Acta Polytechnica https://doi.org/10.14311/AP.2022.62.0303 Acta Polytechnica 62(2):303–312, 2022 © 2022 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague RESULTS OF RESEARCH ON BACKLASH COMPENSATION IN A POWER ELECTRIC DRIVE BY LOW-POWER ELECTRONIC DEVICE Semen L. Samsonovich, Boris K. Fedotov, Nikolay B. Rozhnin, Roman V. Goryunov∗ National Research University, Moscow Aviation Institute, Department 702, A-80, Volokolamskoye Av. 4, 125993 Moscow, Russia ∗ corresponding author: radiofizika01@mail.ru Abstract. This article considers the feasibility of restoring and maintaining the kinematic accuracy of the support-rotary device drives by introducing a backlash compensation device into the control system. The power electromechanical drives of support-rotary device considered in this article contain two motors, the summation of the torques of which is carried out on a common output shaft. It is shown that the restoration of the required kinematic accuracy of the drives can be achieved by introducing one of two variants of an electronic device for backlash compensation into the control system. In the first variant, equal and opposite displacement signals are introduced into the control signals of the motors. The second variant introduces an electronic cross-connections backlash compensation scheme was into the control system. The study of the operation of the support-rotary device drive system with two backlash compensation devices carried out by a simulation method showed that the use of a cross-connection scheme is the most preferable and effective. As a result of the research, it was shown that the introduction of an electronic backlash compensation device into the control system makes it possible to ensure the operability of the power electromechanical drives of a support-rotary device with initial kinematic accuracy. Keywords: Backlash, backlash compensation device, multi-motor drive, tandem control. 1. Introduction The long-time presence of a large-sized support-rotary device (SRD) in an open atmosphere leads, as a result of corrosion, to the appearance of additional gaps in the gearboxes, and this impairs the kinematic accuracy of electromechanical drives. It was found that after the 30 years of SRD being in the open air, the gears of the drive systems were corrosive, as a result of which the loss of the metal layer occurred, which in turn led to the appearance of backlash (gaps) and a decrease in the kinematic accuracy of the drive system [1]. The restoration of the kinematic accuracy of the electromechanical drive of a large-sized SRD after a long stay in an open atmosphere is of a great practical importance, and the way to restore it is an actual scientific task. There are known ways to compensate for backlash in mechanical transmissions of electromechanical drives, described in [2–10], based on the following principles: a) using mechanical spring devices to compensate for backlash [2]; b) frequency correction and system bandwidth degra- dation [4, 5]; c) the use of a backlash and elastic deformation sensor [5, 6]; d) converting signals from speed and torque sensors to determine the amount of backlash and elastic deformations [4, 7]; e) introducing a nonlinear corrective element “dead zone” into the error signal circuit [6]. Since the drive systems of SRD consist of two drives operating with the same load (Figure 1), it is possi- ble to restore the kinematic accuracy by using special drive channels control circuits to compensate the back- lash and improve the operation in dynamic tracking modes. The greatest development in the multi-motor elec- tric drive was made using two ways of backlash com- pensation. The first way of backlash compensation is similar to the operation of an “electromechanical spring”, based on the creation of, opposite in sign, but equal in magnitude, torques that compensate for the gap, which is implemented by introducing constant displacements of a constant value into the control signals of the motors of the drive. Methods to imple- ment this way are described in [11–17]. Another way is “tandem control”, based on phase displacement of control signals for individual electric motors, depend- ing on the calculated coordinates [18–24]. A feature of this way is the need to carry out a large amount of calculations and build a complex digital control system using microprocessors for its implementation. 303 https://doi.org/10.14311/AP.2022.62.0303 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en S. L. Samsonovich, B. K. Fedotov, N. B. Rozhnin, R. V. Goryunov Acta Polytechnica Figure 1. Kinematic diagram of support-rotary device drive. Figure 2. Block diagram of a system with non-linearity of backlash. 2. Methods The article discusses two ways to compensate for the backlash of a multi-motor electric drive gears, based on the transformation of a dynamic error signal: the well- known method of backlash compensating with the in- troduction of displacement signals (electromechanical spring) [11–17], and a newly developed method with a delay of the dynamic error signal [25]. Each of the methods is implemented by a special electronic de- vice introduced into the dynamic error channel of the electro drive. A comparison of the schemes was carried out by mathematical modelling. The simulation was carried out in the MatLab Simulink software environment, a mathematical model of the investigated drive system was compiled, consisting of two motors operating on a common load and the backlash model in the form of a dead zone coupled with transmission stiffness. The block diagram of the developed model is shown in Figure 2. The parameters of the SRD drives are considered using the example of the signal φ(t) = Asin (ωt). The following parameter values are used in the model: electric motor armature voltage – 440 V; armature current – 115 A; rated power of the electric motor – 45 kW; rated speed – 750 rpm; the moment of inertia of the rotor – 2.575 kgm2; gear ratio of the gearbox – 400; backlash of mechanical transmissions – 0.017 deg. Initially, the operation of an idealized drive without any backlash was simulated, as a result, the reference characteristics of the drive with the guidance signal was obtained. Then backlash was introduced into the model and the results of its impact were considered. Then, one of the electronic devices for backlash com- pensation was introduced into the control system of the drives and the parameters were synthesized until 304 vol. 62 no. 2/2022 Results of research on backlash compensation in a power . . . Figure 3. Backlash compensation with connecting additional supply voltages. the reference characteristics of the SRD drives corre- sponding to the idealized model without backlash was obtained. 3. Backlash compensation device with input of displacement signals In the well-known scheme with an input of dis- placement control channels (electromechanical spring scheme), a certain constant displacement signal is sup- plied to each channel, equal in magnitude and different in sign. This creates an expansion of two gears relative to the common wheel. In the first known works [2], the thrust torques were created by additional supply voltages to the electric motors (Figure 3). Later, to create thrust torques, instead of supplying voltages to the motors, an electronic device was used, which introduces displacements into the dynamic error signal (Figure 4), which is created by the preliminary displacement block [3]. This ensures opposite torques of the motors at zero value of the control signal, similar to the action of a spring. The control signal θ in a system with the main position feedback is a dynamic error signal. When a control signal arrives, for example, a positive one, the signal value in the corresponding channel is added to the offset signal, and in the opposite channel, the offset signal is subtracted from the control signal. If the values of the control signals are lesser than the offset value, it creates a thrust torque to compensate for backlash in the system. When the value of the control signal exceeds the offset value, the signal in the second channel will change sign, and both motors will create torques in the same direction. 4. Backlash compensation device with cross connections The disadvantage of the known method of backlash compensation, based on the introduction of displace- Figure 4. Backlash compensation device scheme on input of displacement signals. ment signals, is the low efficiency of the electric drive due to the high mutual loading of the electric motors. In the process of research, in order to compensate for the influence of backlash in gears, to ensure the sum- mation of the dynamic capabilities of the channels in the steady-state motion mode, as well as to de- crease the mutual torques and increase the efficiency, a control scheme for the drive channels with the intro- duction of cross-connections has been developed. The scheme implements a method for backlash compen- sation by introducing a delay into the dynamic error signal of one of the drive channels. The developed scheme of the backlash compensation device will be called a cross-connections scheme (Figure 5). This scheme can be considered as a special type of tandem control, in which the phase shift is carried out not by calculating the coordinates of individual electric motors, but by converting the error signal by introducing a dynamic delay that depends on the value of backlash. The backlash compensation device consists of two splitters, two switches, two aperiodic links with time constants T1, T2, a signal module extraction block, four multiplying blocks, and two summing blocks. The input of the backlash compensation device is branched with a splitter to three outputs. Two outputs are con- nected to corresponding switches. One output of the switch is connected to the first input of the summa- tor through the first product block, and the second through the aperiodic link. The second product block forms a cross-connection line to the second input to the second summator. Switches are configured for pos- itive and negative dynamic error signal. The outputs of the switches are signals (0, 1) and (-1, 0), respec- tively. After the switch, one of the branches includes a signal module extraction block, which is necessary to match the signs of signals at the outputs of the products blocks, the second inputs of the four product 305 S. L. Samsonovich, B. K. Fedotov, N. B. Rozhnin, R. V. Goryunov Acta Polytechnica Figure 5. Scheme of backlash compensation device with cross-connections. blocks are connected to the remaining outputs of the input signal splitter. The signals from the outputs of the summation blocks are the output signals of the backlash compensation device θ1, θ2. The principle of operation of a cross-connections scheme is based on the phase shift of the signal in the second channel, the value of which is selected de- pending on the amount of backlash. For this purpose, aperiodic links with time constants T1, T2 are used. Initially, the values of the time constants are equal to T1 = T2, then the value – T1,2 is selected depending on the individual parameters of a separate channel. It is known that the backlash has the greatest in- fluence in the tracking system when the direction of movement is changed; in that moment, there is a change in the working surfaces (sides) of the gear teeth, and for the time of this switching, the system appears to be open. Changing the direction of move- ment of the control object requires switching channels. Switches are used to prevent the backlash from open- ing when the direction of movement is changed. For this purpose, switching filters and cross-connections are used. In the mode of steady motion, after the end of the transient processes, the signal in the second channel is close to the signal in the first channel, therefore, both channels operate in the same direction, in this mode of movement, the drive torques are summed up. The backlash in mechanical transmissions causes amplitude limiting and phase displacement during the guidance signal processing. If the selected time constants T1, T2 provide a displacement in the second channel greater than the displacement produced by the action of the backlash, then in the electric drive consisting of two motors connected by a common mechanical transmission, there will be thrust torques for backlash compensation. 5. Experiment results The study of the electric drive operation with a back- lash was carried out by simulating in Simulink using the example of a harmonic guidance signal. The re- sults of the operation of the drive under study with the known scheme of the backlash compensation device based on the introduction of displacement signals are shown in Figure 6. It follows from the graphs that the dynamics of the drive is close to the dynamics of an idealized model without any backlash. The smooth- ness of the change in the coordinates of the electric drive is ensured in the entire range of development (Figure 6a). Figure 6b shows significant thrust torques exceeding the required total torque. A significant amount of energy is spent on mutual torques of the motors, which leads to a decrease in the efficiency of the electric drive, which does not exceed 30 % in the steady-state motion mode (Figure 6c). The simulation results show that the use of a back- lash compensation device with an input of displace- ment signals makes it possible to compensate for the effect of backlash caused by corrosion and ensure the required accuracy of operation. The operating parameters, in terms of processing the control signal, are as close as possible to the parameters of the drive without backlash, however, the high thrust torque leads to high energy costs and a decrease in efficiency. The results of the operation of the drive with a cross- connection backlash compensation device when small values of T1,T2 = 0.2 s are selected (the displacement in the second channel is lower than the displacement produced by the backlash) and when a harmonic guid- ance signal arrives are shown in Figure 7. The simula- 306 vol. 62 no. 2/2022 Results of research on backlash compensation in a power . . . (a). (b). (c). Figure 6. The operation of the drive with a backlash compensation device with input of displacement signals with harmonic guidance signal: a) guidance signal – φc, execution of the guidance signal by the drive – φobj , and dynamic system error signal θ; b) torques developed by motors and total drive torque; c) efficiency of the electric drive. tion showed the drive execution to the guidance signal; when the sign of the dynamic error signal changes, a shift in the amplitudes of the torques of individual motors is observed (Figure 7b), which compensates for the backlash effect. A feature of the work is the absence of thrust torques. Figure 7c shows the change in the efficiency of the electric drive, which in the steady state motion mode, approaches 80 %. Figure 8 shows the harmonic guidance signal pro- cessing by the drive when high values of the time constants T1, T2 = 1.0 s are selected. In Figure 8b, you can see that an increase in the time constants led to the appearance of thrust torques, which function in almost the entire operating range. Thus, when choosing high values of the time constants T1, T2, the backlash is compensated by creating thrust torques by an electric drive, similar to the action of the known device with the input of displacement signals. The disadvantage of this mode, as in the case of the known device, is the decrease in efficiency of the electric drive (Figure 8c), which in the mode of steady motion is in the range of 30–40 %. The dependence of the efficiency of the electric drive on the selected values of the time constants T1, T2 is shown in Figure 9. The graph was obtained by simulating the processing of a harmonic guidance signal with an amplitude of 10 by an electric drive. The figure shows that an increase in the time constants T1, T2 leads to a decrease in efficiency, since thrust torques begin to appear in the system, which leads to energy losses. By simulation, it was found that for the selected guidance signal and the amount of backlash, there is such a value of the time constant – T1, T2 = 0.65 s, at which the phase displacement in the second channel is close to the displacement produced by the back- lash. Relative to this point, a combined graph of the dependence of the efficiency of the electric drive and 307 S. L. Samsonovich, B. K. Fedotov, N. B. Rozhnin, R. V. Goryunov Acta Polytechnica (a). (b). (c). Figure 7. Operation of the drive with a cross-connection backlash compensation device with a harmonic guidance signal when small values of the time constants T1, T2 are selected: a) guidance signal – φc, execution of the guidance signal by the drive – φobj , and dynamic system error signal θ; b) the torques developed by the motors and total drive torque; c) the efficiency of the electric drive. the torques of individual motors on the value T (Fig- ure 10) is plotted. For convenience, this point will be called the transition point. When choosing values – T1, T2 to the left of the transition point, the electric drive will operate without thrust torques, to the right – there will be thrust torques in the system. An in- crease in the values of T1, T2 significantly to the right of the transition point will lead to a decrease in the participation of the second channel in joint work, up to the transformation of the drive into a single-channel drive with a passive load. This graph is only valid for a specific backlash value and guidance signal parameters. When the values T1, T2 = 0 are selected, the drive will operate without displacements and the signals in the channels will be equal. An increase in backlash will lead to a shift of the transition point to the right, a decrease in backlash – to the left. Specific values – T1, T2 depend on the speed parameters of electric motors and power am- plifiers, therefore, the choice of values must be made individually, based on a combination of parameters. When considering the operation of the cross- connections backlash compensation device, it was found that the electric drive can operate with the device in two modes of operation: with thrust torques and without thrust torques. The thrust torques mode (Figure 8) occurs when the control signal in the second channel (reversible) has a displacement greater than the displacement caused by the backlash. Without thrust torques (Figure 7), the indicated displacement is lesser than the displacement produced by the backlash, and in this mode, the electric drive op- erates more efficiently. If the drive operates only with certain, previously known guidance signals, then it is possible to fine-tune the operating modes of the cross- connections backlash compensation device (with or without thrust torques). When the drive is operating 308 vol. 62 no. 2/2022 Results of research on backlash compensation in a power . . . (a). (b). (c). Figure 8. Operation of the drive with a cross-connection backlash compensation device with a harmonic guidance signal when large values of the time constants T1, T2 are selected: a) guidance signal – φc, execution of the guidance signal by the drive – φobj , and dynamic system error signal θ; b) the torques developed by the motors and total drive torque; c) the efficiency of the electric drive. Figure 9. The dependence of the efficiency of the electric drive on the selected values of the time constants T1, T2. 309 S. L. Samsonovich, B. K. Fedotov, N. B. Rozhnin, R. V. Goryunov Acta Polytechnica Figure 10. A combined graph of the dependence of the drive efficiency and the torques of individual motors on the value – T . with arbitrary (random) guidance signals, a variable operation of the electric drive with backlash in gears in two modes is possible: with and without thrust torques. 6. Comparison results The comparison of the schemes of the backlash com- pensation devices shows that the device based on the introduction of the displacement signal is the simplest to implement and gives an effect similar to the ef- fect of a mechanical spring. The simulation results shown, when choosing the smallest value of the er- ror signal displacements according to the condition of the absence of self-oscillations, one of the channels develops a torque that is almost twice the required one (Figure 6b), while excess energy is expended to create thrust torques. The effect of backlash com- pensation in the dynamics is achieved by significant energy losses for the mutual torques of the channels. The efficiency of a drive with a device with an input of displacement signals with a harmonic guidance signal does not exceed 40 %. The cross-connection scheme shows that, when a small value of the time constant of the aperiodic block is selected due to the absence of self-oscillations in the steady-state mode of motion, the summation of the torques of individual motors is provided; the backlash is compensated by shifting the control sig- nals in individual channels. The dynamics of the main movement is close to the dynamics of the ideal model without any backlash. The efficiency of the electric drive approaches 80 % when processing the harmonic guidance signal. An increase in the time constants T1, T2 of the aperiodic links leads to a change of the operation of the electric drive. The thrust torques of the elec- tric drive appear (Figure 8b), which increases the energy consumption and leads to a decrease in effi- ciency (Figure 8c), similar to the device with an input of displacement signals. The use of a backlash compensation device for a drive containing two control channels will ensure the required kinematic accuracy of drive systems during the operation and will not require any additional effort to restore accuracy. The simulation showed that the developed device for backlash compensation with cross-connections al- lows ensuring the accuracy of an electromechanical drive with backlash in mechanical transmissions, and compensating for the gap caused by prolonged idling periods so that when the dynamic error signal changes, it creates a shift in control signals in individual chan- nels, providing a compensation for backlash, and in the mode of steady motion, it creates the summation of the torques of the channels. When choosing large values of the time constants T1, T2 of a cross-connection device, the backlash is compensated by creating thrust torques, similar to a device with an input of displacement signals; in this case, the efficiency does not exceed 40 %. The choice of small values of the time constants T1, T2 of the aperiodic links of the backlash compensation device provides high-speed performance, an increase in the accuracy of operation (the value of the dynamic error is lower (Figure 7a)) and an increase in efficiency of up to 85 %. An analysis of the operating parameters of a drive with various schemes for constructing backlash com- pensation devices testifies that it is advisable to use a circuit with cross-connections. 310 vol. 62 no. 2/2022 Results of research on backlash compensation in a power . . . 7. Conclusions (1.) The conducted research on compensation of back- lash in mechanical transmissions of a power elec- tromechanical drive by introducing various devices for backlash compensation shows that the devices provide the required dynamic characteristics with different energy efficiency. (2.) 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Method and device for selection of backlash in kinematic transmission of support-rotary device with two interconnected electric drives, 2020. Patent RU2726951C1, Bull. No. 20. 312 Acta Polytechnica 62(2):303–312, 2022 1 Introduction 2 Methods 3 Backlash compensation device with input of displacement signals 4 Backlash compensation device with cross connections 5 Experiment results 6 Comparison results 7 Conclusions References