Hybrid MPC: An Application to Semiactive Control of Structures
In clipped LQR, a common strategy for semiactive structural control, a primary feedback controller is designed using LQR and a secondary controller clips forces that the semiactive control device cannot realize. However, when the primary controller commands highly non-dissipative forces, the frequent clipping may render a controller far from being optimal. A hybrid system model is better suited for semiactive control as it accurately models the passivity constraints by introducing auxiliary variables into the system model. In this paper, a hybrid model predictive control (MPC) scheme, which uses a system model with both continuous and discrete variables, is used for semiactive control of structures. Optimizing this control results in a mixed integer quadratic programming problem, which can be solved numerically to find the optimal control input. It is shown that hybrid MPC produces nonlinear state feedback control laws that achieve significantly better performance for some control objectives (e.g., the reduction of absolute acceleration). Responses of a typical structure to historical earthquakes, and response statistics from a Monte Carlo simulation with stochastic excitation, are computed. Compared to clipped LQR, hybrid MPC is found to be more consistent in the reduction of the objective functions, although it is more computationally expensive.
KeywordsStructural control Semiactive dampers Hybrid systems Model predictive control Clipped LQR
The authors gratefully acknowledge the partial support of this work by the National Science Foundation, through awards CMMI 08-26634 and 11-00528, and by a USC Viterbi Doctoral Fellowship. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation or of the University of Southern California.
- 3.Soong TT, Dargush GF (1997) Passive energy dissipation systems in structural engineering. Wiley, ChichesterGoogle Scholar
- 9.Sun L, Goto Y (1994) Application of fuzzy theory to variable dampers for bridge vibration control. In: Proceedings of the 1st world conference on structural control, pp WP1:31–40, Los Angeles, CA, August 1994Google Scholar
- 12.Iemura H, Pradono MH (2009) Advances in the development of pseudo-negative-stiffness dampers for seismic response control. Struct Contr Health Monit 16(7–8):784–799Google Scholar
- 23.Alur R, Courcoubetis C, Henzinger T, Ho P (1993) Hybrid automata: an algorithmic approach to the specification and verification of hybrid systems. In: Grossman R, Nerode A, Ravn A, Rischel H (eds) Hybrid systems. Lecture notes in computer science, vol 736. Springer, Berlin, pp 209–229Google Scholar
- 24.Bemporad A (2002) An efficient technique for translating mixed logical dynamical systems into piecewise affine systems. In: Proceedings of the 41st IEEE conference on decision and control, 2002, vol 2, pp 1970–1975, 2002Google Scholar
- 25.Heemels WPMH, De Schutter B, Bemporad A (2001) On the equivalence of classes of hybrid dynamical models. In: Proceedings of the 40th IEEE conference on decision and control, 2001, vol 1, pp 364–369, 2001Google Scholar
- 27.Chow GP (1976) Analysis and control of dynamic economic systems. Wiley, New YorkGoogle Scholar
- 29.Giorgetti N, Bemporad A, Tseng HE, Hrovat D (2005) Hybrid model predictive control application towards optimal semi-active suspension. In: Proceedings of the IEEE international symposium on industrial electronics, 2005. ISIE 2005, vol 1, pp 391–398, 2005Google Scholar
- 30.Löfberg J (2004) YALMIP: a toolbox for modeling and optimization in MATLAB. In: 2004 IEEE international symposium on computer aided control systems design, pp 284–289, 2004Google Scholar
- 31.IBM (2012) IBM ILOG CPLEX Optimizer. http://www.ibm.com/software/integration/optimization/cplex-optimizer/. Accessed 9 Sept 2012
- 32.Gurobi (2012) Gurobi Optimizer Reference Manual. http://www.gurobi.com. Accessed 9 Sept 2012