Non‐Linear Model Predictive Control: A Personal Retrospective

Bequette, B. Wayne

doi:10.1002/cjce.5450850403

Cited by 40 publications

(21 citation statements)

References 31 publications

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“…Solutions to Equations (10,11) result, under the hypotheses made, the optimal state and costate trajectories (denoted by x * (t) and * (t), respectively), which are also related through the valuefunction by (see [22])…”

Section: The Hamiltonian Formalism For Nonlinear Systems and General mentioning

confidence: 99%

“…Equation (29) allows to calculate the optimal Hamiltonian H 0 (x * , * ), and to pose the Hamiltonian mixed-boundary-conditions problem equations (10)(11), and to construct the corresponding PDEs developed in Section 3.2.…”

Section: Cstr Optimal Trajectory Generationmentioning

confidence: 99%

“…(ii) The nominal optimal trajectory is generated by online integration of Hamiltonian equations of the optimal control problem (10,11). This can be done thanks to the initial value of the costate , i.e.…”

mentioning

confidence: 99%

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Hamiltonian two‐degrees‐of‐freedom control of chemical reactors

Costanza

Rivadeneira

2011

Optim Control Appl Methods

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A novel unified approach to two-degrees-of-freedom control is devised and applied to a classical chemical reactor model. The scheme is constructed from the optimal control point of view and along the lines of the Hamiltonian formalism for nonlinear processes. The proposed scheme optimizes both the feedforward and the feedback components of the control variable with respect to the same cost objective. The original Hamiltonian function governs the feedforward dynamics, and its derivatives are part of the gain for the feedback component. The optimal state trajectory is generated online, and is tracked by a combination of deterministic and stochastic optimal tools. The relevant numerical data to manipulate all stages come from a unique off-line calculation, which provides design information for a whole family of related control problems. This is possible because a new set of PDEs (the variational equations) allow to recover the initial value of the costate variable, and the Hamilton equations can then be solved as an initial-value problem. Perturbations from the optimal trajectory are abated through an optimal state estimator and a deterministic regulator with a generalized Riccati gain. Both gains are updated online, starting with initial values extracted from the solution to the variational equations. The control strategy is particularly useful in driving nonlinear processes from an equilibrium point to an arbitrary target in a finite-horizon optimization context. Figure 1. Two-degrees-of-freedom control design.involve changes in the final equilibrium value of the manipulated variable (a parameter whose value may have been optimized a priori). These types of behavior present severe operation problems and demonstrate the need for feedback control, particularly when the process is open-loop unstable or when it exhibits nonlinear oscillations [4]. Other common process characteristics that cause control difficulty for nonlinear systems are multivariable interaction between manipulated and controlled variables, unmeasured states and frequent disturbances in the input-output signals [5].Chemical reactors are usual classical examples in the nonlinear control literature ([2, 6-8], and their references). Several nonlinear advanced techniques have been developed (and these can be consulted in an extensive survey done by Bequette [5]), where the resulting controls were either linear or nonlinear. It is clear that nonlinear control in CSTR becomes more important if set-point changes are made, since significant departures from equilibrium are most probable to occur. Other (not necessarily equilibrium) points may be desirable to achieve, as it happens in batch processes. In such situations, both the nominal trajectory and its tracking must be optimized until a stop condition is reached in a finite time.Apart from heuristic methods, there is a range of model-based approaches such as Model Predictive Control (MPC), which is becoming the most widely quoted in the recent literature. This method is essentially numerical, usually impl...

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Section: The Hamiltonian Formalism For Nonlinear Systems and General mentioning

confidence: 99%

Section: Cstr Optimal Trajectory Generationmentioning

confidence: 99%

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Hamiltonian two‐degrees‐of‐freedom control of chemical reactors

Costanza

Rivadeneira

2011

Optim Control Appl Methods

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“…More advanced control techniques evolved as an effect of better models describing the pH process developed by by McAvoy et al [18] and Gustafsson and Waller [8]. The improved models led to the use of different model based controllers like internal model controllers and model predictive controller (MPC), where the latter has a become the most commonly used advanced control technique [17], [2], [1], [19]. The problem faced when applying MPC to the neutralization problem is to incorporate the nonlinearities into the MPC scheme without creating a too costly and time consuming minimization problem.…”

Section: Introductionmentioning

confidence: 99%

Control of pH neutralization system using nonlinear model predictive control with I-controller

Hermansson

Syafiie

2014

2014 IEEE International Conference on Industrial Engineering and Engineering Management

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In the process industry controlling the pH is considered to be one of the toughest tasks among the most commonly controlled variables. This is due to the nonlinear behavior of the pH and the time dependence of the nonlinearity, requiring an advanced controller. In this paper a multi-model nonlinear model predictive control (MMNMPC) scheme is applied to describe and handle the nonlinearities, were the multi-model description gives a piecewise linear description enabling a simple and swift computation of control moves. MPC implementation requires the knowledge, through measurement or by estimation, of the states of the neutralization system, both creating various problems. Here problem is addressed by including integral action in the controller to compensate for the unmeasured states. The MMNMPC combined with integral action is tested by simulation of a pH system in Matlab and the control structures were applied in Matlab/YALMIP showing good control performance.

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“…Model predictive control (MPC) has been the most successful advanced control technique applied in the process industries [1], [2]. Like many other model based control algorithms, the performance of MPC is directly related to model accuracy.…”

Section: Introductionmentioning

confidence: 99%

Linear offset-free model predictive control: A minimum-variance unbiased filter based approach

Wang

Zhao

et al. 2013

52nd IEEE Conference on Decision and Control

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The problem of linear offset-free model predictive control (MPC) with a minimum-variance unbiased (MVU) filter is addressed in this paper. Apart from traditional Kalman filter based approaches, a MVU filter is used in the design of a MPC system. In this framework, the disturbance is allowed to have arbitrary statistics. The MVU filter has the advantage of quick transient estimation behavior, and zero offset output estimation can be obtained for every sample time. We show that the choice of the disturbance model will not affect the estimated output as long as the rank condition is satisfied. 52nd IEEE Conference on Decision and Control

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Non‐Linear Model Predictive Control: A Personal Retrospective

Cited by 40 publications

References 31 publications

Hamiltonian two‐degrees‐of‐freedom control of chemical reactors

Hamiltonian two‐degrees‐of‐freedom control of chemical reactors

Control of pH neutralization system using nonlinear model predictive control with I-controller

Linear offset-free model predictive control: A minimum-variance unbiased filter based approach

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