A new robust LMI-based model predictive control for continuous-time uncertain nonlinear systems

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.

Robust active finite-time control of gas compressor system surge in the presence of unmatched disturbance and uncertainty

“…Although the compression rate obtained by the two of robust and nonlinear control methods 52 is more than the robust active finite time (RAFT) technique presented in the article, but with a little reflection in Figure 6, we find that the control signals obtained from both robust and nonlinear methods 52 experience negative values, and therefore will not be operational signals due to the nature of CCV actuator. Despite the positive values of the control signal in the robust LMI-based MPC method, 39 the compression rate obtained is lower than other methods.…”

“…It can be seen from Figure 8 that using RAFT method, the pressure rise reaches its steady-state value in less time, although this value is less than the other two of robust and nonlinear control methods 52 used for the simulation. As in the first scenario, the robust LMI-based MPC method 39 gives the lowest compression rate among the methods used in the simulation. Figure 9 shows the effect of transient disturbances on the compressor flow, but all four methods are able to ensure surge-free operation.…”

“…In this section, a proposed robust control method has been implemented on the compressor system by simulating in MATLAB (2014a) environment. For better evaluation, a comparison has been made with robust and nonlinear control methods 52 and robust linear matrix inequality (LMI)-based MPC 39 which have been published in 2019 and 2020, respectively. The simulation is performed by an Intel Ò Coreä i7-4702MQ Processor (6M Cache, up to 3.20 GHz) equipped with 8 GB RAM using of the Greitzer model, and the parameters used for the system are based on Ziabari et al 20 B = 1:8, l c = 3, H = 0:18, W = 0:25, c c0 = 0:3…”

“…As shown in Figure 6, the control signal obtained from the robust active finite time and robust LMIbased MPC 39 methods have a non-negative value and is therefore a signal with a physical and operational meaning. It is important that the control signal obtained from the robust LMI-based MPC method exhibits a high slew rate, which is a negative dimension for the control method.…”

“…Imani Marrani et al [36][37][38] have used the advantages of the model predictive control method to control the compressor pressure, and of course, the controller is robust to uncertainty and disturbance. [37][38][39][40][41] However, several points have been overlooked in this regard. In the Greitzer model, as the most common model used to describe the compressor system, the compressor characteristic curve is assumed to be accurate and known, [42][43][44][45] while this characteristic curve is unclear when is operated in the compressor system.…”