Model predictive control with tracking error bound and an influence function approach to moving horizon estimation

The development of robust and efficient algorithms for nonlinear optimization is an important matter; because they make possible the solution of models with increasingly sizeand complexity. In this context, the Interior Point Optimizer (IPOPT) has been proven to be a competitive algorithm, because of its ability to handle large scale problems. However, there are some specific situations in which convergence can not be guaranteed. For instancethe violation of a regularity condition given by the Linear Independence Constraint Qualification (LICQ). This property is given in terms of the consistency of local linearizationsof the set of constraints, i.e. the gradients. If the set of gradients of equality and active bound inequality are linearly independent, then the LICQ holds. It turns out that if thisproperty is not satisfied, IPOPT would attempt to regularize the system by perturbing it, with the hope to overcome regions of local inconsistency. However, if the LICQ does nothold globally or if the system has severe ill-conditioned, the regularization strategies will fail. Thus, we present the `1-exact penalty-barrier strategy to deal with this lack of regularity. This works by penalizing the infeasibility with a parameter at the objective; and then by reformulating the problem to obtain a higher dimensional problem, the LICQ property holds at all points for which the new variables are nonzero. Thus achieving higher level of robustness as opposed to the regular IPOPT. Moreover, an unified framework for nonlinear model-based state-estimation and control with parametric sensitivity is presented. Typically, control strategy of a processes is tied to the ability to accommodate online computations; in this sense nonlinear optimization strategies like Moving Horizon Estimation (MHE) and Model Predictive Control (NMPC) are overlooked. Nevertheless, it has been proposed to use the parametric nature of these optimization problems to create a scheme in which the bulk of computations is partitioned into a background phase with all the most computationally expensive steps, and an online phase, in which the sensitivity information is used to make inexpensive calculations for the state estimate or controller input. These ideas have been put together into a Python framework, that streamlines the creation of a state-estimation and control strategy with the additional benefit of having parametric sensitivity embedded into it. This framework works by using the Pyomo libraries to create optimization objects and automatically discretize the models given by the user. We demonstrate the effectiveness of the frameworkin two problems of vastly different complexity. A benchmark distillation case study and a Bubbling Fluidized Bed Reactor (BFB) for the capture of CO2. The results show thatsensitivity is effective for online implementations of the controller and it was seamlessly enabled by our framework.

MHE Based State and Parameter Estimation for Systems subjected to Non-Gaussian Disturbances

Nearly every model predictive control (MPC) algorithm is premised on knowledge of the system’s state. As a result, state estimation is vital to good MPC performance. Moving horizon estimation (MHE) is an optimization-based state estimation algorithm. Similar to MPC, it relies on the minimization of a sum of stage costs subject to a dynamic model. Unlike MPC, however, conditions under which MHE is robustly stable have been slow to emerge. Recently, several results have appeared about the robust stability of MHE. We generalize the result on the robust stability of MHE without a max-term presented in Muller (Automatica 79:306–314, 2017). using assumptions inspired by the result in Hu (Robust stability of optimization-based state estimation under bounded disturbances. ArXiv e-prints, 2017). Furthermore, we show that all systems that are covered by the assumptions used in those previous works satisfy a certain form of exponential incremental input/output-to-state stability.

NONLINEAR MODEL PREDICTIVE CONTROL BASED ON SEQUENTIAL MONTE CARLO STATE ESTIMATION

Based on a simplified control-oriented hybrid linear delayed model, model predictive control (MPC) of a sewer network designed to reduce pollution during heavy rain events is presented. The lack of measurements at many parts of the system to update the initial conditions of the optimal control problems (OCPs) leads to the need for estimation techniques. A simple modification of the OCP used in the MPC iterations allows to formulate a state estimation problem (SEP) to reconstruct the full system state from a few measurements. Results comparing the system performance under the MPC controller using full-state measurements and a moving horizon estimation (MHE) strategy solving a finite horizon SEP at each time instant are presented. Closed-loop simulations are performed by using a detailed physically-based model of the network as virtual reality.

This paper deals with load frequency control (LFC) problem for power system. The control is conducted to retain power demand supply balance by controlling output of generators in power network. In order to realize LFC with low power generation cost while maintaining control performance, this paper proposes frequency control method using Moving Horizon Estimation (MHE) and Model Predictive Control (MPC). First, MHE is used to estimate the state of the system. Next, optimization calculation is performed using MPC to determine the command values for each generator. Finally, simulation of load frequency control is carried out to verify the effectiveness of the proposed method.

In order to reduce the energy consumption and CO2 emissions in the building sector, an efficient control strategy, such as model predictive control (MPC) is required. However, MPC is rarely applied in buildings since the implementation and modeling is complex, time consuming and costly. To bring MPC into practice, controllers and models are needed, that automatically adapt their behavior to the controlled system. In this work, such a self-adjusting MPC applicable to heating, ventilation and air-conditioning (HVAC) systems is developed. The MPC is based on a simple grey-box model that is able to cover the general dynamics of the considered subsystem. The controller adapts the model parameters online according to the past measurements of the controlled system using a moving horizon estimation. The developed self-adjusting MPC is applied to three heating coils in a simulation. Compared with a PID controller, the self-adjusting MPC is able to increase the control quality up to 10%, while no manual tuning is needed. Additionally, the model predictive approach is able to reduce the power consumption of the pump by 80%.

An industrial case study on the combined identification and offset-free control of a chemical process

Adaptive model predictive control for a class of constrained linear systems based on the comparison model

In Model Predictive Control (MPC) closed-loop performance heavily depends on the quality of the underlying prediction model, where such a model must be accurate and yet simple. A key feature in modern MPC applications is the potential for online model adaptation to cope with time-varying changes, part-to-part variations, and complex features of the system dynamics not caught by models derived from first principles. In this paper, we propose to use a physics-informed, or gray-box, model that extends the physics-based model with a data-driven component, namely a Recurrent Neural Network (RNN). Relying on physics-informed models allows for a rather limited size of the RNN, thereby enhancing online applicability compared to pure black-box models. This work presents a method based on Moving Horizon Estimation (MHE) for simultaneous state estimation and learning of the RNN sub-model, a potentially challenging issue due to limited information available in noisy input-output data and lack of knowledge of the internal state of the RNN. We provide a case study on a quadruple tank benchmark showing how the method can cope with part-to-part variations.

To deal with plant−model mismatches in control practice, this paper proposes two variations of an offset-free framework which integrates nonlinear model predictive control (NMPC) and moving horizon estimation (MHE). We prove that the proposed method achieves offset-free regulatory behavior, even in the presence of plant−model mismatches. If the plant uncertainty structure is known, the MHE can be tuned to estimate uncertainty parameters, to remove the plant−model mismatch online. In addition, we incorporate the advanced step NMPC (as-NMPC) and the advanced step MHE (as-MHE) strategies into the proposed method to reduce online computational delay. Finally, the proposed method is applied on a large scale air separation unit, and the steady state offset-free behavior is observed.

Model Predictive Control (MPC) has proven to be successful in numerous advanced high-level process control applications based on software implementation in PC/server technology. However, for challenging applications offshore and subsea, ultra-reliable industrial embedded hardware, such as Programmable Logic Controllers (PLCs), are usually more suitable. The limited computational resources in low power industrial embedded devices, in combination with increased demands for computational speed and system reliability, motivate the development of new solution methods and software tools that enable the use of MPC in industrial embedded realtime applications. This tutorial aims at presenting different approaches for both formulating and efficiently solving industrial MPC problems. A brief review of existing methods will be covered, and new results that expand the computational toolbox for solving step response MPC problems will be presented. The new results include a novel MPC scheme that incorporates step response data in a traditional manner, while facilitating the use of block factorization in efficient QP solution methods. The new MPC scheme introduces a stage-wise prediction formulation that enables the use of both tailored Riccati recursion and condensing algorithms that can be embedded into an interior-point method. Implementation aspects necessary for high performance on embedded platforms are discussed, and results on a PLC are presented. Efficient MPC implementations for a subsea compact separation process application, using fast QP solvers such as HPMPC, qpOASES, FiOrdOs, and CVXGEN, will be used in the discussions.

State and parameter estimation of a dynamic froth flotation model using industrial data

Model predictive control has been recognized as one of the essential solutions to achieve considerable energy savings in buildings. However, its performance on a building zone level can be inferior to a well-tuned conventional controller, especially in situations with constant energy prices and conservative comfort constraints. Optimization problem in the background has to be chosen to guarantee recursive feasibility and considerable energy savings without compromising the users comfort at the same time. This paper gives a novel formulation of the model predictive temperature control problem in buildings and its fair comparison with conventional controllers with the same level of flexibility allowed in zone temperature control. All controllers are tested for a system with seasonal heating and cooling, which is the most common case in real applications. It is shown that the introduced formulation leads to the model predictive controller that significantly outperforms conventional controllers both in energy consumption and users comfort.

There are varieties of time-varying processes in chemical engineering industrial applications. These processes are abundant among lumped and distributed parameter systems and in batch systems they involve time-dependent change of parameters and/or geometry within lumped and/or distributed parameter systems settings. The focus of this thesis is on optimal state estimation and tracking regulation of two fed-batch processes with time-varying parameters and geometry. The first process is nonlinear time-varying microalgae growth and lipid production. An optimal reference trajectory is identified for maximum lipid production and moving horizon estimator along with model predictive control is realized for reference trajectory tracking of lipid production model. The second process is Czochralski crystal growth process which has moving boundary parabolic partial deferential equation describing heat transfer as dynamic model coupled with a lumped parameter model of pulling dynamics. Galerkin’s method is used to reduce the distributed parameter model’s order and an observer is developed to reconstruct temperature distribution evolution over the entire crystal domain during growth process. The performance of the observer is examined by implementing the observer on finite element model of the heat transfer in crystal. Furthermore, finite element model of the heat transfer along with finite element model of anisotropic thermal stresses in growing crystal are utilized to identify