Speed Control of Torsional Drive Systems with Backlash

Transcription

1 Speed Control of Torsional Drive Systems with Backlash S.Thomsen, F.W. Fuchs Institute of Power Electronics and Electrical Drives Christian-Albrechts-University of Kiel, D-2443 Kiel, Germany Phone: +49 ) Fax: +49 ) sot@tf.uni-kiel.de URL: Acknowledgements This work was funded by the Deutsche Forschungsgemeinschaft German Research Foundation). Keywords <<Adjustable speed drive>>, <<Control of drive>>, <<Active damping>>, <<Variable speed drive>>, <<Mechatronics>>. Abstract This paper presents the design, analysis and comparison of the conventional PI-control to two state space controllers for speed control of drive systems with elastically coupled loads. A state space controller of fourth order which considers only the mechanical system and a state space controller of fifth order which takes an approximation of the electrical system into account are analyzed. Thereby, the effects of backlash in the drive are analyzed in each control. State space control yields a high performance, is able to damp torsional oscillations effectively and to reduce backlash effects. Measurement results confirm these statements. Introduction Torsional oscillations in electrical drive systems with elastic shafts are a well known problem []. The natural damping of such systems is very low and yields to a slow decay characteristic of torsional oscillations. Backlash is present in many mechanical systems [2]. If a motor is not directly connected to the load, backlash effects can disturb the system. They yield to high torque impulses which can excite torsional vibrations and reduce lifetime of the system significantly. Active damping of torsional vibrations in drive systems with elastic shafts is a counter measure but yields to high requirements for the controller. Normally, control structures with proportional-integral PI) controller are used for speed control of twomass drive systems [3]. There are various design methods for tuning the PI control parameters which lead to different control performances. For example the restricted pole placement with identical radius, with identical damping coefficient or with identical real part [4]. Another parameter tuning concept of PI-controllers which yields to a maximum value for the phase margin in presented in [5]. However, PI control method without additional feedback provides no free pole placement of the closed control loop and is not appropriate to damp torsional vibrations effectively [6]. Better results can be achieved by feeding back additional system states. In [7] the derivative of the estimated shaft torque is used as additional feedback. But this approach is sensitive to measurement noise. A load torque observer and the results of this additional feedback are presented in [8]. A good tuning of a disturbance observer is shown in [] and [9]. A systematic analysis of speed control with different additional feedbacks is done in [3]. All these approaches achieve an improved suppression of torsional oscillations. Nevertheless, poles of the closed control loop and the resulting system dynamic cannot be set freely. The most promising approach for suppression of torsional oscillations can be obtained with the feedback of all system states. The state space control method allows a free pole placement of the closed control EPE 29 - Barcelona ISBN: P.

2 loop. Therefore the performance of the controlled system can be chosen nearly freely. The problem of state space control is the design of the control parameters and the measurement of all system states or the reconstruction from measurable signals. Control is especially difficult when not all system states are measurable [3]. Typically motor speed is the only measured variable of the mechanical system. Load speed and shaft torque are usually not measured in industrial applications [4]. State space control is analyzed in [], [], [2], [3], [4] and [5]. Whereas [3], [4] and [5] present only simulation results. In [] and [2] Kalman filters are used for estimation of the system states. Thus good results are received by feeding back the estimated states. Backlash and the resulting effects are not analyzed. The attempt to reduce backlash effects is done in []. A gear torque observer is introduced which is used to compensate the backlash effects. However, by feeding back this estimated gear torque, the overshoot of the load speed and the settling time increases. There has been a lot research activity in the area of controlling drive systems with elastic coupled loads. But the differences between control with and without backlash in the drive and the consequences for state space control have not been clearly shown. The aim of this paper is to present three different control structures for speed control of drive systems with elastically coupled loads. A conventional PI-controller, a state space controller of fourth order and a fifth order state space controller will be designed, analyzed and compared. Thereby, backlash effects will be considered and investigated. Measurements will be shown to confirm theoretical results. System Description Conventional speed controlled drive systems may include an inverter-fed motor which powers a load via gear and shaft, as shown in Fig.. The considered system can be divided into an electrical and a mechanical subsystem. The electrical system consists of a current controller, a frequency converter and the electromagnetic part of an induction motor. The mechanical system consists of the inertias of motor, gear, shaft and load and of the connecting elements between these parts. Multi-mass drive systems with a dominant resonant frequency can often be reduced to a two-mass system. The structure of a two-inertia system is presented in Fig. 2. The inertias of the motor Θ M and of the load Θ L are coupled by an elastic shaft which is modeled as a spring with torsional stiffness c and damping d. For this analysis the gear is located close to the motor and is modeled as a dead zone with transmission ratio Ω M /Ω L =. The value of the backlash gap is ±ϕ L =. The dynamics of the electrical part of the drive are approximated as a first-order time-delay element with a time constant T E. Normally, this time constant is much smaller than the time constant of the mechanical part. Due to this T E is neglected in most cases. Figure : Overview of the drive system Figure 2: Block diagram of two-inertia Figure 3: Backlash system with backlash as dead zone element Backlash Backlash is one of the most important non-linearities in many applications that limit the performance of speed control [2]. Backlash can be modeled as a dead zone element as shown in Fig. 3. In dependence of the value of the backlash gap ϕ L and the angle α = α M α L difference between motor position and load position) a new output angle ϕ is generated which causes a rotation of the shaft. When the backlash is open, the output angle ϕ is zero. Consequently the transmitted torque is equal to zero. In this case motor and load side are decoupled. The inertia which affects the motor is no longer the sum of all inertias of the drive system, but only the inertia of the motor and the transmission parts before the backlash. Hence the dynamic behavior varies. The movement of the load is autonomous while the backlash gap is open and accordingly the load is neither observable nor controllable. When the backlash closes, high torque impulses occur, which can excite torsional oscillations and reduce lifetime. Based on this, the aim of the control has to be that the backlash opens as seldom as possible and closes softly. The influence of backlash will be shown in the section with measurement results. EPE 29 - Barcelona ISBN: P.2

3 Two-Mass Model The internal damping d of the shaft is very low and can be neglected for control design analysis [6]. The mathematical model is described in a per-unit system with time constants, T L, T C and T E, time constant of motor, load, spring and approximated electrical part, respectively. The state space model of the two-mass system is given by: d dt ω M m S = ω L T C T C T L ω M m S ω L + m M + T L m L ) If the approximated time delay of the inner control loop is taken into account, the state space model is given by: ω M T d m S M ω M dt ω L = T C T C T L m S ω L + m M + m L 2) m M T L m E T E Where ω M is the motor speed and ω L the load speed. m S, m M, m L and m M are the torsional shaft torque, electromagnetic torque of the motor, load torque and the reference value of the torque. Control This section shows the design of a conventional PI-controller and a state space controller for a twoinertia system. Two state space controllers are introduced. The first state space controller is designed by neglecting the inner control loop whereas the second one takes this control loop into account. All presented control methods are designed with neglected internal damping coefficient d of the shaft. Conventional PI-Control Fig. 4 shows the block diagram of the conventional PI-controller with proportional gain k P and integral gain k I. The disadvantage of the conventional PI-speed controller is the limited pole placement. The conventional control method contains no additional feedback from system states. Therefore it s not possible to locate all poles of the closed control loop independently. Consequently the dynamics of the closed loop cannot be set freely and the torsional vibrations cannot be damped effectively. Electrical System Mechanical System Figure 4: Block diagram of conventional control with PI speed controller The design of the control parameters k I and k P typically is done using standard optimization methods with the aim to achieve a trade-off between reference reaction and disturbance reaction of the closed control loop. Standard optimization methods such as the symmetrical optimum are not suitable for drive systems with elastic shafts and yield to a high excitations of torsional oscillations. A restricted pole placement is more appropriate to design the parameter of the PI-controller. Three different restricted pole locations with either identical radius, identical damping coefficient or identical real part can be distinguished [4]. An appropriate design for ratios from load inertia to motor inertia above two is a pole location with identical damping coefficient, which will be presented and compared to state space control. Design of Conventional PI-Control The electrical system is neglected for design of the PI-controller. Then the transfer function of the closed control loop from motor speed to motor reference speed is given by a fourth order function: ) G W s) = ω k Ms) I + s k P ) s 2 ω M s) = + s 4 + s 3 kp + s 2 kit L T C + +T L k + s P + k 3) I EPE 29 - Barcelona ISBN: P.3

4 The design of the control parameters takes place using pole placement. Therefore a forth order polynomial function Ps) with the desired poles of the closed control loop p z to p z4 is introduced: Ps) = s p z )s p z2 )s p z3 )s p z4 ) 4) with: ) p z/z2 = ω z D ± j D 2 ); p z3/z4 = ω z2 D 2 ± j D 2 2 5) The poles of the closed control loop are characterized by damping coefficients D and D 2 and by the eigenfrequencies ω z and ω z2. Comparing the coefficients of the denominator of the closed loop transfer function 3) and the forth order polynomial Ps) from equation 4) arises the following equations [4]: ω 2 z + ω 2 z2 + 4ω z ω z2 D D 2 ω 2 zω 2 z2t L T C = ω z D ω 2 z2 ) T L T C k P = 2 ω z D + ω z2 D 2 ) 6) k I = ω 2 z ω 2 ) z2 7) + 8) T L T C T C = ω z2 D 2 T L T C ω 2 z For the design with identical damping coefficient D = D = D 2, the following control parameters arise: k P = 2 Dω z + ω z2 ) ) k I = ω 2 z ω 2 ) z2 ) The eigenfrequencies result by system parameters and the selected damping coefficient D: TL 4D TL 4D 2 ω z/z2 = 2 2) T L T C A good trade-off between reference reaction and disturbance reaction can be obtained with a damping coefficient D = / 2 =.77 [7]. The two-mass mechanical system contains three poles. One is located in the origin and a conjugatecomplex pole pair is located on the imaginary axis of the pole zero map. The resonance frequency of the conjugate-complex pole pair of the mechanical system amounts to ω = 269 rad/s = 42.8 Hz. Designing the PI-controller with identical damping coefficient yields to the poles of the closed control loop, as can be seen in Fig. 7. The eigenfrequencies ω z and ω z2 arise in dependence on the choice of this damping coefficient D. A damping coefficient D =.77 yields with the considered system to the following frequencies of the closed control loop: ω z = 73. rad/s and ω z2 = 225 rad/s. The pole of the approximated inner control loop is located on the real axis with eigenfrequency ω = 5 rad/s and is outside of the display area. PI State Space Control The state space control method includes feedback of all system states. Fig. 5 shows the block diagram of the state space control if the electrical system is neglected and Fig. 6 shows the block diagram if the electrical system is taken into account. A PI-controller is included to eleminate stationary control error. The reference value of the torque is calculated depending on the feedback of the system states, as can be seen in figures 5 and 6. The advantage of state space control is a theoretically free pole placement of the closed-loop control. Therefore high dynamic and high damping of torsional vibrations can be achieved. The disadvantage of state space control is the number of control parameters. The conventional control method includes two control parameters k I and k P. The PI state space control includes five, respectively six control parameters, if the electrical system is considered. An appropriate method to design the control parameters for drive systems with elastic shafts and backlash will be presented in this analysis. ) 9) EPE 29 - Barcelona ISBN: P.4

5 Electrical System Figure 5: Block diagram of PI state space control Figure 6: Block diagram of PI state space control of fifth of fourth order electrical system is neglected) order electrical system is taken into account) 4 Design of PI State Space Control The closed-loop transfer function of the PI state space controlled system with neglected electrical system is given by a fourth order function: ) G W s) = ω k Ms) I + s k P ) s 2 ω M s) = + s 4 + s 3 kp k + s 2 kit L T C k 2 T L + +T L + s kp k k 3 + k 3) I The design of control parameters takes place using pole placement [8]. Comparing the denominator of the closed loop transfer function 3) with the polynomial Ps) from equation 4) and solving a system of equations yields to following control parameters for the state space controller: k I = ω 2 zω 2 z2 ; k P = k I ω z ; k = k P 2 ω z D 2 ω z2 D 2 4) k 2 = + + TC ω 2 T zω 2 z2 ω 2 z ω 2 ) z2 4ω z ω z2 D D 2 L 5) k 3 = 2 ω z D + 2 ω z2 D 2 2 ω z ω 2 z2d T L T C 2 ω 2 zω z2 D 2 T L T C 6) The dynamics of the closed-loop control can be chosen by the design parameters D, D 2, ω z and ω z2. In contrast to the conventional PI-controller, all considered poles of the closed control loop can be set freely. If the electrical System is taken into account, the closed-loop transfer function increases to a fifth order function: G W s) = ω Ms) k I + s k P ) ω M s) = s 5 + s 4 k 4 + s 3 kpt C k T L + +T R T R +s k P k T R + T C T R k I T R ) s 2 T R + T R + s 2 kit L T C k 2 T L k 4 +T L )+ +T L T R For the design of the control parameters, the order of the polynomial Ps) from equation 4) must be increased to a fifth order function: Ps) = s p z )s p z )s p z2 )s p z3 )s p z4 ) 8) with one real pole p z = ω z. Comparing the denominator of the closed loop transfer function 7) with the polynomial Ps) from equation 8) and solving a system of equations yields to the control parameters of the state space controller. Due to limited space and long equations, the equations of control parameters are not shown here explicitly. The poles of the closed control loop of the state space controlled system can be seen in Fig. 7. The poles of the fourth order state space control are shown in the middle picture and the considered poles of the fifth order control are shown in the right picture. The damping of the poles are chosen as before D = D 2 =.77. The eigenfrequencies are set to ω z = 3 rad/s and ω z2 = 3 rad/s. The fifth order state space control is able to influence the inner control loop. In order to reduce control input power, the pole of the inner control loop is shifted from ω z = 5 rad/s to the eigenfrequency ω z = 3 rad/s. Damping coefficients D and D 2 and eigenfrequencies ω z and ω z2 are chosen as with state space control of fourth order. EPE 29 - Barcelona ISBN: P.5 7)

6 Figure 7: Pole-zero maps: left: PI-controller tuned with identical damping coefficient D =.77; middle: fourth order state space controller tuned with ω z = 3 rad/s, ω z2 = 3 rad/s, D = D 2 =.77; right: fifth order state space controller tuned with ω z = 3 rad/s, ω z = 3 rad/s, ω z2 = 3 rad/s, D = D 2 =.77 Reconstruction of System States In most applications it is not possible to measure all system states such as the load speed and the shaft torque. Therefore an observer is required which reconstructs these states. For an appropriate reconstruction of all system states, a disturbance observer is used in this analysis [8]. Motor speed is the only measured variable of the mechanical system which is used for the disturbance observer. Motor torque M M is calculated by machine parameters and current. Load speed, shaft torque and disturbance torque are estimated by the disturbance observer. To be fast enough and not too sensitive due to measurement noise, the poles of the observer are three times further left of those of the closed control loop. Load side is decoupled from the motor side, if the backlash is open. In this case, load variables are no longer observable. This influence, relating to the state space control is analyzed in the next section. Measurement Results and Backlash Effects Measurements were taken on the drive system shown in Fig. 8. A 5.5 kw induction motor is connected via backlash clutch, long shaft, torque sensor and flywheel to a 6.4 kw servo induction machine which can induce a disturbance torque. Incremental encoders with 5 pulses/revolution on motor side and 52 pulses/revolution on load side are used for speed measurement. The nominal speed of the induction motor amounts to 455 /min. The motor torque is limited to 36 Nm. A variable backlash gap can be chosen with an adjustable clutch on the motor side. A flywheel on the load side is used to increase the load inertia. The ratio of load inertia to motor inertia amounts to 3.4. The shaft torque is measured by a torque sensor with a strain gauge. The long shaft consists of aluminum with a quill shaft and a length of 5 mm. The control algorithm is implemented on a dspace DS3 PPC controller board and data are updated with a sampling frequency of 6 khz. Previous simulation results are presented in [9]. Measurement results of the PI-controller designed with poles with identical damping coefficient Figure 8: Laboratory setup as described in the previous section are shown in Fig. 9. The upper picture on the left side shows the step responses of motor speed blue line) and load speed red line). At the time t = s, the reference value black dashed line) changes from zero to 2 % of the nominal motor speed and at the time t =.5 s from 2 % to. It can be seen that torsional oscillations are excited during the changes of the reference speed. The resonance frequency amounts to 42.8 Hz. The overshoot is about 9 % and the settling time amounts to.3 seconds. The lower picture on the left side shows the shaft torque during the step responses. Tosional oscillations can be seen in the shaft torque to high amount. The maximum shaft torque amounts EPE 29 - Barcelona ISBN: P.6

7 to.65 times of the nominal value of motor torque. Results of disturbance steps can be found on the right side. The upper picture shows motor blue line) and load red line) speeds during a step change in the load. At the time t = s, a load torque with 5 % of the nominal motor torque is induced and removed at the time t = s. The sag of motor and load speed amounts to 7.5 % and the overshoot to.8 %. The corresponding shaft torque is shown in the lower picture on the right side. In contrast to standard optimization methods like the symmetrical optimum, this design can avoid periodical torsional oscillations. In Fig., results of the PI-controlled drive system with backlash ϕ = ± ) are shown. Figure 9: PI-controller tuned with identical damping D =.77) without backlash It can be seen, that the amplitude of the oscillations of speeds and shaft torque are significantly higher than without backlash. The difference between motor speed and load speed increases, consequently the shaft torque increases. The maximum value of the shaft torque exceeds 2.4 times the nominal value of the motor torque. This effect increases with increasing backlash gap. Furthermore, the backlash opens after reaching the reference value and closes a short time later again, as can be seen in the enlarged view upper picture, left side). This leads to a torque impulse peak value amounts.3 times the nominal value of the motor torque) which excites oscillations in the shaft torque, as can be seen in the enlarged view in the lower picture on the left side. This effect is repeated during the reference step response from 2 % to standstill at the time of.7 s. Overshoot and settling time are similar to the results without backlash. The effects of backlash due to disturbance reaction can be seen on the right hand side. The behavior during a load step from to 5 % of the nominal value of the motor torque is very similar to the behavior without backlash. However, if the load torque jumps back to, backlash opens and closes again which yields to torque impulses in the shaft torque, as can be seen in the lower picture at the time of.5 s and.3 s. This effect increases with increasing backlash gap, as well. Results of the state Figure : PI-controller tuned with identical damping D =.77) with backlash space controller of fourth order with backlash in the drive system can be found in Fig.. It can be seen, that the settling time of motor and load speed is similar to previous results but the overshoot is somewhat EPE 29 - Barcelona ISBN: P.7

8 smaller and amounts to 3.5 % upper picture on the left side). Furthermore, the backlash does not open after the reference step and therefore, no impulse in the shaft torque is induced. The measured shaft torque during the dynamic processes is similar to torque of the PI-controlled system. The maximum value of the shaft torque exceeds 2.4 times the nominal value of the motor torque and is comparable to previous results. The disturbance reaction of the speeds and the shaft torque can be seen in the pictures on the right side. It can be found out that the impulses of the shaft torque during closing of the backlash are smaller than with PI-control. State space control achieves a better closing of the backlash during dynamic processes. However, this state space control requires high control input power and cannot damp torsional oscillations during reference steps because of systems limitations. Measurement results of the Figure : Fourth order state space controller with backlash state space controller fifth order are shown in Fig. 2. The consideration of the electrical system provides to reduce the control input power and to damp torsional oscillations during dynamic processes effectively. It can be seen that oscillations during reference steps are reduced significantly. The maximum value of the shaft torque is much smaller than the PI-controlled system and amounts to.26 times the nominal value of the motor torque. High torque impulses in the shaft are eliminated. Overshoot amounts to 2.5 % and the settling time to.3 seconds. The disturbance step response shows good results, as well. There are no high torque impulses and almost no effects of backlash. In the previous results, measured system Figure 2: Fifth order state space controller with backlash states were fed back. If load speed and shaft torque is estimated by a disturbance observer, following results were achieved, see Fig. 3. Motor and load speeds looks almost the same as with measured states. The overshoot is slightly smaller 2 %) and the maximum value of the shaft torque is slightly bigger.42 times the nominal value of motor torque). Results of the disturbance step response show the same performances as with measured states. The estimated load speed and shaft torque during the reference steps and disturbance steps are shown in Fig. 4 and compared to the measured values. The red lines show the estimated values and the blue lines show the measured values. The estimated load speed and shaft torque show a good conformity with EPE 29 - Barcelona ISBN: P.8

9 measured values. Load side variables are not observable if the backlash opens. But the backlash opens only for a short time and yields just to small differences between measured and estimated values. This has almost no influence on the state space control. Analog results are achieved for other operating points. Figure 3: Fifth order state space controller with backlash and observer Conclusion Figure 4: Comparison of measured and estimated states Three different control structures for speed control of drive systems with elastically coupled loads are presented in this paper. A conventional PI-controller, a state space controller fourth order and a fifth order state space controller are designed, analyzed and compared to each other. Thereby, the effects of backlash are considered. It has been shown that the conventional PI control method is not able to damp torsional vibrations and to reduce backlash effects effectively. Nevertheless, the design of the PI control parameters is of importance for standard applications. A suitable design of the PI control parameters is given in this paper. The state space controller of fourth order is appropriate to reduce torsional oscillations. But this approach requires high control input power and yields to oscillations during reference steps due to system limitations. Backlash effects are reduced but not eliminated. State space control of fifth order is able to damp torsional vibrations effectively. Backlash effects are reduced significantly, as well. A suitable design of both state space controls has been shown in this analysis. Load speed and shaft torque are reconstructed using a disturbance observer. It has been shown that the peak shaft torque of the PI-controlled system increases significantly if backlash is located in the drive system. Furthermore, the maximum value of the torque impulses increases with increasing backlash gap. To apply fifth order PI state space control gives best results concerning reference and disturbance reaction as well as in avoiding resonances and backlash influence. Measurement results confirm the statements. EPE 29 - Barcelona ISBN: P.9

10 Appendix Table I: System parameters Motor Power Torque Speed 5.5 kw 36 Nm 455 min Load Power Torque Speed 6.4 kw 39 kw 249 min Mechanics Inertia of motor side.37 kgm 2 Inertia of load side.258 kgm 2 Shaft stiffness 27 Nm/rad References [] Hori, Y., Sawada, H. and Chun, Y., Slow Resonance Ratio Control for Vibration Suppression and Disturbance Rejection in Torsional System, IEEE Transactions on Industrial Electronics, vol. 46, no., pp , 999. [2] Nordin, M., Controlling mechanical systems with backlash - a survey Automatica, 38, pp , 22. [3] Szabat, K. and Orlowska, K. T., Vibration suppression in a two-mass drive system using PI speed controller and additional feedbacks - comparative study, IEEE Transactions on Industrial Electronics, vol. 54, no. 2, pp , 27. [4] Zhang, G., Speed control of two-inertia system by PI/PID control, IEEE Transactions on Industrial Electronics, vol. 47, no. 3, pp , 2. [5] Preitl, S. and Precup, R.-E., An extension of tuning relations after symmetrical optimum method for PI and PID controllers, Automatica, 35, pp , 999. [6] Eutebach, T. and Pacas, J. M., Damping of torsional vibrations in high-dynamic-drives, 8th European Conference on Power Electronics and Applications EPE 99), 999. [7] Sugiura, K. and Hori, Y., Vibration Suppression in 2- and 3-Mass System Based on the Feedback of Imperfect Derivative of the Estimated Torsional Torque, IEEE Transactions on Industrial Electronics, vol. 43, no., pp , 996. [8] Ohmae, T., Matsuda, T., Kanno, M., Saito, K. and Sukegawa, T., A Microprocessor-Based Motor Speed Regulator Using Fast-Response State Observer for Reduction of Torsional Vibration, IEEE Transactions on Industry Applications, vol. IA-23, no. 5, pp , 987. [9] Komada, S., Iyama, K., Yubai, K. and Hori, T., Suppression of limit cycle and improvement of robust performance in two-mass resonant systems with nonlinearity, vol.3, pp , 2. [] Szabat, K. and Orlowska, K. T., Performance Improvement of the Industrial Drives with Mechanical Elasticity using Nonlinear Adaptive Kalman Filter, IEEE Transactions on Industrial Electronics, vol. 55, no. 3, pp , 28. [] Dhaouadi, R., Kubo, K. and Tobise, M., Analysis and Compensation of Speed Drive Systems with Torsional Loads, IEEE Transactions on Industry Applications, vol. 3, no. 3, pp , 994. [2] Ji, J.-K. and Sul, S.-K., Kalman Filter and LQ Based Speed Controller for Torsional Vibration Suppression in a 2-Mass Motor Drive System, IEEE Transactions on Industrial Electronics, vol. 42, no. 6, pp , 995. [3] Qiao, F., Zhu, Q.M., Li, S.Y. and Winfield, A., Torsional Vibration Suppression of a 2-Mass Main Drive System of Rolling Mill with KF Enhanced Pole Placement, Proceedings of the 4th World Congress on Intelligent Control and Automation, 22. [4] Zhang, R., Chen, Z., Yang, Y. and Tong, C., Torsional Vibration Suppression Control in the Main Drive System of Rolling Mill by State Feedback Speed Controller Based on Extended State Observer, IEEE International Conference on Control and Automation, 27. [5] Hara, K., Hashimoto, S., Funato, H. and Kamiyama, K., Robust Comparison between Feedback-Based Speed Control Systems without State Observers in Resonant Motor Drives, Power Electronics and Drive Systems, 997. [6] O Sullivan, T. M., Bingham, C. M. and Schofield, N., Enhanced servo-control performance of dual-mass systems, IEEE Transactions on Industrial Electronics, vol. 54, no. 3, pp , 27. [7] Leonhard, W., Control of Electrical Drives, 3rd edition, Springer, 2. [8] Lutz, H. and Wendt, W., Taschenbuch der Regelungstechnik, Verlag Harri Deutsch, 27. [9] Thomsen, S. and Fuchs, F.W., Conventional and State Space Control for Active Damping of Mechanical Vibrations in Speed Drive Systems with Backlash, VDE/VDI-Fachtagung - Elektrisch-mechanische Antriebssysteme, Böblingen - Germany, 28. EPE 29 - Barcelona ISBN: P.