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Constrained online trajectory planning for nonlinear flat SISO systems using a switched state variable filter. (English) Zbl 1429.93383

Summary: The problem of constrained online trajectory planning (OTP) for flatness-based feedforward controllers (FFC) is discussed for online tracking problems with a-priori unknown reference signals for the system output. As plant, nonlinear minimum phase single input single output (SISO) systems with input constraints as well as polytopic constraints on the flat state are assumed. The goal is to achieve both, fast reference tracking and a prioritization-based constraint satisfaction despite avoiding an online optimization. Therefore, the OTP is set up by means of a switched state variable filter (SSVF). The switching results from the limitation of the filter’s highest derivative in accordance to the above requirements and is derived with a piecewise solution of an underlying optimization problem. The paper shows the derivation of the SSVF, discusses necessary stability conditions of the proposed concept, and finally demonstrates the SSVF’s performance by means of a simulation study. A comparison to a respective optimal control problem solution and model predictive controller (MPC) is furthermore provided.

MSC:

93E11 Filtering in stochastic control theory
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93C10 Nonlinear systems in control theory

Software:

GRAMPC
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References:

[1] Ariens, D., Diehl, M., Ferreau, H. J., Houska, B., Logist, F., & Quirynen, R., et al. ACADO Toolkit User’s Manual, (2014). Optimization in Engineering Center.; Ariens, D., Diehl, M., Ferreau, H. J., Houska, B., Logist, F., & Quirynen, R., et al. ACADO Toolkit User’s Manual, (2014). Optimization in Engineering Center.
[2] Delaleau, E., & Strankovic, A. (2004). Flatness-based hierarchical control of the PM synchronous motor. In Proc. ACChttps://ieeexplore.ieee.org/document/1383580; Delaleau, E., & Strankovic, A. (2004). Flatness-based hierarchical control of the PM synchronous motor. In Proc. ACChttps://ieeexplore.ieee.org/document/1383580
[3] Englert, T.; Völz, A.; Mesmer, F.; Rhein, S.; Graichen, K., A software framework for embedded nonlinear model predictive control using a gradient-based augmented Lagrangian approach (GRAMPC), Springer Optimization and Engineering, 1-41 (2019) · Zbl 07123819
[4] Faiz, N.; Agrawal, S. K.; Murray, R. M., Trajectory planning of differentially flat systems with dynamics and inequalities, Journal of Guidance, Control, and Dynamics, 24, 219-227 (2001)
[5] Faulwasser, T.; Hagenmeyer, V.; Findeisen, R., Constrained reachability and trajectory generation for flat systems, Automatica, 50, 1151-1159 (2014) · Zbl 1298.93064
[6] Fliess, M.; Lévine, J.; Martin, P.; Rouchon, P., Flatness and defect of non-linear systems: introductory theory and examples, International Journal of Control, 61, 1327-1361 (1995) · Zbl 0838.93022
[7] Graichen, K.; Zeitz, M., Feedforward control design for finite-time transition problems of nonlinear mimo systems under input constraints, International Journal of Control, 81, 417-427 (2008) · Zbl 1152.93374
[8] Hagenmeyer, V., Streif, S., & Zeitz, M. (2004). Flatness-based Feedforward and Feedback Linearisation of the Ball & Plate Lab Experiment. In Proc. IFAC NOLCOShttps://www.sciencedirect.com/science/article/pii/S1474667017312260; Hagenmeyer, V., Streif, S., & Zeitz, M. (2004). Flatness-based Feedforward and Feedback Linearisation of the Ball & Plate Lab Experiment. In Proc. IFAC NOLCOShttps://www.sciencedirect.com/science/article/pii/S1474667017312260
[9] Hagenmeyer, V.; Zeitz, M., Internal dynamics of flat nonlinear siso systems with respect to a non-flat output, Systems & Control Letters, 52, 323-327 (2004) · Zbl 1157.93349
[10] Johansson, M., Piecewise linear control systems (2003), Springer · Zbl 1008.93002
[11] Joos, S., Bitzer, M., Karrelmeyer, R., & Graichen, K. (2017). Online-trajectory planning for state- and input-constrained linear SISO systems using a switched state variable filter. In Proc. IFAC World Congresshttps://www.sciencedirect.com/science/article/pii/S2405896317308297; Joos, S., Bitzer, M., Karrelmeyer, R., & Graichen, K. (2017). Online-trajectory planning for state- and input-constrained linear SISO systems using a switched state variable filter. In Proc. IFAC World Congresshttps://www.sciencedirect.com/science/article/pii/S2405896317308297
[12] Joos, S., Bitzer, M., Karrelmeyer, R., & Graichen, K. (2018). Prioritization-based switched feedback control for linear SISO systems with time-varying state and input constraints. In Proc. ECChttps://ieeexplore.ieee.org/document/8550172; Joos, S., Bitzer, M., Karrelmeyer, R., & Graichen, K. (2018). Prioritization-based switched feedback control for linear SISO systems with time-varying state and input constraints. In Proc. ECChttps://ieeexplore.ieee.org/document/8550172
[13] Joos, S., Bruder, R., Specker, T., Bitzer, M., & Graichen, K. (2019). Kinematic real-time trajectory planning with state and input constraints for the example of highly automated driving. In Proc. 23rd International Conference on System Theory, Control and Computing (ICSTCC); Joos, S., Bruder, R., Specker, T., Bitzer, M., & Graichen, K. (2019). Kinematic real-time trajectory planning with state and input constraints for the example of highly automated driving. In Proc. 23rd International Conference on System Theory, Control and Computing (ICSTCC)
[14] Joos, S., Trachte, A., Bitzer, M., & Graichen, K. (2019). Constrained real-time swivel angle control for hydraulic axial piston motors. In Proc. 8th IFAC Mechatronics; Joos, S., Trachte, A., Bitzer, M., & Graichen, K. (2019). Constrained real-time swivel angle control for hydraulic axial piston motors. In Proc. 8th IFAC Mechatronics
[15] Khalil, H. K., Nonlinear systems (2003), Prentice Hall
[16] Knierim, K.; Sawodny, O., Real-time trajectory generation for three-times continuous trajectories, (IEEE Conf. on Industrial Electronics and Applications (2012))
[17] Kotman, P., Modeling and control of diesel engine air systems (2018), Shaker, Dissertation TU Vienna
[18] Kotman, P., Bitzer, M., & Kugi, A. (2012). Prioritization-based constrained trajectory planning for a nonlinear turbocharged air system with EGR. In Proc. ACChttps://ieeexplore.ieee.org/document/6315365/; Kotman, P., Bitzer, M., & Kugi, A. (2012). Prioritization-based constrained trajectory planning for a nonlinear turbocharged air system with EGR. In Proc. ACChttps://ieeexplore.ieee.org/document/6315365/
[19] Lin, H.; Antsaklis, P. J., Stability and stabilizability of switched linear systems: a survey of recent results, IEEE Transactions on Automatic Control, 54, 308-322 (2009) · Zbl 1367.93440
[20] Nocedal, J.; Wright, S. J., Numerical optimization (2006), Springer · Zbl 1104.65059
[21] Petit, N., Milam, M., & Murray, R. (2001). Inversion based constrained trajectory optimization. In Proc. IFAC NOLCOShttps://www.sciencedirect.com/science/article/pii/S1474667017353491; Petit, N., Milam, M., & Murray, R. (2001). Inversion based constrained trajectory optimization. In Proc. IFAC NOLCOShttps://www.sciencedirect.com/science/article/pii/S1474667017353491
[22] Stumper, J.-F., & Kennel, R. (2011). Computationally efficient trajectory optimization for linear control systems with input and state constraints. In Proc. ACChttps://ieeexplore.ieee.org/document/5990741; Stumper, J.-F., & Kennel, R. (2011). Computationally efficient trajectory optimization for linear control systems with input and state constraints. In Proc. ACChttps://ieeexplore.ieee.org/document/5990741
[23] Suryawan, F.; Dona, J. D.; Seron, M., Minimum-time trajectory generation for constrained linear systems using flatness and B-splines, International Journal of Control, 84, 1565-1585 (2011) · Zbl 1230.49032
[24] Zanasi, R.; Bianco, C. G.L.; Tonielli, A., Nonlinear filters for the generation of smooth trajectories, Automatica, 36, 439-448 (2000) · Zbl 0967.93014
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