Cluster Computing https://doi.org/10.1007/s10586-018-1919-3

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Research of manipulator trajectory tracking based on adaptive robust iterative learning control Xiaokan Wang1,2

•

Dong Hairong1 • Wang Qiong2

Received: 21 November 2017 / Revised: 11 January 2018 / Accepted: 20 January 2018 Ó Springer Science+Business Media, LLC, part of Springer Nature 2018

Abstract The manipulator control system is a dynamic system with the stronger nonlinear coupling feature and the higher position repetitive precision. In order to solve the problems of quickly load changes, many random disturbances, big measurement error and difficult dynamic modeling in the manipulator system, we designed a PD adaptive robust iterative learning controller, established the two degrees of freedom manipulator dynamics equation and used the Lyapunov function to analyze the stability and convergence of the system. MATLAB simulation of manipulator trajectory tracking shows that the control method can effectively inhibit various disturbances which cause by parameter variations, nonlinear mechanical and non-models dynamic characteristics. So the proposed method can make the system achieve good performance and verify the effectiveness of the algorithm, and the efficiency increases by 8%. Keywords Manipulator  Iterative learning control  Robust control  Trajectory

1 Introduction With the high development of the social industrialization, the degree and level of industrial mechanization have been continuously improved. The automation of all kinds of machines is becoming more and more high, the robot system will be bound to replace the traditional manual work and become the mainstream of social development. The robot control system is a multiple-input, multipleoutput, highly coupled nonlinear complex systems, the system are many uncertain influence and interference factors. Especially the robot trajectory control is very complicated and difficult to build dynamic models. In recent years, a practical iterative learning control method was proposed by Arimoto [1, 2]. This method has the characteristics of simple structure, small calculation, and does not require accurate mathematical model of the system, so it is

& Wang Qiong [email protected] 1

State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China

2

Henan Mechanical and Electrical Vocational College, Xinzheng 451191, China

well suitable to solve the problems of the control object with repetitive working mode. The PD iterative learning control algorithm proposed by [3] could not provide a larger initial torque for the actual mechanism, so the application of PD control system will be limited. Wang and co-authors [4] proposes a new rapid iterative learning algorithm to control of tracking for n joint manipulator systems with initial error, which could eliminate the limitation that the initial state of each iterative must be equal to its ideal value in Kawamura’s method or fixed. Zhang [5] presented an adaptive iterative learning control to realize a typical non-minimum phase system of the tip trajectory tracking based on the flexible-link manipulator. Sun [6] used the D-type ILC of train trajectory tracking algorithm to satisfy the high safety requirement of high-speed railways. Zhang [7] presented a robust adaptive iterative learning control (ILC) algorithm for three-DOF permanent magnet (PM) spherical actuators to improve its trajectory tracking performance. Based on the study of Arimoto and the other scholars have put forward different iterative learning control algorithms [8–19]. Robot motion system is an uncertainty and nonlinear system [1, 2, 5, 8, 15]. The trajectory changes of robot manipulators will be affected by the parameters of surrounding noise and system noise and its rotational inertia,

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when it is working. The traditional control method is not easy to achieve high accuracy and fast tracking, although the artificial algorithm [3–17] and the iterative learning control system [4–16] can achieve the better trajectory tracking in a certain extent, its can not well deal with the robot system with unknown disturbances and uncertain parameters, so these methods can not guarantee the stability and robustness of the system. By using the adaptive robust control to handle the unknown upper bound of the non periodicity uncertainty system, the iterative learning control can deal with the period uncertainty problems, and combining with the traditional PD control algorithm [6] and the linearly parameterized technology, then we put forward the PD type adaptive robust iterative learning control system to control the manipulator trajectory tracking. Lyapunov method [9–15] make the whole system be close to the global asymptotic stability in the iteration domain, and can ensure that the closed-loop iteration system is uniformly bounded at each iteration, the tracking error will asymptotically converge to zero with the increasing of the iteration numbers; at the same time the method can guarantee the manipulators system to achieve convergence in the least iteration numbers, and the fastest achieve the control requirements of the system with disturbance term. The rest of this paper is organized as follows. Section 2 puts forward the related basic problems, followed by the adaptive robust iterative controller designed in Sect. 3. The convergence analysis of the system is discussed in Sect. 4. Section 5 shows the simulation experimental results, and Sect. 6 concludes the paper with summary and future research directions.

2 Posing problems The dynamic equation of the N joint manipulator is: þ Ta ðtÞ ¼ T j ðtÞ ð1Þ In which, j is the iteration times, t 2 ½0; t1 , q ðtÞ 2 Rn , q_ j ðtÞ 2 Rn , q€ j ðtÞ 2 Rn are respectively the joint angle, the angular velocity and the angular acceleration, Dðq j ðtÞÞ 2 Rnn is the inertia term, Cðq j ðtÞ; q_ j ðtÞÞq_ j ðtÞ 2 Rn is the centrifugal and Coriolis force, Gðq j ðtÞ; q_ j ðtÞÞ 2 Rn is the gravity and friction term, Ta ðtÞ 2 Rn is the repeatable unknown disturbance, T j ðtÞ 2 Rn is the control input [19–22]. The dynamic equation of the manipulator satisfies the following characteristics:

123

(2)

Dðq j ðtÞÞ is the bounded matrix of symmetric positive definite; _ j ðtÞÞ  2Cðq j ðtÞ; q_ j ðtÞÞ is the skew symmetric Dðq _ j ðtÞÞ matrix, it meets the equation xT ðDðq 2Cðq j ðtÞ; q_ j ðtÞÞÞx ¼ 0.

The manipulator characteristics satisfy the following assumptions: 1. 2.

The expected trajectory qd ðtÞ is the three order derivable in the range of t 2 ½0; t1 . The iterative procedure satisfies the initial condition, that is, qd ð0Þ  q j ð0Þ ¼ 0, q_ d ð0Þ  q_ j ð0Þ ¼ 0, 8j 2 N.

3 The design of the adaptive robust iterative controller According to the Formula (1), the control law would be designed to meet the characteristics of the robot characteristics (1) and (2) and the assumptions (1) and (2): _ þ T j1 ðtÞ; T j ðtÞ ¼ Kpj eðtÞ þ Kdj eðtÞ

j ¼ 0; 1; . . .; N;

ð2Þ

The gain switching rule in the control law is: Kpj

¼ bðjÞKp0 ;

Kdj ¼ bðjÞKd0 ;

bðj þ 1Þ [ bðjÞ;

ð3Þ

In which, j ¼ 0; 1; . . .; N, T 1 ðtÞ ¼ 0, e j ðtÞ ¼ qd ðtÞ  q j ðtÞ, e_ j ðtÞ ¼ q_ d ðtÞ  q_ j ðtÞ, Kp0 Kd0 is the initial diagonal gain matrix of the PD control, and its are the positive definite. bðjÞ is the control gain and it meets bðjÞ [ 1. The learning controller can continuously revise the control torque according to the history error change, so it can greatly improve the trajectory tracking performance. The PD type iterative learning controller can reduce the steady state error and improve the dynamic response speed of the system.

3.1 The linearization of dynamic equations

Dðq j ðtÞÞ€ q j ðtÞ þ Cðq j ðtÞ; q_ j ðtÞÞq_ j ðtÞ þ Gðq j ðtÞ; q_ j ðtÞÞ

j

(1)

Along the instruction trajectory, Eq. (1) can be linearized by using the Taylor formula. The linearization formula DðqÞ is:  oD DðqÞ ¼ Dðqd Þ þ  ðq  qd Þ þ OD ðÞ ð4Þ oq qd

OD ðÞ is the residual of the first order expansion DðqÞ, that is   oD oD € Dðqd Þ€ e þ  qd e   oq qd oq qd ð5Þ qd  Dðqd Þ€ q þ OD ðÞ€ q e€e ¼ Dðqd Þ€

Cluster Computing

_ e_ þ Cðq; qÞ

    oC oC  oC  oC  _ _ _ _ e þ q q e  ee  d d oq qd ;q_d oq_ qd ;q_d oq qd ;q_d oq qd ;q_d

The control gain is required to meet the following conditions:

_ q_  OC ðÞq_ e_e_ ¼ Cðqd ; q_ d Þq_ d  Cðq; qÞ

  oG oG _ þ OG ðÞ _ e ¼ Gðqd ; q_ d Þ  Gðq; qÞ e  oq_ qd ;q_d oq qd ;q_d

ð6Þ ð7Þ

Combining the equation of (5)–(7), the results can be got: _ e; tÞ DðtÞ€ e þ ½C þ C1 e_ þ Fe þ nð€ e; e; ¼ H  ðD€ q þ Cq_ þ GÞ ð8Þ      oC oC  _ e; tÞ ¼ oD € _ In which, nð€ e; e; e e  ee    oq q oq q ;q_ oq q ; d d d q þ OC ðÞq_ þ OG ðÞ: d q_ d e_e_ þ OD ðÞ€ _ e; tÞ, the Formula By ignoring the residual term nð€ e; e; (1) is brought into the Formula (8) [23, 24], and the j iteration dynamic equations of the robot are obtained: DðtÞ€ e j ðtÞ þ ½CðtÞ þ C1 ðtÞe_ j ðtÞ þ FðtÞe j ðtÞ  Ta ðtÞ ¼ HðtÞ  T j ðtÞ

lp ¼kmin ðKd0 þ 2C1  2KDÞ [ 0 8 > lp ¼ kmin ðKd0 þ 2C1  2KDÞ [ 0 > > < lr ¼ kmin ðKd0 þ 2C  2F=K  2C_ 1 =KÞ [ 0 > > > : l l  kF=K  ðC þ C  KDÞk2 p r 1 max ð10Þ kmin ðAÞ is the minimum eigenvalue of the matrix A, kM kmax ¼ maxkMðtÞk, t 2 ½0; tf , kM k is the Euclidean norm of the matrix M.

4 The convergence analysis of the system The definition of Lyapunov function is [28–32], Z t T j V ¼ expðqsÞyj Kd0 y j ds

ð11Þ

0

In which,

In which, Kd0 [ 0 is the initial gain of the D control term in the PD control. q is the positive real number. The following equation can obtain by the Formula (9),

DðtÞ ¼Dðqd ðtÞÞ CðtÞ ¼Cðqd ðtÞ; q_ d ðtÞÞ   oC  oG C1 ðtÞ ¼  q_ d ðtÞ þ  oq_ oq_ qd ðtÞ;q_d ðtÞ

  oD oC FðtÞ ¼  q€d ðtÞ þ  oq qd ðtÞ oq 

DðtÞð€ ejþ1 ðtÞ  e€j ðtÞÞ ¼  ½CðtÞ þ C1 ðtÞðe_jþ1 ðtÞ  e_ j ðtÞÞ  FðtÞðejþ1 ðtÞ  e j ðtÞÞ  ðT jþ1 ðtÞ  T j ðtÞÞ

qd ðtÞ;q_d ðtÞ

qd ðtÞ;q_d

  oG q_ d ðtÞ þ  oq  ðtÞ

ð12Þ So the following equation also can get by the Formulae (11) and (12),

qd ðtÞ

HðtÞ ¼Dðq_ d ðtÞÞ€ qd ðtÞ þ Cðqd ðtÞ; q_ d ðtÞÞq_ d ðtÞ þ Gðqd ðtÞÞ

Ddy_ j ¼Dd€ ejþ1 þ DKde_ j ¼ Dð€ ejþ1  e€j Þ þ Dðe_jþ1  e_ j Þ

Equation (8) can be written as followings in the j iteration and the j ? 1 iteration: 

DðtÞ€ e j ðtÞ þ ½CðtÞ þ C1 ðtÞe_ j ðtÞ þ FðtÞe j ðtÞ  Ta ðtÞ ¼ HðtÞ  T j ðtÞ DðtÞ€ ejþ1 ðtÞ þ ½CðtÞ þ C1 ðtÞe_jþ1 ðtÞ þ FðtÞejþ1 ðtÞ  Ta ðtÞ ¼ HðtÞ  T jþ1 ðtÞ

ð9Þ

¼  ½CðtÞ þ C1 ðtÞde_ j  FðtÞde_ j  ðKpjþ1 ejþ1 ðtÞ þ Kdjþ1 e_jþ1 ðtÞÞ þ DKðe_jþ1  e_ j Þ

ð13Þ

For Kp0 ¼ KKd0 and the formula (13), Kpjþ1 ¼ KKdjþ1 , considering the formula, the results can be deduced,

For simplicity, taking Kp0 ¼ KKd0 , and defining the formula,

Ddy_ j ¼ ðC þ C1 Þde_ j  FðtÞde j þ DKðe_jþ1  e_ j Þ  ðKKdjþ1 ejþ1 þ Kdjþ1 e_jþ1 Þ

y j ðtÞ ¼ e_ j ðtÞ þ Ke j ðtÞ:

Here, DKðe_jþ1  e_ j Þ ¼ DK½ðyjþ1  Kejþ1 Þ  ðy j  Ke j Þ

3.2 Theorem

¼ DKdy j  DKde j

If the system of the Formula (1) satisfies the manipulator characteristics (1) and (2) and the assumed condition (1) and (2), the control law of Eq. (2) and the gain switching law of the Formula (3) [25–27]. Fo r t 2 ½0; tf , then j

j!1

q ðtÞ ! qd ðtÞ;

j

KKdjþ1 ejþ1 þ Kdjþ1 e_jþ1 ¼ Kdjþ1 ðKejþ1 þ e_jþ1 Þ ¼ Kdjþ1 yjþ1 ¼ Kdjþ1 ðdy j þ y j Þ So,

j!1

q_ ðtÞ ! q_ d ðtÞ;

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Z

Ddy_ j ¼  ðC þ C1 Þðdy j  Kde j Þ  Fde j j

2

þ DKdy  DK de

j

¼  ðC þ C1  KD þ

 Kdjþ1 ðdy j Kdjþ1 Þdy j j

j

þy Þ

 ðF  KðC þ C1  KDÞÞde  Kdjþ1 y j

t

T

expðqsÞdyj Ddy_ j ds

2 0

T

¼ expðqtÞdyj ðtÞDðtÞdy j ðtÞ Z t Z t T T þq expðqsÞdyj Ddy j ds  expðqsÞdyj Ddy j ds 0

0

Then, Kdjþ1 y j ¼ Ddy_ j  ðC þ C1  KD þ Kdjþ1 Þdy j  ðF  KðC þ C1  KDÞÞde j The definition of V j is, Z t T expðqsÞyjþ1 Kd0 yjþ1 ds V jþ1 ¼ 0

Defining DV j ¼ V jþ1  V j , so the following formula can get by the formula (3), (11) and (13): Z t T DV j ¼ expðqsÞðdyj þ y j ÞT Kd0 ðdy j þ y j Þds 0 Z t T  expðqsÞyj Kd0 y j ds 0 Z t T T ¼ expðqsÞðdyj Kd0 dy j þ 2dyj Kd0 y j Þds 0 Z t 1 T T ¼ expðqsÞðdyj Kdjþ1 dy j þ 2dyj Kdjþ1 y j Þds bðj þ 1Þ 0 Z t 1 T ¼ expðqsÞðdyj Kdjþ1 dy j ds  2 bðj þ 1Þ 0 Z t T  expðqsÞdyj Ddy_ j ds 0 Z t T  2 expðqsÞdyj ððC þ C1  KD þ Kdjþ1 Þdy j Þ 0

þ ððF  KðC þ C1  KDÞÞde j ÞÞds By applying the partial integration method, dy j ð0Þ ¼ 0 can get according to the initial condition (2), then Z t T expðqsÞdyj Ddy_ j ds 0 t Z t T T  ¼ expðqsÞdyj Ddy j   ðexpðqsÞdyj DÞdy j ds 0 0 Z t T jT j ¼ expðqtÞdy ðtÞDðtÞdy ðtÞ þ q expðqsÞdyj Ddy j ds 0 Z t Z t T jT j  expðqsÞdy Ddy_ ds  expðqsÞdyj Ddy j ds 0

0

Merge the two ends of the above equation together, then:

The equation can get from the manipulator characteristics (2): Z t Z t T T dyj Ddy j ds ¼ 2 dyj Cdy j ds 0

0

In which, Z

t 0

Z t T T expðqsÞdyj Kdjþ1 dy j ds ¼ bðj þ 1Þ expðqsÞdyj Kd0 dy j ds 0 Z t T expðqsÞdyj Kd0 dy j ds  0

So, DV j 

n 1 T  expðqsÞdyj Ddy j ðtÞ bðj þ 1Þ Z t T q expðqsÞdyj Ddy j ds 0 T

 K expðqsÞdej lp de j  Z t Z t T  qK expðqsÞdej lp de j ds expðqsÞwds 0

0

In the above in-equation, T

w ¼de_j ðKd0 þ 2C1  2KDÞde j T

þ 2Kde_j ðF=K  ðC þ C1  KDÞÞde j K2 dej   ðK 0 þ 2C þ 2F=K  2C_ 1 KÞde j

T

d

If Q ¼ F=K  ðC þ C1  KDÞ, we have the following inequation on the basis of the formula, w  lp kde_k2 þ2Kde_T Qde þ K2 lr kdek2 : Further by using the Cauchy-Schwartin equation, then de_T Qde   kde_kkQkmax kdek w  lp kde_k2 2Kkde_kkQkmax kdek þ K2 lr kdek2 K ¼ lp ðkde_k  kQkmax kdekÞ2 lp 1 þ K2 ðlr  kQk2max Þkdek2  0 lp so DV j  0, that is V jþ1  V j Kd0 is the positive definite matrix,V j [ 0 and V j is bounded, then when j ! 1, y j ðtÞ ! 0, e j ðtÞ and e_ j ðtÞ are the

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T To Workspace1 qd Tj

To Workspace7

plant input

q To Workspace2

S-Function Mux

S-Function1

ctrl S-Function2

k

u+1

Tj-1

[t T] To Workspace3

Fcn

From Workspace1

t Clock

To Workspace

j

[t k] From Workspace1

Switch 0 Constant

Fig. 1 The simulation implementation of adaptive robust iterative learning control of the robot trajectory tracking based on the Simulink 2

1

q1d,q1

q1d,q1

1 0 -1 -2

0

0.5

1

1.5

2

2.5 time(s)

3

3.5

4

4.5

0

0.5

1

1.5

2

2.5 time(s)

3

3.5

4

4.5

5

0

0.5

1

1.5

2

2.5 time(s)

3

3.5

4

4.5

5

2

q2d,q2

1 q2d,q2

-1

-2

5

2

0 -1 -2

0

0

0.5

1

1.5

2

2.5 time(s)

3

3.5

4

4.5

5

Fig. 2 The double joints trajectory tracking curves of 5 iterative process

independent variables, K is the positive definite constant matrix, if j ! 1, then e j ðtÞ ! 0, e_ j ðtÞ ! 0, t 2 ½0; tf . So the conclusion can get by the analysis: j!1

j!1

For t 2 ½0; tf , q j ðtÞ ! qd ðtÞ, q_ j ðtÞ ! q_ d ðtÞ, that is, when the j tends to the infinity, the actual value always reaches the desired value.

5 Simulation examples To simulate the dynamic equations (1) of the manipulator, the terms of the equations are respectively [33–35]:

1

0

-1

Fig. 3 The double joints position tracking curves of 5 iterative process



 i1 þ i2 þ 2m2 r2 l1 cos q2 i2 þ m2 r2 l1 cos q2 DðqÞ ¼ i2 þ m2 r2 l1 cos q2 i2   m2 r2 l1 q_ 2 sin q2 m2 r2 l1 ðq_ 1 þ q_ 2 Þ sin q2 _ ¼ Cðq; qÞ m2 r2 l1 q1 sin q2 0   ðm1 r1 þ m2 l1 Þg cos q1 þ m2 r2 g cosðq1 þ q2 Þ GðqÞ ¼ m2 r2 g cosðq1 þ q2 Þ The repeatable interference is d1 ðtÞ ¼ 0:3a sin t, d2 ðtÞ ¼ 0:1að1  et Þ, a ¼ 1, Ta ¼ ½d1 d2 T , the system parameters are m1 ¼ 10, m2 ¼ 5, l1 ¼ 1, l2 ¼ 0:5, r1 ¼ r2 ¼ 0:5, i1 ¼ 0:83 þ m1 r12 þ m2 l21 , i2 ¼ 0:3 þ m2 r22 .

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The desired trajectory is q1 ¼ sin 3t, q2 ¼ cos 3t. If " # 1 0 K¼ ; the controller parameters are 0 1 " # 210 0 Kp0 ¼ Kd0 ¼ ; bðjÞ ¼ 2j; Kpj ¼ 2jKp0 ; Kdj ¼ 0 210 2jKd0 ; j ¼ 1; 2; . . .; N: The initial state of the system is x ¼ ½ 3 0 0 1 T , tf ¼ 5 and the iteration number is 5. The Simulink is used to simulate the control system of the manipulator which is shown in Fig. 1. The position, velocity, and the error change curves are shown in Figs. 2, 3, 4, 5, 6 and 7. When the 5 iteration is not achieved, the system still has some fluctuations, and it can’t well reach the equilibrium

point. When the 5 iteration is achieved, the stability and robustness of the system are optimal. So the proposed method uses 5 iterations. Seen from Figs. 2, 3, 4, 5 and 6, the results show that the double joints velocity and position tracking can well realize the the trajectory tracking control in the 5 tracking processes of the iterative learning control, the actual trajectory after 5 iterations is basically close to the desired trajectory; Seen from Fig. 5, with the iterations numbers changes the output error of position decreases gradually, the double joints has been achieved perfect tracking in the second iterations; and the velocity error is also become more and more small with the iterations increase, the double joints has been achieved perfect tracking in the fifth iterations. The system is carried out simulating under the external interference, from the

4 0.5

0

0.45

-2

0.4

-4

0.35

0

0.5

1

1.5

2

2.5 time(s)

3

3.5

4

4.5

5

4

dq2d,dq2

2

derror1 and derror2

dq1d,dq1

Change of maximum absolute value of derror1 and derror2 with times i

2

0.3 0.25 0.2

0

0.15

-2

0.1

-4

0.05

0

0.5

1

1.5

2

2.5 time(s)

3

3.5

4

4.5

5 0

Fig. 4 The double joints velocity tracking curves of 5 iterative process

0

0.5

1

1.5

2

2.5 times

3

3.5

4

4.5

5

Fig. 6 The velocity error convergence process of the double joints in the 5 iterative process

Change of maximum absolute value of error1 and error2 with times i 0.45 0.5

0.4

ILC traditional method

0.45

0.35 0.4 0.35

0.25

0.3

error

error1 and error2

0.3

0.2

0.25

0.15

0.2

0.1

0.15 0.1

0.05

0.05

0

0

0.5

1

1.5

2

2.5 times

3

3.5

4

4.5

5

Fig. 5 The position error convergence process of the double joints in the 5 iterative process

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0

0

0.5

1

1.5

2

2.5 times

3

3.5

Fig. 7 Comparison of traditional method and ILC

4

4.5

5

Cluster Computing Table 1 Performances comparison of traditional method and ILC

Method

Position error

Velocity error

Iteration times

Traditional control

0.11

0.26

[5

ILC

0.05

0.11

2

simulation curves, the system can realize the system perfect tracking after a few iterations, so we think that the robust performance of the system is the better. At the same time, it has the better stability and convergence (Table 1). The above analysis shows that the tracking control problem of the uncertain state disturbances and output interference nonlinear systems can use the adaptive robust iterative learning control, which has the advantages of fast learning speed, good stability and strong robustness; the system has good convergence that it makes the actual reference approaching rapidly the desired parameters, and has the good target tracking and the error converges can quickly reach 0, so the system can be well applied in robot control system.

6 Conclusions The iterative learning control can be convenient for decision-making and adjusting the gap between the repeated dynamic results and expected results by repeated iterative learning, so that it can meet the various requirements of the object and expectation results achieve the tracking purpose in the iterative learning control process. The highly nonlinear, strong coupling, time-varying systems by using the iterative learning control and the combination of other intelligent control method to optimize control, it can improve the robustness and adaptability of the system, and achieve the good tracking error convergence and high tracking precision. By combining with the simulation of MATLAB into the iterative learning control system, it can quickly verify the effectiveness and real-time of the iterative learning intelligent control method, which can improve the applied efficiency of the new method in the practical control system. The proposed method in this paper is suitable for the control objects with repetitive motion properties, and the improvement of some control targets is achieved through iterative correction. The algorithm does not depend on the precise mathematical model of the system, and it can achieve the control of nonlinear strong coupling dynamic uncertain systems with a very simple algorithm in a given time range and obtain a high precision tracking of the given desired trajectory, and realize the stability and robustness of the system, so it can be widely applied in the field of motion control.

Convergence Good Best

Acknowledgements This work was supported by the youth backbone teachers training program of Henan colleges and universities under Grant No. 2016ggjs-287, and the project of science and technology of Henan province under Grant No. 172102210124.

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Xiaokan Wang mainly engaged in the intelligent control system research.

Dong Hairong The research direction is intelligent transportation system Intelligent Transportation System (ITS); train automatic driving, rail transit parallel control and management system research; complex control system stability and robustness research.

Wang Qiong mainly engaged in the research of computational control technology.