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Development of an adaptive model predictive reference tracking controller for hard real-time hybrid simulation
Author(s):
Tsokanas, Nikolaos; Pastorino, Roland; Peeters, Bart; Stojadinovic, Bozidar Publication Date:
2021
Permanent Link:
https://doi.org/10.3929/ethz-b-000473422
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In Copyright - Non-Commercial Use Permitted
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Extended Abstract COSIM 2021 - International Symposium on Co-Simulation and Solver Coupling in Dynamics May 23 – 26, 2021, Ferrol, Spain
Development of an adaptive model predictive reference tracking controller for hard real-time hybrid simulation
Nikolaos Tsokanas1, Roland Pastorino2, Bart Peeters2, Boˇzidar Stojadinovi´c1
1Dept. of Civil, Environmental and Geomatic Engineering, ETH Zurich, Stefano-Franscini Platz 5, 8093 Zurich, Switzerland,{tsokanas, stojadinovic}@ibk.baug.ethz.ch
2Siemens Industry Software NV, Interleuvenlaan 68, 3001 Leuven, Belgium,{roland.pastorino, bart.peeters}@siemens.com
Hybrid simulation (HS), a.k.a hardware-in-the-loop (HiL) or model-based system testing, is an experimental co-simulation method used to obtain the dynamic response of a system whose components consist of loading-rate- sensitive numerical (NS) and physical substructures (PS). The coupling of these substructures forms the so-called hybrid model. More precisely, HS is conducted using a step-by-step numerical solution of the equations governing the motion of the hybrid model in combination with experimental measurements obtained from the PS [1]. HS is an effective technique since it merges the flexibility and risk-free testing of numerical simulations with the realism of experimental campaigns. The substructure coupling is achieved by actuation systems, i.e. an arrangement of motors or actuators, who are responsible for continuously synchronizing the interfaces of the substructures and are commanded in closed-loop control setting. To ensure high fidelity of the simulations, performing HS in real-time is necessary. Although essential, real-time hybrid simulation (RTHS) poses challenges as the inherent dynamics of the actuation system introduce time delays modifying the dynamic response of the investigated system and hence compromising the simulation’s fidelity and trust. Therefore a reference tracking controller is required to adequately compensate for these delays [2]. In this study, a novel tracking controller is proposed for time delay compensation of the actuation dynamics in hard real-time HS. It is based on adaptive model predictive control (MPC) and Kalman filter. The prediction model of the MPC is adapting in real-time using polynomial ARX models. Fig. 1 shows the architecture of the tracking controller.
To demonstrate the performance of the proposed tracking controller, a case study involving a virtual hybrid model is employed. In order to first investigate the behavior of the controller, all hybrid model substructures are simulated numerically and hence virtual PS (vPS) are used instead of physical specimen. The prototype system corresponds to a motorcycle. The hybrid model consists of four NS: i) the engine crankshaft, ii) the motorcycle body dynamics, iii) the rear and iv) front wheel braking systems. The vPS includes the electrically continuously variable transmission (eCVT) of the motorcycle. Specifically, the eCVT vPS consist of a multi-input-multi-output (MIMO) model with two sets of inputs/outputs. The first set is connected to the engine crankshaft NS and the second to the motorcycle body dynamics NS. The latter connection corresponds to the transmission output shaft of the motorcycle. The engine crankshaft NS aims to simulate the behavior of the combustion engine and it is a single-input-single-output (SISO) model, with input and output the angular velocity ωen and torque τen of the engine crankshaft respectively. The motorcycle body NS addresses the inner body dynamics of the motorcycle along with the dynamics of the suspension and the tires. It is a MIMO model with 3 sets of inputs/outputs. The first set is connected to the eCVT vPS with input and output the torqueτvd and angular velocityωvd of the transmission output shaft respectively. The second and third sets are connected to the rear and front wheel braking system NSs.
Both braking system NSs are SISO models with input and output the angular velocity and torque of the rearωrw, τrwand frontωf w,τf w wheel respectively. Fig. 2 shows the block diagram of the hybrid model and substructure interconnections.
Since the vPS has two inputs,τen andωvd, two actuation systems are needed and therefore two tracking con- trollers are instantiated. The actuation systems are assumed to be two identical servo-controlled motors modelled by second-order transfer functionsGm1,2=a/(b2s2+b1s+b0). The tracking controllers have the same structure, but are tuned differently for the specific control mode of each motor. The prediction model of MPC corresponds toGm1,2 since this is the control plant. Therefore, the parameters ofGm1,2, i.e. a,b2,b1andb0are adapted on-line during a HS. The reference signal of each tracking controller, i.e. re f in Fig. 1, correspond toτenr andωvdR of
Figure 1: Tracking controller architecture.
Figure 2: Hybrid model block diagram.
Fig. 2. Accordingly, the measured system outputs are the outputs of the motorsτen andωvd. Results demonstrate the effectiveness and robustness of the proposed adaptive tracking controller scheme. Future work aims to deploy the presented controller in a test bench and evaluate its performance physically.
References
[1] A. H. Schellenberg, S. A. Mahin, and G. L. Fenves, “Advanced Implementation of Hybrid Simulation,” Tech.
Rep. PEER 2009/104, Pacific Earthquake Engineering Research Center, University of California, Berkeley, 2009.
[2] N. Tsokanas, D. Wagg, and B. Stojadinovic, “Robust Model Predictive Control for Dynamics Compensation in Real-Time Hybrid Simulation,”Frontiers in Built Environment, vol. 6, 2020.
