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

This paper presents a new approach for robust open-loop and closed-loop control of nonlinear processes with parameter uncertainties and a comparison with classical concepts. The approach leads to trajectories that show small variations 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.

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.

Dynamic modelling and nonlinear model predictive control of a Fluid Catalytic Cracking Unit

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

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.

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.

A robust model predictive control approach for post-disaster relief distribution

In this paper two model predictive control (MPC) approaches, an on-line and an off-line MPC approach, for constrained uncertain continuous-time systems with piecewise constant control input are presented. Both MPC approaches guarantee robust asymptotic stability by taking into account the hybrid dynamics of the closed-loop system, resulting from the continuous-time system dynamics and the discrete-time model predictive controller dynamics. Examples are presented to demonstrate the applicability of the proposed MPC approaches.

This paper presents an advanced market bidding and operation strategy for the joint participation of a solar plant with storage in Energy and secondary reserve markets (SRMs). A linear optimization is applied in order to calculate the optimal day-ahead and intraday market bids through a model predictive control (MPC) approach, considering solar generation forecast, hourly market prices as well as battery acquisition, operating and degradation costs. Moreover, several rule-based strategies are selected to participate in secondary reserve markets, focused on more profitable and reliable hours through the estimation of market prices and the expected operation of the battery. Finally, the real-time operation tackles all the uncertain parameters, such as the reserve requirements and solar forecast errors, with the objective of achieving an optimal tradeoff between market profits, battery costs and market technical fulfillments. Several market strategies have been compared in techno-economic terms with annual real market data. Regarding the most advanced strategy, market benefits are improved 6.42% from base case and non-fulfillment level of SRM is reduced up to 1.49%.

Some robust control methods have been developed in the past in order to increase tracking performance in the presence of parametric uncertainties. In the presence of parametric uncertainty, unmodelled dynamics and other sources of uncertainties, robust control laws are used. Corless-Leitmann [1] approach is a popular approach used for designing robust controllers for robot manipulators. In early application of Corless-Leitmann [1] approach to robot manipulators [2, 3], it is difficult to compute uncertainty bound precisely. Because, uncertainty bound on parameters depends on the inertia parameters, the reference trajectory and manipulator state vector. Spong [4] proposed a new robust controller for robot manipulators using the Lyapunov theory that guaranties stability of uncertain systems. In this approach, Leithmann [5] or Corless-Leithman [1] approach is used for designing the robust controller. One of the advantage of Spong’s approach [4] is that uncertainty on parameter is needed to derive robust controller and uncertainty bound parameters depends only on the inertia parameters of the robots. Yaz [6] proposed a robust control law based on Spong’s study [4] and global exponential stability of uncertain system is guaranteed. However, disturbance and unmodelled dynamics are not considered in algorithm of [4, 6]. Danesh at al [7] develop Spong’s approach [4] in such a manner that control scheme is made robust not only to uncertain inertia parameters but also to robust unmodelled dynamics and disturbances. Koo and Kim [8] introduce adaptive scheme of uncertainty bound on parameters for robust control of robot manipulators. In [8], upper uncertainty bound is not known as would be in robust controller [4] and uncertainty bound is estimated with estimation law in order to control the uncertain system. A new robust control approach is proposed by Liu and Goldenerg [9] for robot manipulators based on a decomposition of model uncertainty. Parameterized uncertainty is distinguished from unparameterized uncertainty and a compensator is designed for parameterized and unparameterized uncertainty. A decomposition-based control design framework for mechanical systems with model uncertainties is proposed by Liu [10]. In order to increases tracking performance of uncertain systems, design of uncertainty bound estimation functions are considered. For this purpose, some uncertainty bound estimation functions are developed [11-15] based on a Lyapunov function, thus, stability of

Preliminary study for motion sickness reduction in autonomous vehicles: an MPC approach

This paper presents a model predictive control (MPC) approach to control the steering angle in an autonomous vehicle. In designing a highly automated driving control algorithm, one of the research issues is to cope with probable risky situations for enhancement of safety. While human drivers maneuver the vehicle, they determine the appropriate steering angle and acceleration based on the predictable trajectories of surrounding vehicles. Likewise, it is required that the automated driving control algorithm should determine the desired steering angle and acceleration with the consideration of not only the current states of surrounding vehicles but also their predictable behaviors. Then, in order to guarantee safety to the possible change of traffic situation surrounding the subject vehicle during a finite time-horizon, we define a safe driving envelope with the consideration of probable risky behaviors among the predicted probable behaviors of surrounding vehicles over a finite prediction horizon. For the control of the vehicle while satisfying the safe driving envelope and system constraints over a finite prediction horizon, a MPC approach is used in this research. At each time step, MPC based controller computes the desired steering angle to keep the subject vehicle in the safe driving envelope over a finite prediction horizon. Simulation and experimental tests show the effectiveness of the proposed algorithm.

The problem of path following for marine surface vessels using the rudder control is addressed in this paper. The need to enforce the roll constraints and the fact that the rudder actuation is limited in both amplitude and rate make the model predictive control (MPC) approach a natural choice. The MPC design is based on a linearized model for computational and implementation considerations, while the evaluation of the performance of MPC controller is performed on a nonlinear 4 degree of freedom surface vessel model. The simulation results are presented to verify the effectiveness of the resulting controller and a simulation based tuning process for the controller is also presented. Furthermore, the performance of the path following MPC control in wave fields is evaluated using an integrated maneuvering and seakeeping model, and the simulation confirms its robustness.

This paper presents a practical off-line approach for tuning Model Predictive Control (MPC) parameters with constraints. The MPC parameters values are computed from the expected closed-loop performances. Our original approach based on the exponential data weighting can be applied to a wide set of controllable Multi-Input Multi-Output (MIMO) processes and plants. It guarantees the stability of closed-loop systems and permits the controller's designer to set a trade-off between accuracy and rapidity. Some simulation results shown emphasize its effectiveness when compared to several existing methods.

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.