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See detailProbabilistic analysis and control of dynamic systems with uncertain parameters over non-hypercube domain
Duong, Pham UL

in Journal Process Control (2014), 22(4), 358-367

Generalised polynomial chaos expansion provides a computationally efficient way of quantifying the influence of stochastic parametric uncertainty on the states and outputs of a system. In this study, a ... [more ▼]

Generalised polynomial chaos expansion provides a computationally efficient way of quantifying the influence of stochastic parametric uncertainty on the states and outputs of a system. In this study, a polynomial chaos-based method was proposed for an analysis and design of control systems with para-metric uncertainty over a non-hypercube support domain. In the proposed method, the polynomial chaosfor the hypercube domain was extended to non-hypercube domains through proper parameterizationto transform the non-hypercube domains to hypercube domains. Based on the proposed polynomialchaos framework, a constrained optimization problem minimizing the mean under the maximum allow-able variance was formulated for a robust controller design of dynamic systems with the parametricuncertainties of the non-hypercube domain. Several numerical examples ranging from integer to frac-tional order systems were considered to validate the proposed method. The proposed method providedsuperior control performance by avoiding the over-bounds from a hypercube assumption in a compu-tationally efficient manner. From the simulation examples, the computation time by gPC analysis was approximately 10–100 times lower than the traditional approach. [less ▲]

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See detailRobust PID controller design for processes with stochastic parametric uncertainties
Duong, Pham UL

in Journal Process Control (2012), 22(9), 15591566

The stability and performance of a system can be inferred from the evolution of statistical characteristics of the system’s states. Wiener’s polynomial chaos can provide an efficient framework for the ... [more ▼]

The stability and performance of a system can be inferred from the evolution of statistical characteristics of the system’s states. Wiener’s polynomial chaos can provide an efficient framework for the statistical analysis of dynamical systems, computationally far superior to Monte Carlo simulations. This work proposes a new method of robust PID controller design based on polynomial chaos for processes with stochastic parametric uncertainties. The proposed method can greatly reduce computation time and can also efficiently handle both nominal and robust performance against stochastic uncertainties by solving a simple optimisation problem. Simulation comparison with other methods demonstrated the effectiveness of the proposed design method. [less ▲]

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