2020 28th Mediterranean Conference on Control and Automation (MED), 2020
Several distributed model predictive control (MPC) strategies have been presented in the last few... more Several distributed model predictive control (MPC) strategies have been presented in the last few years. Those strategies are usually suited for large applications, when it is not interesting to use centralized controllers. Sub-optimal solutions are normally achieved by those controllers, although most of them can converge to optimal solutions as well. This paper presents a distributed MPC strategy with guaranteed feasibility and stability. Infinity horizon and cooperation between controllers are considered in this new strategy.
2020 IEEE Congreso Bienal de Argentina (ARGENCON), 2020
Gas lift, like every other artificial lift methods is used when the natural source of energy for ... more Gas lift, like every other artificial lift methods is used when the natural source of energy for lifting crude oil from the reservoir into the production platforms and then into the downstream facilities becomes insufficient. Interaction of the two-phase fluid in the tubing results in casing heading instability that is undesirable. We remove this instability and enhance crude oil recovery from gas-lifted oil well by use of advanced control system of nonlinear model predictive control (NMPC) with input target and control zones. The infinite Horizon NMPC is presented with the feasibility and convergence. Models of gas-lifted system which is a differential algebraic equation (DAE) system is presented. The oscillatory behavior of the system is shown. The developed NMPC is applied to the DAE gas lift system, where it is used in stabilizing the system and improving oil production rate by 3.4 percent compared to mean open loop production when both are operating at their maximum allowable inputs. The zone controller enables us to select state zones that favor instability removal while driving the input towards more economical value. The advantage of this approach is that instability can be removed or minimized while operating the system as close as possible to its optimal input from the optimization layer
Abstract We propose a cooperative distributed MPC that is designed to lay in an intermediary laye... more Abstract We propose a cooperative distributed MPC that is designed to lay in an intermediary layer of the process control structure. The distributed controller will deal with optimal targets defined by the real time optimization layer. The outputs are driven to artificial set points that are kept inside control zones while the inputs are driven to the optimum targets. Stability is assured by terminal constraints softened with slacks. These constraints are included in the control problem to bound the control cost. It is shown that convergence to the optimum target is related to the tuning parameters of the controller. The application of the proposed cooperative-distributed controller is simulated in an industrial crude distillation system including two distillation columns and a heating furnace.
This paper proposes a single layer MPC + RTO strategy with guaranteed nominal stability, suitable... more This paper proposes a single layer MPC + RTO strategy with guaranteed nominal stability, suitable for systems with stable and unstable modes. The control law applies an approximation of the gradient of an economic function, which drives the closed-loop system towards its desired economic performance, using a quadratic programming based optimization. Included in the optimization problem is a set of slack variables in order to provide a feasible solution at any time step. A reactor with unstable behavior is used to evaluate the effectiveness of the proposed controller and demonstrates its recursive feasibility and the convergence of the closed-loop system towards the desired economic performance. Two case studies are assessed: the first examines the nominal characteristics of the proposed strategy, while the second assesses the robustness of the proposed strategy by controlling the nonlinear model of the plant.
Industrial & Engineering Chemistry Research, 2019
The proposed auto-tuning method is a layer of receding horizon optimization problem whose objecti... more The proposed auto-tuning method is a layer of receding horizon optimization problem whose objective function is able to consider the performance/robustness through the trade-off representation combining the responses of the process variables and the control actions. The tuning parameters are evaluated based on a closed-loop simulation in the presence of model-plant mismatch, which is compared to the desired tunnel response in the time domain. The method is tested for two types of model predictive control and its flexibility and suitability for different scenarios of fit criteria are presented. The results point to the feasibility of the applications of the method, keeping the system close to the ideal setting and highlighting the importance of evaluating the behavior of control actions in the tuning problem.
Both real-time and off-line optimizations are commonly performed in order to enhance productivity... more Both real-time and off-line optimizations are commonly performed in order to enhance productivity. The optimization problem is often posed as a nonlinear programming (NLP) problem solved by a SQP algorithm. When processes need to be described by differential equations, difficulties will arise in using SQP algorithms, since Jacobians of constraints described by differential equations will have to be evaluated. In this paper, we show how to derive analytical expressions for both Jacobian and Hessian matrices for the constraints described by ordinary differential equations, without increasing the dimension of the resultant NLP problem to be solved.
Stability studies of linear model predictive control usually include the assumption that the cont... more Stability studies of linear model predictive control usually include the assumption that the control input can be interpreted as a static feedback of the system state vector. When the state of the system is measured, a suitable parameterization of the Lyapunov function renders it linear and a stabilizing constraint of the closed loop can be included in the MPC optimization problem. However, when not all the states are measured MPC becomes a control algorithm with output feedback. In this case, no such linearizing parameterization of the Lyapunov function has been found yet. The consequence is that the inclusion of the Lyapunov inequality requires an iterative algorithm to solve the MPC problem. Here, it is proposed a new formulation of MPC that is based on the idea of dynamic feedback. This approach allows the linearization of the Lyapunov function and the robust stable MPC problem can be formulated as a standard LMI optimization problem.
Dynamics and Control of Chemical Reactors, Distillation Columns and Batch Processes (Dycord'95), 1995
This paper describes the industrial application of a multivariable predictive controller to a typ... more This paper describes the industrial application of a multivariable predictive controller to a typical crude oil fractionator where jet fuel and diesel fuel are the main specified products. The controller functional specification includes the main targets of the column operation, accounting for 14 controlled variables. 6 manipulated variables and 2 disturbances. The implemented algorithm is a linear DMC. that makes use of a linear programming routine specifically developed to approach the problem of bounded variables, since the system variables are assumed to be controlled by range. The controller was successfully implemented in one of the Petrobras refineries at Paulinia (Brazil) and some practical results are presented here.
The Canadian Journal of Chemical Engineering, 2014
This work addresses the application of the Robust Infinite Horizon Model Predictive Control (RIHM... more This work addresses the application of the Robust Infinite Horizon Model Predictive Control (RIHMPC) to a heat integrated propylene distillation system at a Petrobras refinery. The approach proposed here is tested on the rigorous dynamic simulation software (Dynsim 1) that reproduces the system as a virtual plant and is able to communicate with the MPC algorithms developed in Matlab, through an Open Platform Communication (OPC) interface. The controller is based on a minimal order state-space model that is equivalent to the system step response and considers the zone control of the outputs and optimizing targets for the inputs. The optimizing targets are obtained through the steady-state economic optimization using the realtime optimization package (ROMeo 11). The proposed integration approach provides convergence and stability to the closed-loop system. The propylene distillation system is simulated with the proposed control and optimization strategies and the results show that, from the economic performance and robustness viewpoint, for this particular system, the proposed robust MPC is significantly better than the nominal IHMPC based on a single linear model obtained at the most probable operating point.
Abstract Here, it is studied the stable integration of real time optimization (RTO) and model pre... more Abstract Here, it is studied the stable integration of real time optimization (RTO) and model predictive control (MPC) for the case where the controller has a two layer structure. Stability is also obtained when model uncertainty is considered in both the target calculation and dynamic layers.
ABSTRACT In this work, it is reported the practical implementation of a predictive controller tha... more ABSTRACT In this work, it is reported the practical implementation of a predictive controller that integrates the control and the optimization of a toluene distillation column. The controller is based on an optimization problem where the control cost function includes an additional term related to the economic objective of the system. As in the distillation system studied here, the usual economic objectives are convex in terms of the decision variables of the control problem, the optimum economic conditions can be obtained, in the unconstrained case, by zeroing the gradient of the economic function. When, there are active constraints, the same approach can be followed by considering the reduced gradient of the objective function, which is included as an additional term in the cost function of the controller. In the case of the toluene column the controller includes a rigorous model of the distillation system that is used in the computation of the economic objective. An advantage of the proposed approach is that the predictive controller with economic objective is still a quadratic program that can be easily solved with conventional QP solvers. The method has been already implemented in an industrial toluene separation column in the Petrobras refinery at Cubatão (Brazil).
Comprehensive mathematical modeling for AIDS pathogenesis is developed. Mechanisms underlying the... more Comprehensive mathematical modeling for AIDS pathogenesis is developed. Mechanisms underlying the immunological effects of IL-2 therapy are investigated. Sustained CD4 T-cell expansion is not justified by increased CD4 T-cell survival. Instead, changed dynamics of Fas-dependent apoptotic pathways can play a critical role. IL-2+HAART has a greater effect on immunocompetence restoration than does HAART alone.
Model predictive control (MPC) applications in the process industry usually deal with process sys... more Model predictive control (MPC) applications in the process industry usually deal with process systems that show time delays (dead times) between the system inputs and outputs. Also, in many industrial applications of MPC, integrating outputs resulting from liquid level control or recycle streams need to be considered as controlled outputs. Conventional MPC packages can be applied to time-delay systems but stability of the closed loop system will depend on the tuning parameters of the controller and cannot be guaranteed even in the nominal case. In this work, a state space model based on the analytical step response model is extended to the case of integrating time systems with time delays. This model is applied to the development of two versions of a nominally stable MPC, which is designed to the practical scenario in which one has targets for some of the inputs and/or outputs that may be unreachable and zone control (or interval tracking) for the remaining outputs. The controller is tested through simulation of a multivariable industrial reactor system.
This paper concerns the development of a multivariable controller for the FCC Kellog Orthoflow F ... more This paper concerns the development of a multivariable controller for the FCC Kellog Orthoflow F reactor/regenerator unit. A nonlinear dynamic model, based on the model of Kurihara, is used as a reference for the design of the control algorithm. This model is compared with the plant data, for open loop changes on the air flow and the regenerated catalyst valve opening. The adopted control algorithm incorporates both the regulatory and optimization functions. The regulatory layer is based on the usual DMC algorithm, while the optimization layer solves a linear programming problem, based on the DMC formulation, to perform steady-state economic optimizations. The calculated variables of the LP are the setpoints to the regulatory layer. The proposed control structure is simulated for a particular set of manipulated and controlled variables of the Kellog FCC converter and the results indicate good potential for the application to the real system.
In this paper, the application of a linear predictive controller to an industrial distillation co... more In this paper, the application of a linear predictive controller to an industrial distillation column that presents a nonlinear behavior is described. The system is represented by a set of linear approximating models, where each model corresponds to a possible operating point of the system. The control sequence computed by the control algorithm is based on a min–max optimization problem
Sequential quadratic programming (SQP) algorithms are often considered to be the best choice for ... more Sequential quadratic programming (SQP) algorithms are often considered to be the best choice for solving nonlinear programming problems (NLP). The interest in solving NLPs has increased recently. It has become advantageous to perform on-line economic optimization and non-linear process control in the chemical industries. SQP methods may not be always robust and efficient. They depend on the solution of an
... Marco A. Rodrigues E-mail The Corresponding Author and Darci Odloak Corresponding Author Cont... more ... Marco A. Rodrigues E-mail The Corresponding Author and Darci Odloak Corresponding Author Contact ... University of São Paulo, PO Box 61548, 05424-970, São Paulo, SP, Brazil. ... a semi-infinite approach for continuous nonlinear systems and De Nicolao, Magni, and Scattolini ...
ABSTRACT This paper studies a simplified methodology to integrate the real time optimization (RTO... more ABSTRACT This paper studies a simplified methodology to integrate the real time optimization (RTO) of a continuous system into the model predictive controller in the one layer strategy. The gradient of the economic objective function is included in the cost function of the controller. Optimal conditions of the process at steady state are searched through the use of a rigorous non-linear process model, while the trajectory to be followed is predicted with the use of a linear dynamic model, obtained through a plant step test. The main advantage of the proposed strategy is that the resulting control/optimization problem can still be solved with a quadratic programming routine at each sampling step. Simulation results show that the approach proposed may be comparable to the strategy that solves the full economic optimization problem inside the MPC controller where the resulting control problem becomes a non-linear programming problem with a much higher computer load.
Here, we study the stable integration of real time optimization (RTO) with model predictive contr... more Here, we study the stable integration of real time optimization (RTO) with model predictive control (MPC) in a three layer structure. The intermediate layer is a quadratic programming whose objective is to compute reachable targets to the MPC layer that lie at the minimum distance to the optimum set points that are produced by the RTO layer. The lower layer
2020 28th Mediterranean Conference on Control and Automation (MED), 2020
Several distributed model predictive control (MPC) strategies have been presented in the last few... more Several distributed model predictive control (MPC) strategies have been presented in the last few years. Those strategies are usually suited for large applications, when it is not interesting to use centralized controllers. Sub-optimal solutions are normally achieved by those controllers, although most of them can converge to optimal solutions as well. This paper presents a distributed MPC strategy with guaranteed feasibility and stability. Infinity horizon and cooperation between controllers are considered in this new strategy.
2020 IEEE Congreso Bienal de Argentina (ARGENCON), 2020
Gas lift, like every other artificial lift methods is used when the natural source of energy for ... more Gas lift, like every other artificial lift methods is used when the natural source of energy for lifting crude oil from the reservoir into the production platforms and then into the downstream facilities becomes insufficient. Interaction of the two-phase fluid in the tubing results in casing heading instability that is undesirable. We remove this instability and enhance crude oil recovery from gas-lifted oil well by use of advanced control system of nonlinear model predictive control (NMPC) with input target and control zones. The infinite Horizon NMPC is presented with the feasibility and convergence. Models of gas-lifted system which is a differential algebraic equation (DAE) system is presented. The oscillatory behavior of the system is shown. The developed NMPC is applied to the DAE gas lift system, where it is used in stabilizing the system and improving oil production rate by 3.4 percent compared to mean open loop production when both are operating at their maximum allowable inputs. The zone controller enables us to select state zones that favor instability removal while driving the input towards more economical value. The advantage of this approach is that instability can be removed or minimized while operating the system as close as possible to its optimal input from the optimization layer
Abstract We propose a cooperative distributed MPC that is designed to lay in an intermediary laye... more Abstract We propose a cooperative distributed MPC that is designed to lay in an intermediary layer of the process control structure. The distributed controller will deal with optimal targets defined by the real time optimization layer. The outputs are driven to artificial set points that are kept inside control zones while the inputs are driven to the optimum targets. Stability is assured by terminal constraints softened with slacks. These constraints are included in the control problem to bound the control cost. It is shown that convergence to the optimum target is related to the tuning parameters of the controller. The application of the proposed cooperative-distributed controller is simulated in an industrial crude distillation system including two distillation columns and a heating furnace.
This paper proposes a single layer MPC + RTO strategy with guaranteed nominal stability, suitable... more This paper proposes a single layer MPC + RTO strategy with guaranteed nominal stability, suitable for systems with stable and unstable modes. The control law applies an approximation of the gradient of an economic function, which drives the closed-loop system towards its desired economic performance, using a quadratic programming based optimization. Included in the optimization problem is a set of slack variables in order to provide a feasible solution at any time step. A reactor with unstable behavior is used to evaluate the effectiveness of the proposed controller and demonstrates its recursive feasibility and the convergence of the closed-loop system towards the desired economic performance. Two case studies are assessed: the first examines the nominal characteristics of the proposed strategy, while the second assesses the robustness of the proposed strategy by controlling the nonlinear model of the plant.
Industrial & Engineering Chemistry Research, 2019
The proposed auto-tuning method is a layer of receding horizon optimization problem whose objecti... more The proposed auto-tuning method is a layer of receding horizon optimization problem whose objective function is able to consider the performance/robustness through the trade-off representation combining the responses of the process variables and the control actions. The tuning parameters are evaluated based on a closed-loop simulation in the presence of model-plant mismatch, which is compared to the desired tunnel response in the time domain. The method is tested for two types of model predictive control and its flexibility and suitability for different scenarios of fit criteria are presented. The results point to the feasibility of the applications of the method, keeping the system close to the ideal setting and highlighting the importance of evaluating the behavior of control actions in the tuning problem.
Both real-time and off-line optimizations are commonly performed in order to enhance productivity... more Both real-time and off-line optimizations are commonly performed in order to enhance productivity. The optimization problem is often posed as a nonlinear programming (NLP) problem solved by a SQP algorithm. When processes need to be described by differential equations, difficulties will arise in using SQP algorithms, since Jacobians of constraints described by differential equations will have to be evaluated. In this paper, we show how to derive analytical expressions for both Jacobian and Hessian matrices for the constraints described by ordinary differential equations, without increasing the dimension of the resultant NLP problem to be solved.
Stability studies of linear model predictive control usually include the assumption that the cont... more Stability studies of linear model predictive control usually include the assumption that the control input can be interpreted as a static feedback of the system state vector. When the state of the system is measured, a suitable parameterization of the Lyapunov function renders it linear and a stabilizing constraint of the closed loop can be included in the MPC optimization problem. However, when not all the states are measured MPC becomes a control algorithm with output feedback. In this case, no such linearizing parameterization of the Lyapunov function has been found yet. The consequence is that the inclusion of the Lyapunov inequality requires an iterative algorithm to solve the MPC problem. Here, it is proposed a new formulation of MPC that is based on the idea of dynamic feedback. This approach allows the linearization of the Lyapunov function and the robust stable MPC problem can be formulated as a standard LMI optimization problem.
Dynamics and Control of Chemical Reactors, Distillation Columns and Batch Processes (Dycord'95), 1995
This paper describes the industrial application of a multivariable predictive controller to a typ... more This paper describes the industrial application of a multivariable predictive controller to a typical crude oil fractionator where jet fuel and diesel fuel are the main specified products. The controller functional specification includes the main targets of the column operation, accounting for 14 controlled variables. 6 manipulated variables and 2 disturbances. The implemented algorithm is a linear DMC. that makes use of a linear programming routine specifically developed to approach the problem of bounded variables, since the system variables are assumed to be controlled by range. The controller was successfully implemented in one of the Petrobras refineries at Paulinia (Brazil) and some practical results are presented here.
The Canadian Journal of Chemical Engineering, 2014
This work addresses the application of the Robust Infinite Horizon Model Predictive Control (RIHM... more This work addresses the application of the Robust Infinite Horizon Model Predictive Control (RIHMPC) to a heat integrated propylene distillation system at a Petrobras refinery. The approach proposed here is tested on the rigorous dynamic simulation software (Dynsim 1) that reproduces the system as a virtual plant and is able to communicate with the MPC algorithms developed in Matlab, through an Open Platform Communication (OPC) interface. The controller is based on a minimal order state-space model that is equivalent to the system step response and considers the zone control of the outputs and optimizing targets for the inputs. The optimizing targets are obtained through the steady-state economic optimization using the realtime optimization package (ROMeo 11). The proposed integration approach provides convergence and stability to the closed-loop system. The propylene distillation system is simulated with the proposed control and optimization strategies and the results show that, from the economic performance and robustness viewpoint, for this particular system, the proposed robust MPC is significantly better than the nominal IHMPC based on a single linear model obtained at the most probable operating point.
Abstract Here, it is studied the stable integration of real time optimization (RTO) and model pre... more Abstract Here, it is studied the stable integration of real time optimization (RTO) and model predictive control (MPC) for the case where the controller has a two layer structure. Stability is also obtained when model uncertainty is considered in both the target calculation and dynamic layers.
ABSTRACT In this work, it is reported the practical implementation of a predictive controller tha... more ABSTRACT In this work, it is reported the practical implementation of a predictive controller that integrates the control and the optimization of a toluene distillation column. The controller is based on an optimization problem where the control cost function includes an additional term related to the economic objective of the system. As in the distillation system studied here, the usual economic objectives are convex in terms of the decision variables of the control problem, the optimum economic conditions can be obtained, in the unconstrained case, by zeroing the gradient of the economic function. When, there are active constraints, the same approach can be followed by considering the reduced gradient of the objective function, which is included as an additional term in the cost function of the controller. In the case of the toluene column the controller includes a rigorous model of the distillation system that is used in the computation of the economic objective. An advantage of the proposed approach is that the predictive controller with economic objective is still a quadratic program that can be easily solved with conventional QP solvers. The method has been already implemented in an industrial toluene separation column in the Petrobras refinery at Cubatão (Brazil).
Comprehensive mathematical modeling for AIDS pathogenesis is developed. Mechanisms underlying the... more Comprehensive mathematical modeling for AIDS pathogenesis is developed. Mechanisms underlying the immunological effects of IL-2 therapy are investigated. Sustained CD4 T-cell expansion is not justified by increased CD4 T-cell survival. Instead, changed dynamics of Fas-dependent apoptotic pathways can play a critical role. IL-2+HAART has a greater effect on immunocompetence restoration than does HAART alone.
Model predictive control (MPC) applications in the process industry usually deal with process sys... more Model predictive control (MPC) applications in the process industry usually deal with process systems that show time delays (dead times) between the system inputs and outputs. Also, in many industrial applications of MPC, integrating outputs resulting from liquid level control or recycle streams need to be considered as controlled outputs. Conventional MPC packages can be applied to time-delay systems but stability of the closed loop system will depend on the tuning parameters of the controller and cannot be guaranteed even in the nominal case. In this work, a state space model based on the analytical step response model is extended to the case of integrating time systems with time delays. This model is applied to the development of two versions of a nominally stable MPC, which is designed to the practical scenario in which one has targets for some of the inputs and/or outputs that may be unreachable and zone control (or interval tracking) for the remaining outputs. The controller is tested through simulation of a multivariable industrial reactor system.
This paper concerns the development of a multivariable controller for the FCC Kellog Orthoflow F ... more This paper concerns the development of a multivariable controller for the FCC Kellog Orthoflow F reactor/regenerator unit. A nonlinear dynamic model, based on the model of Kurihara, is used as a reference for the design of the control algorithm. This model is compared with the plant data, for open loop changes on the air flow and the regenerated catalyst valve opening. The adopted control algorithm incorporates both the regulatory and optimization functions. The regulatory layer is based on the usual DMC algorithm, while the optimization layer solves a linear programming problem, based on the DMC formulation, to perform steady-state economic optimizations. The calculated variables of the LP are the setpoints to the regulatory layer. The proposed control structure is simulated for a particular set of manipulated and controlled variables of the Kellog FCC converter and the results indicate good potential for the application to the real system.
In this paper, the application of a linear predictive controller to an industrial distillation co... more In this paper, the application of a linear predictive controller to an industrial distillation column that presents a nonlinear behavior is described. The system is represented by a set of linear approximating models, where each model corresponds to a possible operating point of the system. The control sequence computed by the control algorithm is based on a min–max optimization problem
Sequential quadratic programming (SQP) algorithms are often considered to be the best choice for ... more Sequential quadratic programming (SQP) algorithms are often considered to be the best choice for solving nonlinear programming problems (NLP). The interest in solving NLPs has increased recently. It has become advantageous to perform on-line economic optimization and non-linear process control in the chemical industries. SQP methods may not be always robust and efficient. They depend on the solution of an
... Marco A. Rodrigues E-mail The Corresponding Author and Darci Odloak Corresponding Author Cont... more ... Marco A. Rodrigues E-mail The Corresponding Author and Darci Odloak Corresponding Author Contact ... University of São Paulo, PO Box 61548, 05424-970, São Paulo, SP, Brazil. ... a semi-infinite approach for continuous nonlinear systems and De Nicolao, Magni, and Scattolini ...
ABSTRACT This paper studies a simplified methodology to integrate the real time optimization (RTO... more ABSTRACT This paper studies a simplified methodology to integrate the real time optimization (RTO) of a continuous system into the model predictive controller in the one layer strategy. The gradient of the economic objective function is included in the cost function of the controller. Optimal conditions of the process at steady state are searched through the use of a rigorous non-linear process model, while the trajectory to be followed is predicted with the use of a linear dynamic model, obtained through a plant step test. The main advantage of the proposed strategy is that the resulting control/optimization problem can still be solved with a quadratic programming routine at each sampling step. Simulation results show that the approach proposed may be comparable to the strategy that solves the full economic optimization problem inside the MPC controller where the resulting control problem becomes a non-linear programming problem with a much higher computer load.
Here, we study the stable integration of real time optimization (RTO) with model predictive contr... more Here, we study the stable integration of real time optimization (RTO) with model predictive control (MPC) in a three layer structure. The intermediate layer is a quadratic programming whose objective is to compute reachable targets to the MPC layer that lie at the minimum distance to the optimum set points that are produced by the RTO layer. The lower layer
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