Robust data-driven min–max model predictive control with unknown-input observers

As microgrids are the main carriers of renewable energy sources (RESs), research on them has been receiving more attention. When considering the increase in the penetration of renewable energy sources/distributed generators (DGs) in microgrids, their low inertia and high stochastic power disturbance pose more challenges for frequency control. To address these challenges, this paper proposes a model predictive control (MPC) secondary control that incorporates an unknown input observer and where RESs/DGs use a deloading virtual synchronous generator (VSG) control to improve the system’s inertia. An unknown input observer is employed to estimate the system states and random power disturbance from the RESs/DGs and load to improve the effect of the predictive control. The distributed restorative power of each DG is obtained by solving the quadratic programming (QP) optimal problem with variable constraints. The RESs/DGs are given priority to participate in secondary frequency control due to the proper weighting factors being set. An islanded microgrid model consisting of multiple photovoltaic and wind power sources was built. The simulation results demonstrate that the proposed method improves the system frequency, restoration speed, and reduces frequency deviations compared with the traditional secondary control method.

On input-to-state stability of min–max nonlinear model predictive control

Observer-based fault diagnosis in chemical plants

Voltage source inverter (VSI) with output LC filter can be used to generate sinusoidal output voltages with reduced low frequency harmonics content. This application is suitable for uninterruptible power supply (UPS) systems. Finite control set model predictive control (FCS-MPC) has proved to be a good candidate for controlling such kind of devices. FCS-MPC relies on accurate system model to achieve high performance. However, output load is not always known for UPS applications. Under this condition, the use of observers to estimate the output load currents is a good solution. In this paper, a FCS-MPC strategy using an unknown input observer (UIO) is assessed. To design the UIO, the nature of the output load has been considered. This paper is focused on output loads with sinusoidal output currents. Two different UIO are evaluated. The first one uses a conventional approach and the second one takes into account the sinusoidal nature of the output load currents. Experimental results in a VSI prototype show that the second approach can provide superior performance independently of the output load connected to the power inverter.

This article considers the regulation problem of a constrained linear system with bounded disturbance. The objective is to overcome the offline and online problems of the standard dual‐mode min–max model predictive control (MPC). The offline problem is related to the construction of a polyhedral terminal set, which is prohibitively complex especially for high order systems. We propose to replace the polyhedral set with the ellipsoidal one, which is much easier to construct. The online problem is related to the computational burden, which grows exponentially with the prediction horizon . We show how to employ a new terminal cost function, that results in a new min–max MPC with a large domain of attraction even with or . Hence the computational complexity is drastically reduced. Two numerical examples with comparison to earlier solutions from the literature illustrate the effectiveness of the proposed approach.

Input to state stability of min–max MPC controllers for nonlinear systems with bounded uncertainties

The glycemia regulation is a significant challenge in the Artificial Pancreas (AP) scenario. Several control systems have been developed in the last years, many of them requiring meal announcements. Therefore, if the patients skip the meal announcement or make a mistake in the estimation of the amount of carbohydrates, the control performance will be negatively affected. In this extended version of our previous work, we present a Model Predictive Controller (MPC) for the AP in which the meal is treated as a disturbance to be estimated by an Unknown Input Observer (UIO). The MPC constraints are expressed in terms of Signal Temporal Logic (STL) specifications. Indeed, in the AP some requirements result in hard constraints (in particular, absolutely avoid hypoglycemia and absolutely avoid severe hyperglycemia) and some other in soft constraints (avoid a prolonged hyperglycemia) and STL is suitable for expressing such requirements. The achieved results are obtained using the BluSTL toolbox, which allows to synthesize model predictive controllers with STL constraints. We report simulations showing that the proposed approach, avoiding unnecessary restrictions, provides safe trajectories in correspondence of higher unknown disturbance.

A predictive fault-tolerant control scheme for Takagi-Sugeno fuzzy systems

ABSTRACTThe double‐tooth roll crusher, commonly driven by an induction motor, often faces sensor and actuator malfunctions. To address these, this study proposes a model predictive fault‐tolerant control framework to enhance system reliability and robustness. Initially, based on the system's mathematical model, a state and unknown input observer is developed. This observer effectively detects current sensor faults and isolates unknown disturbances, maintaining system functionality even with single‐sensor operation. Additionally, a velocity observer is designed using the estimated state data. Secondly, system faults are treated as uncertainties, leading to the development of a disturbance observer with fewer tunable parameters. This observer identifies actuator failures by analyzing disturbance values, with its convergence validated theoretically. This enables rapid fault detection and mitigation, reducing performance degradation. Finally, a model predictive torque controller is introduced to improve torque regulation. Experimental results demonstrate the method's strong fault‐tolerant capabilities and control effectiveness across various fault scenarios.

Model predictive control of hybrid systems : stability and robustness

The distribution system's nonlinear loads cause low total harmonic distortion (THD), low distortion power factor, and localized communication interference, among other poor power quality metrics. Shunt active power filter (SAPF) capacity to function depends on the controller's ability to follow the reference signal. To manage larger systems with several inputs and outputs, it would be challenging task to design PID controllers, because excessive controller gains would need to be tuned. Also, every control loop would operate independently of one another, as if there were no interactions between the two loops. This paper proffers Model prediction control for Shunt active power filter (SAPF), which can manage systems with several inputs and outputs that may interact with one another. Luenberger observer (LO) and Proportional Integral observer (PIO) fail to estimates the actual states of SAPF to SAPF, as shown even in the presence of three unknown disturbances, i.e step, triangular and noise type. The proposed unknown input observer (UIO) in the presence of three unknown disturbances perfectly tracks the reference signal. Apart from state estimation, the proposed observer also estimates all the unknown disturbances, when compared to PIO. The results have been simulated in MATLAB environment.

In this paper we extend the classical min–max model predictive control framework to a class of uncertain discrete event systems that can be modelled using the operations maximization, minimization, addition and scalar multiplication, and that we call max–min-plus-scaling (MMPS) systems. Provided that the stage cost is an MMPS expression and considering only linear input constraints then the open-loop min–max model predictive control problem for MMPS systems can be transformed into a sequence of linear programming problems. Hence, the min–max model predictive control problem for MMPS systems can be solved efficiently, despite the fact that the system is non-linear. A min–max feedback model predictive control approach using disturbance feedback policies is also presented, which leads to improved performance compared to the open-loop approach.

Computational burden reduction in min–max MPC

Fault-Tolerant Model Based Predictive Control with Application to Boiler Systems

Due to the features of event‐triggered control in exploiting and saving system resources, they have been widely applied in sensor networks, multi‐agent systems, networked control systems and so on. In this study, the authors focused on robust event‐triggered distributed model predictive control (RETDMPC). Subject to disturbances and parametric uncertainties, they first applied the min–max model to RETDMPC. The min–max RETDMPC methodology is used to guarantee the robustness of the system state by taking the worst possible case of unknown uncertainties into consideration. Furthermore, in this framework, a new cost function is developed in which unknown uncertainties are considered. Next, sufficient conditions are provided to ensure the feasibility and stability of their developed min–max RETDMPC. Finally, a practical example is given to illustrate the advantages of their algorithm by comparing to the conventional model predictive control.