance index function to obtain the reconstructed performance index function; S5所述的重建的性能指标函数满足：The reconstructed performance index function described in S5 satisfies:
Figure FDA0003187845890000012
Figure FDA0003187845890000012
 其中，P为最大预测步数，gi是装置阶跃响应前i项的采样值；Among them, P is the maximum number of prediction steps, and g i is the sampling value of the first item i of the step response of the device; S6：根据重建的性能指标函数得到x方向的控制量ΔVx(k)和y方向的控制量ΔVy(k)，通过无线网络模块将ΔVx(k)和ΔVy(k)从上位机传送给机场跑道检测机器人，其中：S6: Obtain the control amount ΔV x (k) in the x direction and the control amount ΔV y (k) in the y direction according to the reconstructed performance index function, and transfer ΔV x (k) and ΔV y (k) from the host computer through the wireless network module. Sent to the airport runway inspection robot, where:
Figure FDA0003187845890000013
Figure FDA0003187845890000013
Figure FDA0003187845890000021
Figure FDA0003187845890000021
 其中，qT＝(1,0,…,0)(G+λI)-1，其中，
Figure FDA0003187845890000022
λ为控制加权系数。where, q T =(1,0,...,0)(G+λI) -1 , where,
Figure FDA0003187845890000022
λ is the control weighting coefficient. 2.根据权利要求1所述的一种基于网络的机场跑道检测机器人预测控制方法，其特征在于：S1所述机场跑道检测机器人的运动学模型满足：2. a kind of network-based airport runway detection robot predictive control method according to claim 1, is characterized in that: the kinematics model of the airport runway detection robot described in S1 satisfies:
Figure FDA0003187845890000023
Figure FDA0003187845890000023
 其中vx为机场跑道检测机器人在全局坐标系下x方向速度，vy为机场跑道检测机器人在全局坐标系下y方向速度，ω为机场跑道检测机器人的转动角速度，θ为全局坐标系下机场跑道检测机器人与x轴之间的夹角，R代表麦克纳姆轮的半径，l1为每个麦克纳姆轮与个体坐标系下x轴的距离，l2为每个麦克纳姆轮与个体坐标系下y轴的距离，v1,v2,v3,v4分别为控制四个麦克纳姆轮的电机的转速。Where v x is the speed of the airport runway detection robot in the x direction in the global coordinate system, v y is the y direction speed of the airport runway detection robot in the global coordinate system, ω is the rotation angular velocity of the airport runway detection robot, and θ is the airport in the global coordinate system. The angle between the runway detection robot and the x-axis, R represents the radius of the mecanum wheel, l 1 is the distance between each mecanum wheel and the x-axis in the individual coordinate system, l 2 is the distance between each mecanum wheel and the x-axis The distance of the y-axis in the individual coordinate system, v 1 , v 2 , v 3 , and v 4 are respectively the rotational speeds of the motors that control the four Mecanum wheels. 3.根据权利要求1所述的一种基于网络的机场跑道检测机器人预测控制方法，其特征在于：S2所述受控自回归积分滑动平均模型满足：3. a kind of network-based airport runway detection robot predictive control method according to claim 1, is characterized in that: the described controlled autoregressive integral moving average model of S2 satisfies:
Figure FDA0003187845890000024
Figure FDA0003187845890000024
 其中z-1是一步退后算子，Δx、Δy分别为场跑道检测机器人在时间T内在全局坐标系下x、y方向上的位移变化量，d为延时，z-d为引入的延时因子；vx(k-1)表示机器人在全局坐标系下，在采样时间为k-1时x方向速度，vy(k-1)表示机器人在全局坐标系下，在采样时间为k-1时y方向速度。Among them, z -1 is a step backward operator, Δx and Δy are the displacement changes of the field runway detection robot in the x and y directions in the global coordinate system within the time T, d is the delay, and z -d is the introduced delay. Time factor; v x (k-1) indicates the speed of the robot in the x direction when the sampling time is k-1 in the global coordinate system, v y (k-1) indicates that the robot is in the global coordinate system and the sampling time is k -1 speed in y direction. 4.根据权利要求1所述的一种基于网络的机场跑道检测机器人预测控制方法，其特征在于：S3所述x方向的受控自回归积分滑动平均模型满足：4. a kind of network-based airport runway detection robot predictive control method according to claim 1 is characterized in that: the controlled autoregressive integral moving average model of the x-direction described in S3 satisfies: (1-z-1)x＝Tz-dvx(k-1)(1-z -1 )x=Tz- d v x (k-1) S3所述y方向的受控自回归积分滑动平均模型分别满足：The controlled autoregressive integral moving average model in the y direction of S3 satisfies: (1-z-1)y＝Tz-dvy(k-1)(1-z -1 )y= Tz -dv y (k-1) 其中，z-1是一步退后算子，T为机器人在x、y方向上位移所用的时间，z-d为引入的延时因子，vx(k-1)表示机器人在全局坐标系下，在采样时间为k-1时x方向速度，vy(k-1)表示机器人在全局坐标系下，在采样时间为k-1时y方向速度。Among them, z -1 is a step back operator, T is the time it takes for the robot to move in the x and y directions, z -d is the delay factor introduced, and v x (k-1) indicates that the robot is in the global coordinate system , the speed in the x direction when the sampling time is k-1, v y (k-1) represents the speed of the robot in the y direction when the sampling time is k-1 in the global coordinate system. 5.根据权利要求1所述的一种基于网络的机场跑道检测机器人预测控制方法，其特征在于：S6所述根据重建的性能指标函数得到x方向的控制量ΔVx(k)和y方向的控制量ΔVy(k)具体为：5. a kind of network-based airport runway detection robot predictive control method according to claim 1, is characterized in that: according to the reconstructed performance index function described in S6, obtain the control quantity ΔV x (k) of x direction and y direction control quantity ΔV x (k) and y direction. The control amount ΔV y (k) is specifically: 将重建的性能指标函数作为目标函数并转化为向量形式，即：Take the reconstructed performance indicator function as the objective function and convert it into vector form, namely: J＝E{[Y(k+1)-Yr(k+1)]T[Y(k+1)-Yr(k+1)]+λΔU(k)TGΔU(k)}J=E{[Y(k+1)-Y r (k+1)] T [Y(k+1)-Y r (k+1)]+λΔU(k) T GΔU(k)} 其中，z-1是一步退后算子，Y(k+1)＝[y(k+1),y(k+2),...,y(k+P)]T，Yr(k+1)＝[yr(k+1),yr(k+2),...,yr(k+P)]T，ΔU(k)＝[Δu(k),Δu(k+1),...,Δu(k+P-1)]T；Among them, z -1 is a step backward operator, Y(k+1)=[y(k+1),y(k+2),...,y(k+P)] T , Y r ( k+1)=[y r (k+1),y r (k+2),...,y r (k+P)] T , ΔU(k)=[Δu(k),Δu(k +1),...,Δu(k+P-1)] T ; 通过上式得到控制量Δu(k)，根据Δu(k)得到x方向的控制量ΔVx(k)以及y方向的控制量ΔVy(k)，其中Δu(k)满足：The control amount Δu(k) is obtained by the above formula, and the control amount ΔV x (k) in the x direction and the control amount ΔV y (k) in the y direction are obtained according to Δu(k), where Δu(k) satisfies: Δu(k)＝qT[Yr(k+1)-E(z-1)Δu(k-1)-S(z-1)y(k)]。Δu(k)=q T [Y r (k+1)−E(z −1 )Δu(k−1)−S(z −1 )y(k)].
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