Abstract
ABSTRACT This paper presents a new robust predictive controller for a special class of continuous-time non-linear systems with uncertainty. These systems have bounded disturbances with unknown upper bound as well as constraints on input states. The controller is designed in the form of an optimization problem of the ‘worst-case’ objective function over an infinite moving horizon. Through this objective function, constraints and uncertainties can be applied explicitly on the controller design, which guarantees the system stability. Next, LMI tool is used to improve the calculation time and complexity. To do this, in order to find the optimum gain for state-feedback, the optimization problem is solved using LMI method in each time step. Finally, to show the efficiency and effectiveness of the proposed algorithm, a surge phenomenon avoidance problem in centrifugal compressors is solved.
Highlights
In recent years, attention to robust approaches to controller design has increased strictly [1,2,3,4,5,6]
One reason for this is that non-linear predictive control algorithms lead to nonconvex, non-linear optimization problems, the solution requires reiterative methods along with extended calculation times [8]
On the other hand, using linear model and square cost function lead to a convex square optimization problem that can be solved for predictive control algorithms
Summary
Attention to robust approaches to controller design has increased strictly [1,2,3,4,5,6]. In the design of an LMI-based robust MPC, the Lipchitz condition is an essential requirement in the design process [23,24,25] and somehow leads to the linearization of the controller design while in the paper, it has been tried to present a method that removes the Lipchitz condition and includes a greater class of non-linear system in the model. The most important innovation of this paper is to provide an LMI-based predictive control method for a class of continuous non-linear systems in the presence of disturbance and uncertainty, while ensuring simplicity and less time for computation, confirms the optimal control signal and in addition to compliance with constraints of variables and states, it is not necessary to have the Lipchitz condition on the non-linear part.
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