Robust model predictive control using the unscented transformation

This paper presents an approach for robust open-loop and closed-loop control of nonlinear processes with safety constraints. The approach leads to trajectories that establish a dynamic safety margin if uncertain parameters and uncertain initial conditions are present. The algorithm utilizes the Unscented Transformation. It allows a 2nd order approximation of the first two statistical moments of the system's output as a function of the stochastic system's state and uncertain model parameters. Because the numerical burden is low, it can be used for optimization based online closed-loop process control as well.

A new approach for robust model predictive control of biological production processes

A normal vector approach for integrated process and control design with uncertain model parameters and disturbances

Groundwater is a crucial resource for water supply and irrigation in many parts of the world, especially in the Middle East. The Eocene aquifer, located in the northern part of the West Bank, Palestine, is threatened by unsustainable groundwater abstractions and on-ground pollution. Analysis and management of this aquifer are challenging because of limited data availability. This research contributes to the long-term sustainability of the aquifer by model-based design of future abstraction strategies considered within an uncertainty analysis framework. The methodology employed started with development of a single-layer steady-state MODFLOW groundwater model of the area, followed by uncertainty analysis of model parameters using Monte Carlo simulations. The same model was afterwards coupled with a Successive Linear Programming (SLP) optimization algorithm, implemented in the Groundwater Management tool (GWM) of the United States Geological Survey (USGS). The purpose of optimization was deriving five optimal abstraction strategies, each aiming to maximize groundwater abstraction, subject to different constraints regarding groundwater depletion. Given the uncertainty of model parameters, the sensitivity and reliability of these optimal strategies were then tested. Sensitivity was checked for two optimal strategies by performing re-optimization with different values of uncertain model parameters (one at a time). Reliability of the five strategies was tested by analyzing the extent of constraints’ violation for each strategy when varying the uncertain parameters using Monte Carlo simulations. Finally, the model was used for determining capture zones of wells for the five optimal abstraction strategies, land-use in these capture zones, and the associated estimates of on-ground nitrogen loading. The developed strategies were then deployed in a web-based decision support application (named Groundwater Decision Support System—GDSS), together with other relevant information. Users can analyze results of different optimal strategies in terms of groundwater level variations and total water balance results, and test consequences of uncertain parameters. Capture zones of wells for different abstraction strategies, together with land-use and on-ground nitrogen loading in these capture zones, are also presented. Results show that critical uncertain parameters are recharge, hydraulic conductivity, and conductance at key boundary condition locations. Optimal abstraction strategies results indicate that an increase in total abstractions could be between 5% and 20% from the current level (estimated at about 56 × 106 m3/year, which is about 74% of estimated annual recharge). The uncertain parameters, however, are impacting the sensitivity and the reliability of the optimal strategies to variable degrees. Recharge and hydraulic conductivity are the most critical uncertain parameters regarding sensitivity of the optimal strategies, while reliability is also impacted by the level of abstraction proposed in a given strategy (number, locations, and abstraction rates of new wells). The main novelty and contribution of this research is in combining modelling, uncertainty analysis, and optimization techniques in a comprehensive decision support system for the area of the Eocene aquifer, characterized with limited data availability.

We present a Robust Model Predictive Control (RMPC) approach for multi-carrier microgrids, i.e., microgrids based on gas and electricity. The microgrid that we consider includes thermal loads, electrical loads, renewable energy sources, energy storage systems, heat pumps, and combined heat and power plants. Moreover, the system under control is affected by several external disturbances, e.g., uncertainty in renewable energy generation, electrical and thermal demand. The goal of the controller is to minimize the overall economical cost and the energy exchange with the main grid, while guaranteeing comfort. Whereas several RMPC methods have been developed for electrical or thermal microgrids, little or no attention has been devoted to robust control of multi-carrier microgrids. Therefore, we consider a novel RMPC algorithm that can improve the performance with respect to classical deterministic Model Predictive Control (Det-MPC) controllers in the context of multi-carrier microgrids. The RMPC method relies on the box-uncertainty-set robust optimization, where uncertain parameters are assumed to take their values from different intervals independently. The RMPC approach is able to successfully satisfy the constraints even in the presence of the mentioned disturbances. Simulations of a realistic residential case study show the benefits of the proposed approach with respect to Det-MPC controllers.

In this article, a robust model predictive control strategy based on sum‐of‐squares (SOS‐RMPC) is proposed for hypersonic vehicle with state‐dependent input constraints and uncertain parameters. Based on feedback linearization model of hypersonic vehicle, the polytopic linear parameter varying error model with bounded disturbance is established for reference trajectory tracking. The real limits of the actual control inputs are transformed into the constraints of the virtual inputs equivalently with the state‐dependent nonlinear functions. Further, the multivariate linear fitting is used to approximate the state‐dependent input constraints into polynomials. A weighted composite virtual control is formulated as the combination of unconstrained control and auxiliary control. SOS technique is introduced to cast the polynomial constraints into the convex matrix SOS conditions via linear matrix inequality. The virtual control law can be obtained by solving a SOS‐RMPC convex optimization with infinite horizon. The invariant set is designed for the undisturbed error states and the norm‐bounding theory is applied to ensure that the predictive error states with disturbance can remain in the same invariant set. The real control law is obtained by inverse control. The simulation verifies the performance of the designed controller.

The linear Kalman-Bucy filter with both uncertain second-order statistical noise properties and uncertain system model parameters is considered. We investigate the conditions for robust stability based on the upper norm-bound of noise and parametrical uncertainties. Saddlepoint theory and the Gronwall lemma are employed to solve this problem.

Fuzzy Expected Value Analysis of an Industrial Grinding Process

The trajectory tracking method for an unmanned surface vehicle (USV) using integral terminal sliding mode integral backstepping adaptive control (ITSMIBAC) scheme is presented in this paper, which takes into account external disturbances and uncertain model parameters. Furthermore, finite-time convergence and excellent track tracking effect are guaranteed by the differential equations that is made up of the integral terminal sliding mode function. In particular, a backstepping method adding integral term is used to ensure the globally asymptotic stability of system and make the differential equations to converge to zero. The upper bound of the disturbances including external disturbances and uncertain model parameters is estimated by an adaptive control law. Finally, the effectiveness and the feasibility of the proposed controller are demonstrated by numerical example and comparison result through tracking circular orbit.

PurposeGenerally, humanoid robots usually suffer significant impact force when walking or running in a non-predefined environment that could easily damage the actuators due to high stiffness. In recent years, the utilization of passive compliant series elastic actuators (SEA) for driving humanoid's joints has proved the capability in many aspects so far. However, despite being widely applied in the biped robot research field, the stable control problem for a humanoid powered by the SEAs, especially in the walking process, is still a challenge. This paper proposes a model reference adaptive control (MRAC) combined with the back-stepping algorithm to deal with the parameter uncertainties in a humanoid's lower limb driven by the SEA system. This is an extension of our previous research (Lanh et al., 2021).Design/methodology/approachFirstly, a dynamic model of SEA is obtained. Secondly, since there are unknown and uncertain parameters in the SEA model, a Model Reference Adaptive Controller (MRAC) is employed to guarantee the robust performance of the humanoid's lower limb. Finally, an experiment is carried out to evaluate the effectiveness of the proposed controller and the SEA mechanism.FindingsThis paper proposes an effective control algorithm that can be widely applied for the humanoid-SEA system. Besides, the effect of the coefficients in the control law is analyzed to further improve the response's quality.Research limitations/implicationsEven though the simulation shows good results with stable system response, the practical experiment has not been implemented to fully evaluate the quality of the controller.Originality/valueThe MRAC is applied to control the humanoid's lower limb and the back-stepping process is utilized to combine with an external SEA system but still maintain stabilization. The simplified model of the lower-limb system proposed in the paper is proven to be appropriate and can be taken for further research in the future.

Design of a stable adaptive nonlinear observer for an exothermic stirred tank reactor

A self-tuning PID (Proportion-Integral-Derivative) control method based on the adaptive mechanism was proposed for the magnetic suspension active vibration isolation system with the characteristics of nonlinear, time-varying, and model parameter uncertainty. The controller identified the controlled object parameters online and solved the controller parameters in real time. To test the effectiveness of the proposed method, a six degree-of-freedom (DOF) magnetic suspension active vibration isolation system was designed and built. The six DOF dynamic model of the vibration isolation system with uncertain model parameters was derived for control. Experiments were carried out and compared with the control effects of the tradition PID control and cascade PID control algorithm. The experimental results show that the proposed self-tuning PID controller has more outstanding practicality and effectiveness in solving the model parameter uncertainty problem compared with the existing studies at home and abroad, and it also proves that the control method has a good isolation effect on the wide band disturbances.

Robust model predictive control and PID control of shell-and-tube heat exchangers

In engineering systems with uncertain parameters, it is crucial for system analysis and control to analyze the relationship between these uncertain parameters and system outputs (or states). Nevertheless, the acquisition of this parameter-output function, termed parametric problem in this article, is not easy because it is usually a complicated implicit nonlinear function. Polynomial chaos expansion (PCE), based on the generalized Fourier expansion, is a state-of-the-art method for both parametric problems and uncertainty quantification. Its basic idea is to approximate the implicit parameter-output function with a globally optimal explicit polynomial function, which remains accurate in the case of strong nonlinearity compared with the local Taylor expansion. This article provides a review of PCE and its applications in parametric problems. In terms of PCE theory, a rigorous and complete framework of PCE is established and a detailed review of typical PCE methods is presented. In terms of applications, two kinds of general parametric problems, namely parametric nonlinear algebraic equations and parametric differential equations, as well as their examples in some engineering fields, are introduced. Furthermore, some worthwhile future works are presented at the end of this article, which may facilitate the development of PCE.

Sub-optimal control of fuzzy linear dynamical systems under granular differentiability concept