Electr Eng DOI 10.1007/s00202-017-0626-z

ORIGINAL PAPER

Industrial controller-based dynamometer with dynamic emulation of mechanical loads ˇ Karol Kyslan1 · Miran Rodiˇc2 · Luboš Suchý1 · Želmíra Ferková1 · 1 ˇ František Durovský

Received: 20 December 2016 / Accepted: 17 July 2017 © Springer-Verlag GmbH Germany 2017

Abstract Dynamic emulation of mechanical loads belongs to advanced dynamometer control strategies. The main goal of this paper is to analyse and implement a control algorithm for dynamic emulation into an industrial converter by using a standard industrial programming tool. The reference torque of a load machine is calculated through the previously developed closed-loop control algorithm using PI estimator. Proposed torque control structure is analysed and experimentally verified with a linear and a nonlinear model of a mechanical load to be emulated. Presented implementation enables the user the emulation of various mechanical loads with the industrial drive used as a dynamometer. This approach can be used for the advanced testing of motion control techniques in case where the mechanical load is not physically available. Only the equations describing its dynamic are needed.

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Karol Kyslan [email protected] Miran Rodiˇc [email protected] ˇ Luboš Suchý [email protected] Želmíra Ferková [email protected] ˇ František Durovský [email protected]

1

Department of Electrical Engineering and Mechatronics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Letná, 9, 042 00 Košice, Slovakia

2

Institute of Robotics, Faculty of Electrical Engineering and Computer Science, University of Maribor, Smetanova, 17, SI-2000 Maribor, Slovenia

Keywords Control · Dynamic emulation · Dynamometer · Emulator · Inertia · Load torque · Pendulum

Abberivations Bm n em Bem Rem Bˆ m Text Fem (s) Tf g Tˆm h Tm Jm Tm∗ Jem Tl Jˆm Tl∗ k εem lem ϕem m em ωem n ωr

Total viscous friction coefficient [Nms/rad] Speed of the emulated load [rpm] Emulated viscous friction coefficient [Nms/rad] Emulated radius of the pendulum’s ball [m] Estimated viscous friction coefficient [Nms/rad] External torque applied on emulated load [Nm] Transfer function of emulated load Friction torque of the test bench [Nm] Gravitational acceleration [m/s2 ] Estimated torque of the drive under test [Nm] PI estimator gain Actual torque of the drive under test [Nm] Total moment of inertia [kgm2 ] Reference torque of the drive under test [Nm] Emulated moment of inertia [kgm2 ] Actual torque of the load drive [Nm] Estimated total moment of inertia [kgm2 ] Reference torque of the load drive [Nm] Gain of the feedback controller Emulated angular acceleration [rad/s2 ] Length of the emulated pendulum rod [m] Emulated angular position [rad] Mass of the emulated pendulum body [kg] Emulated angular speed [rad/s] Speed of the drive under test [rpm] Actual speed of the test bed [rad/s]

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1 Introduction Dynamic emulation of mechanical loads is a term closely connected to widely known term for special kind of an electrical drive— dynamometer. Dynamometers have been widely used to perform static load tests of electrical machines or combustion engines [1,2]. In case of variable speed drives, static load tests are often insufficient and dynamic tests are necessary. Programmable dynamometers allow realistic testing of electrical drives by providing the behaviour of various kinds of loads. It is beneficial to use dynamometer for the validation of the control algorithms in the laboratory conditions. Even more, if the programmable dynamometer is available, it enables off-site testing of drives driving real industrial applications, which is very advantageous for a commissioning engineer [3]. To verify the effectiveness of a new control algorithm, it is desirable to provide a load in which mechanical parameters (such as inertia or friction) can either be pre-programmed or vary with the speed or the position. Dynamic testing is achieved by the mechanical load emulation, where dynamometer is acting exactly in the same way as is the behaviour of mechanical load driven by the drive under test (DUT). In order to achieve this goal, the dynamics of the mechanical load has to be preserved and, even more, imposed into dynamometer control structure. Dynamic emulation of mechanical loads (DEML) is nowadays an established term for the programmable dynamometers with this kind of torque control. Comprehensive review of earlier dynamometer control approaches can be found in [4]. Common drawback of presented methods is the use of inverse mechanical dynamics model in the control structure, which causes failure of emulation in the discrete implementation on digital signal processor. These undesirable effects are clarified in [5] where also the first DEML approach with experimental results is proposed, together with the detailed analysis of discrete control structure. This approach uses a feedforward speedtracking control scheme with an analytical compensator for elimination of mechanical dynamics. Its extension the emulation of position-dependent mechanical loads is proposed in [6]. However, this approach has some drawbacks, such as a sensitivity to parameter variation, which makes it less accurate for the emulating of high-speed and high-power loads [7]. An improvement in analytical compensator is proposed in [7], where the parametric system identification approach is used. The mathematical model of a dynamic system, which can reproduce the test system input–output properties, is found with the experimental data obtained by system transient step tests. Nonlinear control approach for DEML is proposed in [8]. It uses PI estimator which makes it more robust towards impacts of parameter variations and unmodelled dynamics.

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Its performance is given by setting of two independent parameters, and its extension to the position-dependent loads is presented in [9]. Another group of authors use known DEML control structures in order to emulate different types of mechanical loads, such as multi-mass loads [10], wind turbines [11–13], backlash [14] or mining impacts [15]. General framework for the classification of the dynamic emulation control structures, proposing direct control and indirect control actuation structure, can be found in [16]. This paper presents an extended study of the nonlinear approach with the PI estimator in [8]. The control structure for dynamometer is described, analysed and experimentally verified for the linear and nonlinear (pendulum) type of mechanical load. The motivation was to avoid any rapid control prototyping tools, such as in [17] or [18]. Even if these approaches are widely used in academia research, they are less suitable for industrial use and also expensive. Therefore, the test bed is built solely with the industrial hardware components and software tools which brings several benefits. From our point of view, the main purpose of the test stand with dynamometer is to verify the control algorithms for DUT which will later be used in a real application. It has to be stressed out that the verification of DUT algorithms is, however, not the issue of this paper. Anyway, it is very advantageous if the control algorithm for DUT is developed with the same programming and commissioning tool as it will be used later in a real application. The commissioning engineer is able to prepare overall algorithm in the laboratory conditions and he can create the algorithm with the same programming tool as it is needed in the industry. Only minor adjustments and tuning are then necessary at the commissioning place. The main motivation of this contribution is to propose dynamometer control concerning all these issues.

2 Control structure Mechanical dynamics is defined as a speed response to a given drive torque. The dynamics of two machines connected with the rigid shaft can be expressed as follows: Jm ω˙ r + Bm ωr = Tm − Tl − T f ,

(1)

where all the quantities are explained in nomenclature. Note that friction torque T f is unknown and can be treated as a disturbance to be covered by drive under test torque Tm . Thus, it is not covered by load drive torque Tl . Fast torque control provided by vector control of both machines is considered, with torque loops of both machines having high bandwidth compared to the mechanical dynamics. It results in ideal torque control equations:

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Fig. 1 Control structure of nonlinear DEML approach using PI estimator

Tm = Tm∗ ; Tl = Tl∗ ,

(2)

where Tm∗ is given by the outer speed controller of DUT and Tl∗ is calculated according to chosen dynamometer control strategy. Our goal is to implement such an approach of dynamometer control in which the dynamics of mechanical load is expressed by its equation. The simplest linear mechanical load has adjustable parameters of inertia Jem and viscous friction Bem . If this load is driven by Tm , it starts to rotate with the emulated speedωem , which can be described as follows: Jem ω˙ em + Bem ωem = Tm − Text .

(3)

Text is an additional torque input, usually used for a step torque loading, and its value is known. For simplicity, it is assumed to be zero in the following text. Then, the transfer function of emulated load given by eq. (3) is as follows: Fem (s) =

1 ωem (s) = . Tm (s) Jem s + Bem

Fig. 2 Linear mechanical load driven by Tm

(4)

The model of this load is shown in Fig. 2, and it has to be implemented into the control structure of dynamometer, as shown in Fig. 1. On the right side of Fig. 1, we can see the dynamic model of the test stand, where the dynamometer and the test machine are mechanically connected with the common shaft. The actual torque Tl produced by the dynamometer is acting against the actual torque of the machine under test Tm . Parameters Jm and Bm are total inertia and total viscous friction of the test stand including both machines. The goal is to calculate torque reference for the dynamometer Tl∗ . The reference torque of the dynamometer must be calculated in such a way that the dynamic behaviour of the emulated mechanical load is preserved. This can be explained as follows: if the drive is connected to the mechanical load,

the load starts to rotate with the emulated speed ωem . During off-site testing, the emulated load is replaced by the dynamometer, which should behave in the same way as the emulated load. This means that the dynamometer shaft not only has to rotate with the same emulated speed, but has to closely track its dynamic behaviour, i.e. accelerations and decelerations. This tracking is ensured by the control structure of the dynamometer torque control in Fig. 2. It allows using different linear or nonlinear models of mechanical loads in block Fem . The actual value of angular speed ωr and estimated torque of the drive machine Tˆm are the necessary inputs in Fig. 1. T f is an unknown part of the nonlinear friction torque in the mechanical test stand. It is pre-compensated inside the industrial converter so it can be treated as a disturbance. In order to eliminate the impact of the DUT torque, feedforward compensation of the applied torque Tˆm is added to the load torque reference. Properties of the control structure can be adjusted by the parameters k and h, where k is the gain of the feedback controller used to compensation of numerical errors and h is the PI estimator gain, which removes residual nonlinear friction and other unmodelled dynamics. The calculation of these parameters is shown in the next section.

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3 Analysis of the control structure Note that the control algorithm uses estimated (or calculated) values of total inertia Jˆm and total friction Bˆ m . These parameters are obtained during commissioning of the drive with high precision. The output of the control structure is the reference torque for dynamometer Tl∗ . The transfer function of the output shaft speed is presented as [19]: ωr (s) = F1 (s)ωem (s) + F2 (s)T f (s),

(5) Fig. 3 Experimental setup based on industrial components

F1 (s) and F2 (s) are the transfer functions shown in Appendix. If the parameters of the test stand dynamics are obtained with the good precision: Jm = Jˆm , Bm = Bˆ m ,

(6)

the transfer function (5) is simplified to: ωr (s) = ωem (s) + F2 (s)T f (s).

(7)

This analysis shows, based on eq. (7), that tracking of the emulated speed is assured. Unfavourable influence of the friction torque T f is assumed to be very small and can be neglected. From (5), the parameters of k and h can be calculated as: k = ω1 , h = Jm ω2 − Bˆ m ,

(8)

where ω1 and ω2 are the eigenvalues of the characteristic equation in F1 (s). It can be shown that the transfer function of the actual load torque TL is presented as: Tl (s) = F1 (s) [Jm s + Bm ] Fem (s)Text (s) + +F1 (s) [Jm s + Bm ] Fem (s)Tˆm (s) −F3 (s)Tˆm (s) − F4 (s)T f (s).

(9)

Fig. 4 Topology of the test bench

frequencies, the load machine’s load torque resembles the value of Text , whereas at higher frequencies, tracking can no longer be assured. Therefore, this torque input is used mostly for the static load torque tests (e.g. step reference of load torque).

Transfer functions F3 (s) – F4 (s) are shown in Appendix. If eq. (6) is valid and the following holds: Tˆm = Tm , Fem (s) =

1 Jˆm s + Bˆ m

4 Experimental test stand and implementation ,

(10)

the transfer function (9) is simplified to: Tl (s) = Text (s) − F4 (s)T f (s).

(11)

This analysis shows, based on eq. (11), that if the estimated parameters of inertia and viscous friction are well known and there are no unmodelled dynamics, the load torque reference tracking is achieved, i.e. load torque applied by dynamometer is equal to the external load torque reference Text . At low

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The control structure for DEML has been experimentally verified on the test stand built with industrial components. The stand is shown in Fig. 3 and its topology in Fig. 4. The following devices were used: • • • • •

SIMOTION D425 motion control system (1), Smart Line Module 10 kW (2), Double Motor Module 2 x 9A (3), SITOP 24V DC Power Supply (4), Sensor Module Cabinet SMC 20 (5),

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• • • •

SMPM machine, 3000 rpm, 7.3 Nm (6), IM machine, 1455 rpm, 3 kW, 6,2 A (7), PC with SCOUT and DCC software tools (8), Flexible mechanical clutch (9).

Induction machine is used as a DUT, controlled with the speed control loop. Permanent magnet synchronous machine is used as a dynamometer, controlled with the torque control loop. Note that no torque transducer is used and only internal torque observer inside the converter control is used as the inputTˆm in Fig. 1. Both machines were supplied from modular drive system based on SINAMICS S120 components. The control algorithm was developed in SCOUT commissioning environment. SIMOTION motion control system includes several function blocks, enabling various arithmetical or logical control operations. The appropriate use of these blocks together with the converter’s control circuits allows building of suitable control algorithms to satisfy the user’s requirements. DEML structure as presented in Fig. 1 was programed with Drive Control Chart (DCC) option package [20]. DCC for SINAMICS expands the possibility of the converter, and it is a convenient tool to solve drive-specific tasks directly on the converter. It enables graphic configuration and expansion of the converter functionality by means of freely available control, arithmetic and logic free-blocks. It is possible to connect any signal from the list of readable parameters of converter to the control structure. In the same way, the produced correction signal should be connected back to the control structure of S120, but only to those input points that have the write permission [21]. A part of a developed control structure in DCC charts is shown in Fig. 5. It shows a reading of a signal from the converter to the control structure for DEML.

Fig. 5 DCC implementation of DEML control structure, reading of the signals from the converter to the programming environment

5 Experimental results At first, the experiments were executed for the linear firstorder system, describing a mechanism with linear friction. The parameters (inertia Jem and linear viscous friction coefficient Bem ) were set to several different values. Variable inertia is often present in mechatronic systems, so it is very convenient to possess such programmable dynamometer in a research laboratory. In most cases, inertia load is constructed by connecting a machine shaft to the flywheel with the defined dimensions. This can be avoided by using the proposed method. Performance of the outer PI speed controller for DUT remained the same for all experiments in order to do a fair comparison. Its values are shown in Appendix.

Fig. 6 Response to step speed reference, Jem = Jm

Figure 6 shows the response to the step function of reference speed for the case Jem = J , Bem = B. For these parameters of linear load, the actual dynamometer torque should be zero. This case is important because the impact of unmodelled dynamics can be observed. In case of inaccurate inertia estimation, the transfer function (5) is not valid and the dynamics of mechanical load is violated.

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Fig. 7 Response to ramp speed reference, Jem = Jm

Oscillations of the load torque occur at start, probably due to the non-rigid clutch or algorithm execution delays. Static friction torque is covered only by the tested drive. Its value is 1.2 Nm, and it is observed in t= 0.3–0.4 s. External torque value Text = 3 Nm was applied in t = 0.5 s. Detailed view in Fig. 6 shows good tracking of emulated speed. Figures 7, 8, 9 show the response to the 1s ramp function of reference speed, where Bem = B, Text = 0 Nm, and inertia is varied as follows: Jem = J , Jem = 3J , Jem = 5J.It can be observed that with the raising of emulated inertia, also the load torque values increase. As a consequence, also a test machine actual torque is getting higher values up to the maximum permissible value of Tm M AX = 8 Nm, which is shown in Fig. 9 for the highest value of emulated inertia. It can be concluded that the dynamometer is emulating inertia value. Figure 10 shows the response to the 1 s ramp function of reference speed with immediate reversal and Text = 3 Nm applied at t = 4 s in order to show the emulated speed tracking in all four quadrants of a torque-speed area. Influence of the emulated viscous friction coefficient is shown in Fig. 11, where Bem = 3Bm . Viscous friction is speed dependent, what can be observed in the torque response of the test machine. Comparing Fig. 11 with Fig. 7, a constant load torque is observed in Fig. 7, towards linearly increasing load torque in Fig. 11. Therefore, it can be concluded that dynamometer is emulating viscous friction coefficient. A simple pendulum was chosen as an example of nonlinear load to be emulated. Its dynamics is given by the following equations [19]:

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Fig. 8 Ramp speed reference, Jem = 3Jm

Fig. 9 Ramp speed reference, Jem = 5Jm

Te − Bem ωem − gm emlem sin(ϕem ) − Text , Jem = ωem ,

ω˙ em =

(12)

ϕ˙em

(13)

and the quantities are explained in nomenclature. Note that with the change of emulated mass of the pendulum also its inertia changes. It is given by parallel axis theorem as follows: Jem =

2 2 2 m em Rem + m emlem . 5

(14)

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The first term in eq. (14) gives an inertia of solid sphere with emulated mass and radius. Length of the pendulum rod is given as a perpendicular distance between the axis passing through ball’s centre of gravity and the axis passing through drive under test machine’s shaft. This model of pendulum has been tested for several different cases. Figure 12 shows an experiment for the following emulated values: Text = 0 Nm, Bem = Bm , m em = 0.5 kg, lem = 0.21 m, Jem = 0.0338 kgm2 . Actual speed is following a ramp reference, and a simple PI speed controller is used. Dynamometer is emulating a behaviour of a pendulum, which causes substantial speed and torque oscillations of DUT. These oscillations get higher in Fig. 13, where the emulated mass of the pendulum is raised to m em = 1.5 kg. Detailed speed comparison shows closed tracking of the emulated speed. Figure 14 shows the emulation of the pendulum with the same parameters as shown in Fig. 13 and the same values of acceleration and deceleration. The only difference is the steady-state speed reference, which takes 1s longer in Fig. 14 (t = 1 s to t = 5 s) than in Fig. 13 (t = 1 to t = 4 s). As a consequence, the final pendulum position is different in both cases, which can be observed in the torque responses. Failure of the emulation is observed in Fig. 14 at t = 6.2 s due to the saturated torque reference for the dynamometer. Even in that case the control structure remains stable and if the controller gets out the saturation, tracking of the emulated speed is recovered at t = 6.5 s. The maximum experimentally achievable bandwidth of this control structure for DEML parameters, as given in Appendix, and for pendulum, with parameters the same as shown in Fig. 14, is shown in Fig. 15. Detailed view of a steady state is showing satisfactory speed emulation with the bandwidth of 62.8 rad/s. This tracking can be improved by the change of parameters k and h. However, due to the vibrations occurring at the higher bandwidth due to the elasticity of the mechanical connection of drives (which is necessary), the decision has been made that even the results presented are still better than in the case of static emulation and are fully comparable with other DEML approaches.

6 Conclusion This work presents a dynamometer control strategy based on nonlinear PI estimator approach. The aim was to build a test bed with solely industrial components. The main contribution of this paper is the analysis and experimental verification of a dynamometer control system. The emulation of both linear first-order plant and nonlinear pendulum is presented in the paper with very good results obtained for the tracking of emulated speed.

One of the main drawbacks remains that validation of the results is done only against the model of mechanical load, which can be obtained only with the certain precision. More appropriate validation would have been achieved by comparing the actual responses of test machine, loaded by dynamometer, against the actual responses of test machine, loaded by real mechanical load. However, this comparison put great demands on the laboratory equipment. In authors’ best knowledge, this comparison has not been presented yet in the literature, even if it is the most appropriate evaluation of dynamometer performance. Hence, this comparison will preferentially be a subject of future research. Acknowledgements This work was supported by the Scientific Grant Agency of the Ministry of Education of the Slovak Republic and Slovak Academy of Sciences (VEGA), under the Project code 1/0464/15. This work was also supported by the Slovak Research and Development Agency (APVV), under the Project code APVV-15-0750.

Appendix A Transfer functions

F1 (s) = F2 (s) =

F3 (s) =

F4 (s) =

ˆ Bˆ m +h+ Jˆm k s + k( BJmm+h) Jm ˆ Jˆm k s 2 + Bm +h+ s + k( BJmm+h) Jm s Jm ˆ Jˆm k s 2 + Bm +h+ s + k( BJmm+h) Jm ˆ Jˆm k s + k( BJmm+h) s 2 + Bm +h+ Jm ˆ Jˆm k s 2 + Bm +h+ s + k( BJmm+h) Jm k( Bˆ m +h) h+ Jˆm k Jm s + Jm ˆ ˆ B +h+ J k s 2 + m Jm m s + k( BJmm+h) Jˆm 2 Jm s

+

B Mechanical and other parameters Total shaft inertia (both machines and clutch): J = 0.0112 kg.m2 Viscous friction coefficient: B = 0.01 Nms/rad PI controller values: K p = 0.3, TN = 0.021 DEML control structure parameters: k = 50, h = 1.3

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Fig. 10 Ramp speed reference with reversing, Jem = 3Jm

Fig. 11 Viscous friction emulation, Bem = 3Bm

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Fig. 12 Ramp speed reference, pendulum, m = 0.5 kg

Fig. 13 Ramp speed reference, pendulum, m = 1,5 kg

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Fig. 14 Ramp speed reference, pendulum, m = 1,5 kg, failure of the dynamometer

Fig. 15 Ramp speed reference, pendulum, m = 1,5 kg

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