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State switching in multi-stable systems: control and optimisation.

Liu, Boying


Boying Liu


Wai-Keung Fung

Yang Liu


This thesis studies state-switching in multistable systems, so that they can switch from inefficient operating states to a more efficient one, in order to achieve performance enhancement in real-life engineering systems. Multistable systems have more than one stable state under a set of parameters and the process of switching from an undesired state to a desired state is achieved by the proposed PD-like controller. It exploits the difference of the displacement and velocity between the undesired and the desired stable conditions for feedback in state switching. Three test systems are used for investigating the performance of this PD-like controller, namely: the Duffing oscillator, which is a typical smooth multistable system; the non-smooth soft-impact oscillator; and the soft-impact oscillator with a drift. A randomised triangular subdivision algorithm is proposed to reconstruct the basins of attraction of the target multistable systems, in order to identify the desired state for switching. Due to the limited capacity of physical actuators, behaviours of the constrained PD-like controller are investigated using extensive simulation on the test systems. Moreover, optimisation of the controller (based on multiple performance objectives) can further improve system performance. Two performance objectives - maximum peak of control input and switching duration - are adopted in optimising the proposed PD-like controller. The first objective is minimised in order to avoid output limit and reduce energy consumption in the actuator, while the second objective is minimised in order to shorten the time required for state switching. These two performance objectives are considered independently in performance optimisation, using particle swarm optimisation (PSO). Since these two objectives are in conflict with each other, both objectives are minimised simultaneously in multiobjective optimisation of the performance of the PD-like controller using Non-Dominated Sorting Genetic Algorithms-II (NSGA-II). A trade-off in performance enhancement is achieved through selecting control parameters from the Pareto optimal set.


LIU, B. 2020. State switching in multi-stable systems: control and optimisation. Robert Gordon University [online], PhD thesis. Available from:

Thesis Type Thesis
Deposit Date Jul 22, 2020
Publicly Available Date Jul 22, 2020
Keywords Multistable systems; System state-switching; System efficiency
Public URL
Award Date Jun 30, 2020


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