Hybrid Predictive Control Research Articles

Real-time hybrid predictive modeling of the Teniente Converter

The Teniente Converter (TC) is an important technology for smelting and converting copper concentrates. Due to the complexities of its autogenous operation, which combines continuous input flows with intermittent product extraction, efforts to model and control this dynamic have only been partially successful. This work presents a model of TC operation that combines phenomenological equations with empirical expressions and includes both continuous and discrete variables. Six different operating modes are described. To improve predictive capabilities, an adaptive compensation technique takes account of changes in concentrate mix characteristics. The model predicts five important variables: white metal copper concentration, slag magnetite concentration, white metal temperature, and white metal and slag levels. It is calibrated and validated with real operating data from Codelco’s Potrerillos smelter. Once the model is implemented, it delivers online estimates of process variables that are measured intermittently. Based on the model, a hybrid predictive controller is developed to control the quantities and characteristics of the TC products as a function of the number of dependent units such as Peirce-Smith converters and slag-cleaning furnaces. The controller’s performance is evaluated via simulation under a variety of operating conditions. It is currently employed in an open-loop configuration to provide suggestions on set points for the local flow controllers and on the product extraction sequences.

Genetic Hybrid Predictive Controller for Optimized Dissolved-Oxygen Tracking at Lower Control Level

A hierarchical two-level controller for dissolved-oxygen reference trajectory tracking in activated sludge processes has been recently developed and successfully validated on a real wastewater treatment plant. The upper level control unit generates trajectories of the desired airflows to be delivered by the aeration system to the aerobic zones of the biological reactor. A nonlinear model predictive control algorithm is applied to design this controller. The aeration system itself is a complicated hybrid nonlinear dynamical system. The lower level controller (LLC) forces the aeration system to follow these set-point trajectories, minimizing a cost of energy due to pumping of the air and accounting for system operational limitations such as the limits on the allowed frequency of switching of the blowers and on their capacity. The predictive control is also applied to design the LLC based on a piecewise-linearized hybrid dynamics of the aeration system. Casting the mixed-integer nonlinear optimization problem under heterogeneous constraints due to the limits on the blower switching frequency into the approximated mixed-integer form is done at a cost of introducing large number of auxiliary variables into the lower level predictive controller optimization task. This paper derives another nonlinear hybrid predictive control algorithm for the LLC. It is directly based on the nonlinear hybrid dynamics and logical formulation of the switching constraint. A genetic algorithm is derived with dedicated operators allowing for efficient handling of the switching constraint and nonlinear hybrid system dynamics. The efficiency of the control algorithm is validated by simulation based on real data records.

Hybrid predictive control for real-time optimization of public transport systems’ operations based on evolutionary multi-objective optimization

A hybrid predictive control formulation based on evolutionary multi-objective optimization to optimize real-time operations of public transport systems is presented. The state space model includes bus position, expected load and arrival time at stops. The system is based on discrete events, and the possible operator control actions are: holding vehicles at stations and skipping some stations. The controller (operator) pursues the minimization of a dynamic objective function to generate better operational decisions under uncertain demand at bus stops. In this work, a multi-objective approach is conducted to include different goals in the optimization process that could be opposite. In this case, the optimization was defined in terms of two objectives: waiting time minimization on one side, and impact of the strategies on the other. A genetic algorithm method is proposed to solve the multi-objective dynamic problem. From the conducted experiments considering a single bus line corridor, we found that the two objectives are opposite but with a certain degree of overlapping, in the sense that in all cases both objectives significantly improve the level of service with respect to the open-loop scenario by regularizing the headways. On average, the observed trade-off validates the proposed multi-objective methodology for the studied system, allowing dynamically finding the pseudo-optimal Pareto front and making real-time decisions based on different optimization criteria reflected in the proposed objective function compounds.

MPC for battery/fuel cell hybrid vehicles including fuel cell dynamics and battery performance improvement

In this paper, the performance and durability of hybrid PEM fuel cell vehicles are investigated. To that end, a hybrid predictive controller is proposed to improve battery performance and to avoid fuel cell and battery degradation. Such controller deals with this complex control problem by handling binary and continuous variables, piecewise affine models and constraints. Moreover, the control strategy is to track motor power demand and keep batteries close to a desired battery state of charge which is appropriately chosen to minimize hydrogen consumption. It is important to highlight the consideration of constraints which are directly related to the goals of this paper, such as minimum fuel cell power threshold and time limitation between fuel cell startups and shutdowns. Furthermore, different models have been elaborated and particularized for a vehicle prototype. These models include few innovations such as a reference governor which smooths fuel cell power demand during sharp power profiles, forcing batteries to supply such peaks and resulting a longer fuel cell lifetime. Battery thermal dynamics are also taken into account in these models in order to analyze the effect of battery temperature on its degradation. Finally, this paper studies the feasibility of the real implementation, presenting an explicit formulation as a solution to reduce execution time. This explicit controller exhibits the same performance as the hybrid predictive controller does with a reduced computational effort. All the results have been validated in several simulations.

Fuzzy-model-based hybrid predictive control

In this paper we present a method of hybrid predictive control (HPC) based on a fuzzy model. The identification methodology for a nonlinear system with discrete state–space variables based on combining fuzzy clustering and principal component analysis is proposed. The fuzzy model is used for HPC design, where the optimization problem is solved by the use of genetic algorithms (GAs). An illustrative experiment on a hybrid tank system is conducted to demonstrate the benefits of the proposed approach.

The design of predictive control with characterized set of initial condition for constrained switched nonlinear system

Stabilization of the constrained switched nonlinear systems is an attractive research subject. Predictive control can handle variable constraints well and make the system stable. Its stability is typically based on an assumption of initial feasibility of the optimization problem; however the set of initial conditions, starting from where a given predictive formulation is guaranteed to be feasible, is not explicitly characterized. In this paper, a hybrid predictive control method is proposed for a class of switched nonlinear systems with input constraints and un-measurable states. The main idea is to design a mixed controller using Lyapunov functions and a state observer, which switches appropriately between a bounded feedback controller and a predictive controller, and to give an explicitly characterized set of initial conditions to stabilize each closed-loop subsystem. For the whole switched nonlinear system, a suitable switched law based on the state estimation is designed to orchestrate the transitions between the consistituent modes and their respective controllers, and to ensure the whole closed-loop system’s stability. The simulation results for a chemical process show the validity of the controller proposed in this paper.

Hybrid fuzzy predictive control based on genetic algorithms for the temperature control of a batch reactor

In this paper we describe the design of hybrid fuzzy predictive control based on a genetic algorithm (GA). We also present a simulation test of the proposed algorithm and a comparison with two hybrid predictive control methods: Explicit Enumeration and Branch and Bound (BB). The experiments involved controlling the temperature of a batch reactor by using two on/off input valves and a discrete-position mixing valve. The GA-hybrid predictive control strategy proved to be a suitable method for the control of hybrid systems, giving similar performance to that of typical hybrid predictive control strategies and a significant saving with respect to the computation time.

A strategy for predictive control of a mixed continuous batch process

This paper deals with the on-line control of mixed processes composed of continuous and batch units in which some continuous variables must be kept as close as possible at prescribed values and the batch units must be scheduled in order to avoid bottlenecks in production. In particular, a pilot plant is considered with product recycle involving simultaneous continuous and scheduling decisions. The problem is of hybrid nature and can be formulated as a hybrid predictive control model in terms of integer and continuous variables. However, as the system must be controlled in real-time, an alternative formulation is proposed based on a hierarchical view of the problem and the use of flow patterns and time of occurrence of events in the batch units. The paper describes the process, the control problem formulation, and provides results of some test in the pilot plant.

A Hybrid Predictive Control Scheme for Hygrothermal Process

This work is focused on developing control algorithms for hygrothermal process represented by mixed logical and dynamical models. An example is the closed newborn incubator. Such kind of system promotes a controlled micro-climate, with small heat transfer between the premature and the environment, leading to comfortable and healthful environment. This device can be represented by a piece-wise linear model having discrete values for the input signal range. A hybrid predictive control scheme is proposed for such a process. The algorithm can also be applied to different dynamic systems having the same characteristics and it is easy to be implemented in real-time environments. System identification results based on orthonormal basis functions for finding the set of linear transfer functions are discussed. Closed-loop control experiments, by using an actual laboratory pilot plant (full scale), are performed and presented to validate the proposed method.

Hybrid Predictive Control for the Vehicle Dynamic Routing Problem based on Evolutionary Multiobjective Optimization (EMO)

In this paper, a hybrid adaptive predictive control approach (HAPC) to solve a dynamic pickup and delivery problem (DPDP) is presented based on a dynamic objective function that includes two dimensions: user and operator costs. Because these two costs are opposite components, the problem was formulated and solved by using an Evolutionary Multiobjective Optimization (EMO) technique. The idea is to minimize both, user and operator costs. At every instant, the use of genetic algorithms is proposed to find the optimal Pareto front associated with the DPDP, whose Pareto Optimal set is a set of solutions of the problem. Since only one solution has to be applied to the system every time a new request appears, several criteria will be utilized in order to properly use the information provided by the dynamic optimal Pareto front. Illustrative experiments through simulation of the process are presented to show the potential benefits of the new approach. Thus, by using EMO, the trade off between the two conflicting objectives will become clear for the dispatcher when making dynamic routing decisions.

Applications of Hybrid Predictive Control

Applications of Hybrid Predictive Control

Hybrid adaptive predictive control for a dynamic pickup and delivery problem including traffic congestion

AbstractThis paper presents a hybrid adaptive predictive control approach to incorporate future information regarding unknown demand and expected traffic conditions, in the context of a dynamic pickup and delivery problem with fixed fleet size. As the routing problem is dynamic, several stochastic effects have to be considered within the analytical expression of the dispatcher assignment decision objective function. This paper is focused on two issues: one is the extra cost associated with potential rerouting arising from unknown requests in the future, and the other is the potential uncertainty in travel time coming from non‐recurrent traffic congestion from unexpected incidents.These effects are incorporated explicitly in the objective function of the hybrid predictive controller. In fact, the proposed predictive control strategy is based on a multivariable model that includes both discrete/integer and continuous variables. The vehicle load and the sequence of stops correspond to the discrete/integer variable, adding the vehicle position as an indicator of the traffic congestion conditions. The strategy is analyzed under two scenarios. The first one considers a predictable congestion obtained using historical data (off‐line method) requiring a predictive model of velocities distributed over zones. The second scenario that accepts unpredictable congestion events generates a more complex problem that is managed by using both fault detection and isolation and fuzzy fault‐tolerant control approaches. Results validating these approaches are presented through a simulated numerical example. Copyright © 2007 John Wiley & Sons, Ltd.

Adaptive hybrid predictive control for a combined cycle power plant optimization

AbstractThe design and development of an adaptive hybrid predictive controller for the optimization of a real combined cycle power plant (CCPP) are presented. The real plant is modeled as a hybrid system, i.e. logical conditions and dynamic behavior are used in one single modeling framework. Start modes, minimum up/down times and other logical features are represented using mixed integer equations, and dynamic behavior is represented using special linear models: adaptive fuzzy models. This approach allows the tackling of special non‐linear characteristics, such as ambient temperature dependence on electrical power production (combined cycle) and gas exhaust temperature (gas turbine) properly to fit into a mixed integer dynamic (MLD) model. After defining the MLD model, an adaptive predictive control strategy is developed in order to economically optimize the operation of a real CCPP of the Central Interconnected System in Chile. The economic results obtained by simulation tests provide a 3% fuel consumption saving compared to conventional strategies at regulatory level. Copyright © 2007 John Wiley & Sons, Ltd.

Hybrid adaptive predictive control for the multi-vehicle dynamic pick-up and delivery problem based on genetic algorithms and fuzzy clustering

In this paper, we develop a family of solution algorithms based upon computational intelligence for solving the dynamic multi-vehicle pick-up and delivery problem formulated under a hybrid predictive adaptive control scheme. The scheme considers future demand and prediction of expected waiting and travel times experienced by customers. In addition, this work includes an analytical formulation of the proposed prediction models that allow us to search over a reduced feasible space. Predictive models consider relevant state space variables as vehicle load and departure time at stops. A generic expression of the system cost function is used to measure the benefits in dispatching decisions of the proposed scheme when solving for more than two-step ahead under unknown demand. The demand prediction is based on a systematic fuzzy clustering methodology, resulting in appropriate call probabilities for uncertain future. As the dynamic multi-vehicle routing problem considered is NP-hard, we propose the use of genetic algorithms (GA) that provide near-optimal solutions for the three, two and one-step ahead problems. Promising results in terms of computation time and accuracy are presented through a simulated numerical example that includes the analysis of the proposed fuzzy clustering, and the comparison of myopic and new predictive approaches solved with GA.

SOFTLY SWITCHED HYBRID PREDICTIVE CONTROL

In operational control of hybrid systems, control objectives often change with current operating conditions and switching among a number of control strategies is then inevitable. The proposed softly switched hybrid predictive control utilizes mixed integer programming techniques and achieves better switching transient performance both in system output/state and control input than the traditional hard switching method. Stability of the designed soft switching process is analysed and sufficient stabilization conditions are derived. Numerical examples with simulation results show that the proposed approach can be useful in practical applications.

Fault‐tolerant control of nonlinear processes: performance‐based reconfiguration and robustness

AbstractThis work considers the problem of control system/actuator failures in nonlinear processes subject to input constraints and presents two approaches for fault‐tolerant control that focus on incorporating performance and robustness considerations, respectively. In both approaches, first a family of candidate control configurations, characterized by different manipulated inputs, is identified for the process under consideration. Performance considerations are first incorporated via the design of a Lyapunov‐based predictive controller that enforces closed‐loop stability from an explicitly characterized set of initial conditions (computed using an auxiliary Lyapunov‐based nonlinear controller). A hierarchical switching policy is derived, that uses stability considerations (evaluated via the presence of the state in the stability region of a control configuration) to ascertain the suitability of a candidate backup configuration and then performance considerations are again considered in choosing between the suitable backup configurations. Next, we consider the problem of implementing fault‐tolerant control to nonlinear processes subject to input constraints and uncertainty. To this end, we first design a robust hybrid predictive controller for each candidate control configuration that guarantees stability from an explicitly characterized set of initial conditions, subject to uncertainty and constraints. A switching policy is then derived to orchestrate the activation/deactivation of the constituent control configurations. Finally, simulation studies are presented to demonstrate the implementation and evaluate the effectiveness of the proposed fault‐tolerant control method. Copyright © 2005 John Wiley & Sons, Ltd.

Predictive control of particle size distribution in particulate processes

In this work, we focus on the development and application of predictive-based strategies for control of particle size distribution (PSD) in continuous and batch particulate processes described by population balance models (PBMs). The control algorithms are designed on the basis of reduced-order models, utilize measurements of principle moments of the PSD, and are tailored to address different control objectives for the continuous and batch processes. For continuous particulate processes, we develop a hybrid predictive control strategy to stabilize a continuous crystallizer at an open-loop unstable steady-state. The hybrid predictive control strategy employs logic-based switching between model predictive control (MPC) and a fall-back bounded controller with a well-defined stability region. The strategy is shown to provide a safety net for the implementation of MPC algorithms with guaranteed stability closed-loop region. For batch particulate processes, the control objective is to achieve a final PSD with desired characteristics subject to both manipulated input and product quality constraints. An optimization-based predictive control strategy that incorporates these constraints explicitly in the controller design is formulated and applied to a seeded batch crystallizer. The strategy is shown to be able to reduce the total volume of the fines by 13.4% compared to a linear cooling strategy, and is shown to be robust with respect to modeling errors.

ROBUST STABILIZATION OF NONLINEAR PROCESSES USING HYBRID PREDICTIVE CONTROL

In this work, we consider nonlinear systems with input constraints and uncertain variables, and develop a robust hybrid predictive control structure that provides a safety net for the implementation of any model predictive control (MPC) formulation, designed with or without taking uncertainty into account. The key idea is to use a Lyapunov–based bounded robust controller, for which an explicit characterization of the region of robust closed-loop stability can be obtained, to provide a stability region within which any available MPC formulation can be implemented. This is achieved by devising switching laws that orchestrate switching between MPC and the bounded robust controller in a way that exploits the performance of MPC whenever possible, while using the bounded controller as a fall-back controller that can be switched in at any time to maintain robust closed-loop stability in the event that the predictive controller fails to yield a control move (due, for example, to computational difficulties in the optimization or infeasibility) or leads to instability (due, for example, to inappropriate penalties and/or horizon length in the objective function). The implementation and efficacy of the robust hybrid predictive control structure are demonstrated through simulations using a chemical process example.

LOWER – LEVEL CONTROLLER FOR HIERARCHICAL CONTROL OF DISSOLVED OXYGEN CONCENTRATION IN ACTIVATED SLUDGE PROCESSES

The paper addresses control design for an aeration system within a hierarchical structure for an integrated control of dissolved oxygen in the activated sludge processes. In the paper the hybrid predictive controller for the lower control level is developed and its performance is investigated based on real data records.

Robust hybrid predictive control of nonlinear systems

In this work, we consider nonlinear systems with input constraints and uncertain variables, and develop a robust hybrid predictive control structure that provides a safety net for the implementation of any model predictive control (MPC) formulation, designed with or without taking uncertainty into account. The key idea is to use a Lyapunov-based bounded robust controller, for which an explicit characterization of the region of robust closed-loop stability can be obtained, to provide a stability region within which any available MPC formulation can be implemented. This is achieved by devising a set of switching laws that orchestrate switching between MPC and the bounded robust controller in a way that exploits the performance of MPC whenever possible, while using the bounded controller as a fall-back controller that can be switched in at any time to maintain robust closed-loop stability in the event that the predictive controller fails to yield a control move (due, e.g., to computational difficulties in the optimization or infeasibility) or leads to instability (due, e.g., to inappropriate penalties and/or horizon length in the objective function). The implementation and efficacy of the robust hybrid predictive control structure are demonstrated through simulations using a chemical process example.