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MINISTRY OF EDUCATION AND TRAINING VIETNAM ACADEMY OF SCIENCE AND TECHNOLOGY GRADUATE UNIVERSITY SCIENCE AND TECHNOLOGY - Nguyen Trong Kien STUDY ON ACTIVE-PASSIVE AND SEMI-ACTIVE CONTROL TO REDUCE VIBRATION OF CRANE PAYLOAD Major: Engineering Mechanics Code: 52 01 01 SUMMARY OF MECHANICAL ENGINEERING AND ENGINEERING MECHANICS DOCTORAL THESIS Ha Noi – 2020 The thesis has been completed at: Graduate University of Science and Technology - Vietnam Academy of Science and Technology Supervisors: Assoc.Prof Dr La Đuc Viet Prof DrSc Nguyen Dong Anh Reviewer 1: Reviewer 2: Reviewer 3: Thesis is defended at Graduate University of Science and Technology - Vietnam Academy of Science and Technology at…, on date…month…2020 Hardcopy of the thesis be found at: - Library of Graduate University of Science and Technology - Vietnam National Library PREFACE Reason of choosing the topic The crane’s payload often has excessive sway motion, which limits the crane's operation, reduces the operating speed, affects the durability of the cable, and causes collisions or dangers Since crane is a popular device, reducing sway vibrations for the payload has highly practical value The main approaches to reduce the payload oscillation are categorized into active, passive, and semi-active control Each approach has its own advantages and disadvantages The thesis proposes and studies the combination of control means to achieve the better efficiency than one of each single mean That is the reason to choose the thesis topic: "Study on active-passive and semi-active control to reduce vibration of crane payload " Aim of the thesis The goal of this thesis is to propose a combination of active, passive and semi-active controls in order to improve the efficiency in reducing the vibration of the crane’s payload compared with each single method Research subject and scope of the thesis Research subject: Payload of a crane by a single cable, affected by impulse, harmonic or random loads or impacted by incorrect crane driving The quantities to be reduced are the sway angles of the payload and the cable’s tension Research scope: The thesis only considers the cranes placed on fixed pedestals, but not mobile pedestals The thesis only considers the payload oscillation, but not the oscillation of other crane components The thesis only considers the tensile properties, but not the compressive and flexural properties of the cable Research method The thesis combines the analytical, numerical and experimental methods in research Scientific and practical significance Scientific significance: Developing new methods for reducing the vibration of crane’s payload under incorrect crane driving and external disturbance Practical significance: The vibration reduction methods proposed in this thesis can be deployed for many different types of cranes Thesis layout The layout of the thesis includes: introduction, content chapters, conclusion, list of published works, references and appendices CHAPTER OVERVIEW OF RESEARCH PROBLEMS 1.1 Introdution Crane is a motorized device used to transfer heavy objects or dangerous materials (referred as payload afterward) from one place to another Excessive sway occurred during the payload movement, may slow down the operation or make the danger.These excessive sway needs to be limited Over past two decades there has been a lot of research on reducing the sway vibrations of the payload It can be classified as active and passive methods Each method has its own advantages and disadvantages There are not many studies on the combination between the active and passive method and further, the semi-active method, which can be applied for reducing the vibration of crane payload Therefore, in this thesis, the author proposes a combination of active - passive methods or the semi-active methods to improve the efficiency of vibration control for the crane payload 1.2 Reducing sway of the payload with the active method 1.2.1 Feedback control techniques Feedback control technique (closed loop) uses crane measurements such as strain and position to generate the control signals The feedback technique can eliminate the disturbance, but encounters two basic limitations in the problem of reducing the payload sway First, it is not easy to accurately measure the states of the system Second, the more serious limitation of the feedback technique is that it can cause conflict motions, which are not comfortable for the crane operator 1.2.2 Feedforward control techniques Feedforward control techniques (open-loop) modify the command before sending to the crane motors The input shaping, a typical feedforward technique, is implemented by convolving a series of impulse, called the input shaper, with the reference command The feedforward technique does not use the feedback measurement signal but only partially delays the control signal of the crane operator in a reasonable way (at the right time and with the right intensity) Due to the above properties, the feedforward technique can overcome two fundamental disadvantages of the feedback technique, that is, there is no need to use complicated expensive instrumentation and the control signal after rectification still looks "naturally" for the crane operator However, the feedforward technique can only extinguish the oscillations determined by the control signals Disturbances (such as wind load) or initial oscillation conditions (due to impact ) cannot be determined and cannot be handled by a feedforward technique 1.3 Reducing payload sway with passive method 1.3.1 Passive methods for sway control In addition to the active method as above, in the field of vibration control also uses a passive method, typically using springdamper Besides, the oscillation of a single pendulum with a hard connection can also be reduced by the use of linear dynamic absorbers, Coriolis and gyroscopic 1.3.2 Sway reduction using Coriolis force of payload To reduce the oscillation of the payload, a system of springs and dampers has been proposed to be fitted between the payload and the cable Coriolis force is the main factor reducing swaying vibration When the payload is swaying, the centrifugal force changes and causes the payload to have radial motion Radial motion will create a Coriolis damping that affects the sway of the payload and reduces that sway However, it should be emphasized that the passive devices (due to its nature) only draw energy out of the system, so there is no appropriate adaptation in the problem of vibration control Therefore, the effectiveness of the passive method is more limited than the active method 1.4 Semi-active devices In many cases, changing the resistance characteristics of dampers can help improve the efficiency of vibration control Semiactive devices are passive devices whose properties can change from time to time For the purpose of semi-active drag control, various energy dissipation devices have been used to achieve the desired resistance These devices include hydraulic dampers, electrically variable dampers (Electrorheological: ER) and magnetic (Magnetorheological: MR), semi-active friction devices, and electromagnetic devices 1.5 Conclusion of chapter In this chapter, the thesis presents an overview of the control methods to reduce vibration of the payload Through the above mentioned methods, we see that the methods have their own advantages and disadvantages The thesis proposes and studies the combination of control modes to achieve better efficiency than each single mode Specifically, the thesis will combine active feedback methods with passive spring-damper; combine input shaping method with passive spring-dampers and research on applying semi-active method to control swaying oscillation of the payload in the form of a single pendulum The content of the combination will be detailed in the next chapters CHAPTER COMBINATION OF FEEDBACK CONTROL AND SPRING-DAMPER TO REDUCE THE PAYLOAD 2.1 Introdution This chapter will present a model for vibration of a payload in 2D that combines feedback control with spring-damper The payload's differential equations are constructed according to the Lagrange type II equation In this chapter we will examine the impact of feedback control on the crane driver From there, giving the gain of feedback control suitable to avoid causing big conflicts to the crane driver Models of radial spring-damper will also be introduced in the chapter Thanks to the found results of the optimal parameters of the spring-damper working independently The optimal parameters of the spring-damper in combination with feedback control will be established The results of numerical calculation to demonstrate the effectiveness of the combination of feedback control with spring-damper in reducing the vibration of the payload compared to the single methods will be presented at the end of the chapter 2.2 Vibrational model of the payload The concept of a combination of the feedback control methods and the passive method using a spring-damping set to reduce the swaying of the payload in 2D is shown in figure Trolley O x  c Feedback controller Springdamper k y Coriolis damping P Figure 2.1 Combined feedback control with passive spring-damping Based on Figure 2.1, we establish the oscillation equation of the payload P such as (2.1) 2u  x cos    l  u   g sin   (2.1) mx sin   mu  ku  cu  mg 1  cos   m  l  u   Select the initial condition as:     0 (2.2) Other initial values are chosen to be We reduce equation (2.1) to the following non-dimensional form: 2un  xn cos   1  un   sin   (2.3) xn sin   un   2un  2 un   cos   1  un   2.3 Building control plans 2.3.1 Feedback control method In this section we consider the simplest controller, the PID controller (proportional-integral-derivative) To demonstrate the effects of feedback control on a crane operator We consider the cases of horizontal displacement of the payload, the horizontal displacement of the trolley due to the feedback signal and the operator on the figure 2.2, 2.3 Figure 2.2 Compare the horizontal displacement of the trolley by the operator and the feedback signal, P=0.1, 0=/6 Figure 2.3 Compare the horizontal displacement of the trolley by the operator and the feedback signal, P=1, 0=/6 The results show that the higher the gain coefficient P, the faster the oscillation of the payload turns off, but the horizontal displacement of the trolley due to the feedback signal becomes more and more distant from the horizontal displacement of the trolley by the operator That clearly shows the defect of feedback control The stronger the feedback controller has the impact on the system, the more effective it is to reduce vibrations but distract the crane operator 2.3.2 Using radial spring-dampers Next we consider the case where there is no feedback control and only dampers By the equivalent linearization method and the polar equilibrium method we can determine the optimal value of the spring-dampers such as (2.4) (2.5)  opt  (2.4)  opt  302 32 (2.5) 2.3.3 Combining feedback control and spring-damper The optimal results (2.4) and (2.5) are determined in the above item in the absence of feedback control Consider the case with proportional feedback control: (2.6) xn   P Also by the equivalent linearization method and the polar equilibrium method we can determine the optimal value of the dampers as (2.4) and (2.7)  opt  16 P2  602  4 P (2.7) Summary, this section has determined the optimal parameters of dampers in the case of a combination of proportional feedback control with spring-dampers Analytical results are determined by (2.4) and (2.7) 2.4 Some results of numerical simulation The numerical calculation is performed on the dimensionless motion equation (2.3) The speed of the trolley is determined by: (2.8) xn  vr   P For convenience of notation, we will consider simulation cases in the table 2.1 Bảng 2.1: Simulation cases Notation TH1 TH2 TH3 TH4 Active controls No Yes No Yes Passive controls No No Yes Yes 2.4.1 Case of inactive crane The comparison results of the sway angle of the cable are shown in Figure 2.4-2.5 with different cases of the initial sway angle Figure 2.4 Swing angle versus normalized time 30o, P=0.1 Figure 2.5 Swing angle versus normalized time 10o, P=0.1 Table 2.2 Maximum angle (degree) after periods (percentile beside shows the reduction of swinging) Case 0=30o,P=0.05 0=10o,P=0.05 0=30o, P=0.1 0=10o, P=0.1 TH1 TH1 TH1 TH1 30(0%) 15.94(46.9%) 11.85(60.5%) 7.03(76.6%) 10(0%) 5.31 (46.9%) 5.68 (43.1%) 3.55(64.5%) 30(0%) 8.52 (71.6%) 11.85(60.5%) 4.08(86.4%) 10(0%) 2.84 (71.6%) 5.68 (43.1%) 2.09(79.1%) The results show that: - Case combines both active and passive methods is more effective than the case of each single method 2.4.2 Case of crane in operation The comparison results are shown in Figures 2.6, 2.7 and Table 2.3 11 The general input shaper can be diagrammatized as shown in Fig 3.2 Fig 3.2 Input Shaper represented by block diagram In this thesis, for the demonstration purpose, two simplest input shapers are considered: the zero vibration (ZV) shaper and the zero vibration and derivative (ZVD) shaper They are represented as:  A  0.5 0.5  (3.1) ZV   i      i    /   0.25   A  0.25 0.5 ZVD   i    (3.2)   i    /  2 /   The mathematical model of a boom crane attached with spring and damper as shown in Fig 3.3b x3 z z2 y2 c 1 A x2 L2 z3 L1 B c L3 k 2 P c o y3 y y1 x x1 Fig 3.3a Boom crane Fig 3.3b Symbols used in the boom crane model With the help of MATLAB Symbolic, we obtained the motion equation such as (3.3), (3.4), (3.5): 12  1 cos    cos 1 sin   2 2 cos 1 cos       c sin 1 cos  cos 1  21 sin    L3  u     2  L3  u  1 cos    cos 1 sin   L2 c cos 1 cos  c  (3.3)  L2  sin  c sin 1  L2 cos1 sin   L2  c cos  c sin 1  c  g sin 1  M1 m  L3  u  cos     21 cos1 cos    c sin 1    L3  u     2   c cos sin  cos 1  1 cos  sin     2  L3  u   sin 1    L2  c2 cos  c cos   L2 c2 cos  c cos   L2  sin  cos1 sin   g cos 1 sin   L2  c cos  c cos 1 sin  2 2 L2 sin  sin 1 sin   L2  c sin  c cos   L2 c cos  c sin 1 sin   M2 m  L3  u  (3.4)   cos  cos 1    2 c sin 1  k c u  u  u   L3  u      2  sin  cos cos   cos   m m c 2 2  c c  2 2   L2  c2   c2 cos  c sin   L2 c cos  c sin 1 cos  L2  c cos  c cos 1 cos  L2  c2 sin  c cos1 cos  L3  L2  c sin  c sin   L2 c  c sin  c sin 1 cos   g 1  cos 1 cos    (3.5) 3.3 Numerical simulation The crane model in RECURDYN is shown in Fig 3.3 Fig 3.3 The crane model in RECURDYN 13 The speed control method will be simulated The velocity commands are taken from [60] The effectiveness in reducing tridirectional vibration is evaluated by two indexes: the cable tension and the sway angle (measured from the vertical) The comparisons are shown in Figs 3.4-3.7 Figure 3.4: Cable tension resulting from crane motion Figure 3.5: Sway angle resulting from crane motion 14 Figure 3.6: Cable tension resulting from crane motion and gust disturbance Figure 3.7: Sway angle resulting from crane motion and gust disturbance From the above results we draw the following remarks: - Without disturbance, the damper's effect in reducing the sway angle is not clear (Fig 3.5) However the change of the cable tension is smoother thanks to the damper (Fig 3.4) - With disturbance, the input shaping can not deal with the disturbance but the damper can attenuate the induced vibration (Figs 3.6, 3.7) - In any case, the combination proposed shows its good effectiveness This is due to the combined advantages of two components 3.4 Experimental verification A simple experiment is set up to demonstrate the effectiveness of the proposed approach Figure 11a-b presents the setups used 15 Figure 3.8: Boom crane (a) and spring-damper mechanism (b) The effect of the combination of input shaping and radial spring-damper can also be seen by rotating the crane base The results are shown in Figs 3.9-3.12 Fig 3.9: Payload's orbit in horizontal plane, sway induced by slewing 16 Fig 3.10: Horizontal X deflection, sway induced by slewing Fig 3.11: Horizontal Y deflection, sway induced by slewing Fig 3.12: Sway angle induced by slewing We can see that the input shaping can significantly reduce the sway motion while the radial spring-damper makes some more improvements The experiment's results verify that the combination 17 approach can reduce the payload's sway induced by both human operators and initial conditions 3.5 Conclusion of chapter This chapter achieved the following results: - This chapter is to propose and analysis of the combination between two sensorless approaches to reduce the tridirectional vibration of a crane payload - Experimental model was created to illustrate the combination of the input shaping and the radial spring-damper to control the 3D oscillation of the crane payload - The numerical and experimental analyses show that the proposed combination can effectively reduce the oscillatory responses induced by both initial condition and human - The results of the chapter have been presented in the articles [T1, T3, T5] CHAPTER REDUCING PAYLOAD OSCILLATION BY SEMI-ACTIVE CONTROL 4.1 Introdution This chapter will present a model vibration of a payload in 3dimensional space using a on-off damping coefficient controller for a dampers The oscillation equations of the payload is built according to the equations in chapter In this chapter, we will find the optimal on-off damping coefficient controller of the harmonic plane oscillating pendulum model, applying some simpler assumptions This chapter also proposes a on-off damping coefficient controller for the plane pendulum and the spherical pendulum model which is not simplified The results of numerical calculation to demonstrate the efficiency of the proposed on-off damping coefficient controller compared with the passive dampers and compared to the optimal onoff damping controller will also be presented in chapter 4.2 Investigated model The on-off damping controller is considered as shown in Fig 4.1 18 O z Radial Spring k Disturbance Coriolis damping  x Radial On-off damping c l k y c  Pendulum mass m u m z Fig 4.1 Model of a single pendulum attached with radial spring and on-off damper With the model in Figure 4.1, we will construct the motion equation in dimensionless form as follows: 1  un     sin  cos   2 s   sin  cos  2un   M (4.1) (1  un )s2 ml 1  un   cos   2 sin   2 s cos    sin   2un cos    M (1  un )cos s2 ml (4.2) un  2 un   2un   cos cos  1  un  (   cos2  )  (4.3) In that we use the following symbols: c g k/m c u s  ;  s  s ;  ;  ; un  ;  s t; (4.4) l 2l ms s 2ms l Consider the on-off damping of the radial dampers as follows: certain condition    h (4.5) otherwise  l in which h and l, respectively, are the on-value and off-value of the semi-active damping ratio 19 4.3 Optimal on-off damping control This section presents an optimal on-off damping controller in a class of all on-off controllers that convert the damping coefficient from high to low and back again every quarter period The optimal controller is found in the problem of harmonic planar vibration pendulum The external moment M have form: (4.6) M  2m ss2 ml cos     f  The equations (4.1), (4.2) and (4.3) is simplified into: 1  un    2 s   1  un   sin   2un   2 s m cos     f  , un  2 un   2un  1  un    cos   (4.7) The analysis is performed by assuming the values for the sway angle, radial motion and damping ratio are small Retains the quadratic component of:  , , , un , un , un ,  s The equations (4.7) reduce to: (4.8) 1  2un    s  un   1  un   2 sm cos     f  un  2 un   2un    2  (4.9) The approximate solutions of the systematic response are searched in form of harmonic functions as follows:   0 sin    , un  h02  cos sin  2   sin  cos  2   (4.10) The three unknown 0, h and  satisfy the following conditions: (4.11) 0  0; h  0;      Ta giả sử: 1      l    (4.12)   h     1   2 After some manipulations, the final relation between 0 with P and m has following form: a3  m , P ,0 06  a2  m , P ,0 04  a102  a0  (4.13) In brief, for a given (normalized) frequency , the relation (4.13) gives a curve in the plane of 0 and m Figures 4.2 and 4.3 show some typical curves in the plane of 0 and m for some values of  20 Figure 4.2: Typical relation curves (dashed) between 0 and m and orbit (solid) of minimum points for h=20%, l=5%, =2, m=/6, s=1% Figure 4.3: Typical relation curves (dashed) between 0 and m and orbit (solid) of minimum points for h=100%, l=1%, =2, m=/6, s=1% 21 The following comment of 0 and m can be drawn from the Figs 4.2 and 4.3: - Compare the orbits of minimum points between two figures 4.2 and 4.3, we see that the larger h and the smaller l give a lower value of lower bound - The optimal value of m increases when the excitation frequency ratio  is near Observe the on-off damping law (4.12), we see that increasing m means the low damping is used longer The optimal behavior means that when the frequency ratio  is near 1, the damping should be tuned longer to lower value to increase the radial motion to dissipate more energy 4.4 On-off damping controller based on energy flow 4.4.1 Proposed controller Consider the energy function in the following form: u  2un2 H n  2 Use (4.9), we have the power flow equation:  2  H  un (un   2un )  un  2 un        (4.14) (4.15)  2 un2  un  un    4 After some manipulations and some comments in (4.15) The power-driven controller is proposed as follows:  h un      (4.16)   2  l u     n          4.4.2 Numerical simulation The numerical calculations are carried for the full nonlinear differential equation (4.7) Figure 4.4 is a comparison plot between the amplitude of sway angle produced by passive damping, by the optimal on-off damping, by the power-driven on-off damping over a range of damping values and excitation levels 22 Figure 4.4 Amplitude-frequency plots for α=2, ζs=1%, ζh=20%, ζl=5% a) m = 300, b) m = 100 (1) No damper, (2) Off damping, (3) On damping, (4) Power-driven damping, (5) Optimal damping As seen from Figure 4.4, the performance of the power-driven on-off damping controller is very close to that of the optimal controller 4.5 Spherical pendulum under random excitation In this section we consider the model of a spherical pendulum under random excitation The motion equation has been presented above ((4.1) ,(4.2), (4.3)) but the excitation moments now are random The excitation moments in (4.1), (4.2) are introduced as: M   2s2 ml 2m  s    ; (4.17) M   2s2 ml 2 m  s    in which    ,    are two independent Gaussian white noise with unit intensity, m and m are the two standard deviations of the two sway angles of linear spherical pendulum without springdamper Power-driven controller (4.16) can be easily extended for the spherical pendulum as follows: 23      h un          (4.18)   2 2  l u         n  By carrying out the Monte Carlo simulation, the results comparing between the performances the power-driven on-off damping and passive damping is shown in Figure 4.5 In Figure 4.5 the performances index is shown as: J     un2 m2   m2 (4.19) in which notation  averaged over all 500 simulated samples Figure 4.5 Performance index versus frequency ratio, for m=20o, m=10o, ζs = 1% + diamond marker: passive damping 10%; + square marker: passive damping 0,5%; + triangle marker: passive damping 200%; + solid lines unmarked: power-driven control, ζh = 200%, ζl = 0,5% The results showed that the on-off damping has lower J-index in a larger range of α, when compared with all three cases of passive damping In other words, the robustness performances of the on-off damping is higher 24 4.6 Conclusion of chapter This chapter presents research results using semi-active method to control the swing of the pendulum The results achieved in this chapter are: - Find out the expression of the lower bound solution of the sway angle amplitude of a harmonic planar vibration single pendulum using a spring-damper with on-off damping according to the optimal control law - Proposed semi-active control algorithm for on-off damping based on the energy maximum principle of radial motion, applied to semi-active dampers attached between the cable and the payload - The semi-active dampers extended for the case of the spherical pendulum under random excitation, the results indicate its effectiveness for the closer model to reality The results of the chapter have been presented in the articles [T2,T7] CONCLUSION Some main conclusions of the thesis: The thesis has researched and developed models combining active feedback methods with passive dampers; combining the input shaping method with the passive dampers, has studied the semiactive method to control the payload sway These combinations have overcome the limitations of each single method New contributions of thesis: - The optimal parameters of spring-damper system in the combination between the proportional feedback control and the radial damper to reduce the crane payload’s sway have been derived - The combination of input shaping and radial spring-damper to reduce the tridirectional vibration of crane payload has been proposed, analyzed and modeled - The optimal on-off control law to reduce the sway amplitude of a single pendulum in harmonic planar vibration has been found - The on-off damping control algorithm based on power flow applied to radial spring-damper has been proposed LIST OF AUTHOR’S PUBLISHED WORKS [T1] Viet Duc La, Kien Trong Nguyen, Combination of input shaping and radial spring-damper to reduce tridirectional vibration of crane payload, Mechanical Systems and Signal Processing, Volume 116, Pages 310-321, (2019) (Journal ISI Q1) [T2] La Duc Viet, Nguyen Trong Kien, Lower bound of performance index of anti-sway control of a pendulum using on-off damping radial spring-damper, Vietnam Journal of Mechanics, Vol 41, No 2, pp 193-201, (2019) [T3] La Duc Viet, Nguyen Trong Kien, Study of the spring-damper to reduce the variation in cable tension that lifts the payload in 3D, Collection of scientific works Xth National Conference on Mechanics, Ha Noi, 08-09/12/2017, Vol 2, pp 636-643 [T4] La Duc Viet, Nguyen Trong Kien, Crane anti-sway control using active-passive method, Proceeding of The Fourth International Conference on Engineering Mechanics and Automation (ICEMA4), Hanoi 25-26/08/2016, pp 187-191 [T5] La Đuc Viet, Nguyen Trong Kien, Use the spring-damper to control the boom crane's oscillation caused by wind, Proceedings of the 2nd National Scientific Conference on Engineering Mechanics and Automation, 7-8/10/2016, pp 87-90 [T6] Nguyen Trong Kien, La Đuc Viet, Passive – active control method to reduce the swaying of the crane cable, Proceedings of the national science and technology conference on mechanical – transportation engineering, 13/10/ 2016, Vol 2, pp 181-185 [T7] Nguyen Trong Kien, La Đuc Viet, Nguyen Ba Nghi, Nguyen Thi Thanh Tung, Anti-sway of crane’s cable by damping control of semi-active damper, Vinh University Journal of Science, Vol 47, 2A, 2018, pp 16-22 ... Academy of Science and Technology Supervisors: Assoc.Prof Dr La Đuc Viet Prof DrSc Nguyen Dong Anh Reviewer 1: Reviewer 2: Reviewer 3: Thesis is defended at Graduate University of Science and... disadvantages The thesis proposes and studies the combination of control means to achieve the better efficiency than one of each single mean That is the reason to choose the thesis topic: "Study... reduce the oscillation of the payload, a system of springs and dampers has been proposed to be fitted between the payload and the cable Coriolis force is the main factor reducing swaying vibration