Pornchai Bumroongsri

An ellipsoidal off-line model predictive control strategy for linear parameter varying systems with applications in chemical processes

Abstract In this paper, a novel off-line model predictive control strategy for linear parameter varying systems is presented. The on-line computational burdens are reduced by pre-computing off-line the sequences of state feedback gains corresponding to the sequences of nested ellipsoids. The number of sequences of nested ellipsoids constructed is equal to the number of vertices of the polytope. At each sampling instant, the smallest ellipsoid containing the currently measured state is determined in each sequence of ellipsoids and the scheduling parameter is measured. The real-time state feedback gain is calculated by linear interpolation between the corresponding state feedback gains. An overall algorithm is proved to guarantee robust stability. The controller design is illustrated with two examples of continuous stirred tank reactors.

An interpolation-based robust MPC algorithm using polyhedral invariant sets

This article presents an interpolation-based robust MPC algorithm for uncertain polytopic discrete-time systems using polyhedral invariant sets. Two nested polyhedral invariant sets are constructed off-line by solving robust constrained model predictive control optimization problems. The first one is a large set constructed to cover all of the desired operating spaces. The second one is a small target set constructed to drive the terminal state into. The real-time control law is calculated by linear interpolation between the two state feedback gains corresponding to these nested precomputed polyhedral invariant sets. At each sampling instant, only a computationally low-demanding optimization problem is needed to be solved on-line. The controller design is illustrated with an example. The proposed algorithm can achieve good control performance while on-line computation is still tractable.

An Off-Line Formulation of Tube-Based Robust MPC Using Polyhedral Invariant Sets

In this paper, an off-line formulation of tube-based robust model predictive control (MPC) using polyhedral invariant sets is proposed. A novel feature is the fact that no optimal control problem needs to be solved at each sampling time. Moreover, the proposed tube-based robust MPC algorithm can deal with the linear time-varying (LTV) system with bounded disturbance. The simulation results show that the state at each time step is restricted to lie within a tube whose center is the state of the nominal LTV system that converges to the origin. Finally, the state is kept within a tube whose center is at the origin, so robust stability is guaranteed. Satisfaction of the state and control constraints is guaranteed by employing tighter constraint sets for the nominal LTV system.

An Offline Formulation of MPC for LPV Systems Using Linear Matrix Inequalities

An offline model predictive control (MPC) algorithm for linear parameter varying (LPV) systems is presented. The main contribution is to develop an offline MPC algorithm for LPV systems that can deal with both time-varying scheduling parameter and persistent disturbance. The norm-bounding technique is used to derive an offline MPC algorithm based on the parameter-dependent state feedback control law and the parameter-dependent Lyapunov functions. The online computational time is reduced by solving offline the linear matrix inequality (LMI) optimization problems to find the sequences of explicit state feedback control laws. At each sampling instant, a parameter-dependent state feedback control law is computed by linear interpolation between the precomputed state feedback control laws. The algorithm is illustrated with two examples. The results show that robust stability can be ensured in the presence of both time-varying scheduling parameter and persistent disturbance.

Simultaneous estimation of thin film thickness and optical properties using two-stage optimization

In this work, we proposed the new method for estimation of the thickness and the optical properties of the thin metal oxide film deposited on a transparent substrate. The developed method uses only transmittance spectra measured. Our method is based on the two stage optimization where the thickness is determined in the outer stage and the optical properties are determined in the inner stage. The differential evolutionary algorithm is used in solving the formulated problem. The proposed method was illustrated in the case study of Titanium dioxide film deposited on a glass substrate. The results indicate that the thickness and the optical properties estimated agree well with the experiment. Moreover, we investigated robustness of the proposed method in the case of transmittance spectra containing noises. The data were modelled by adding random noises ranging between 0 and 30% to the transmittance spectra measured. It is seen that the proposed method has better robustness and performance than the existing method based on pointwise unconstrained minimization approach. In solving the estimation problem, the performance of the proposed method was also compared with the well-known Levenberg–Marquardt method and single stage differential evolutionary method. The results indicate that the proposed method has better performance than Levenberg–Marquardt method and single stage differential evolutionary method. Moreover, the proposed method is more robust to random noise than Levenberg–Marquardt method and single stage differential evolutionary method.

Off-Line Robust Constrained MPC for Linear Time-Varying Systems with Persistent Disturbances

An off-line robust constrained model predictive control (MPC) algorithm for linear time-varying (LTV) systems is developed. A novel feature is the fact that both model uncertainty and bounded additive disturbance are explicitly taken into account in the off-line formulation of MPC. In order to reduce the on-line computational burdens, a sequence of explicit control laws corresponding to a sequence of positively invariant sets is computed off-line. At each sampling time, the smallest positively invariant set containing the measured state is determined and the corresponding control law is implemented in the process. The proposed MPC algorithm can guarantee robust stability while ensuring the satisfaction of input and output constraints. The effectiveness of the proposed MPC algorithm is illustrated by two examples.

MPC for LPV systems using perturbation on control input strategy

Abstract In this paper, a model predictive control (MPC) algorithm for linear parameter varying (LPV) systems is proposed. The proposed algorithm consists of two steps. The first step is derived by using parameter-dependent Lyapunov function and the second step is derived by using the perturbation on control input strategy. An overall algorithm is proved to guarantee robust stability. The controller design is illustrated with a case study of continuous stirred-tank reactor. Comparisons with other MPC algorithms for LPV systems have been undertaken. The results show that the proposed algorithm can achieve better control performance.

Interpolation techniques in robust constrained model predictive control

This work investigates interpolation techniques that can be employed on off-line robust constrained model predictive control for a discrete time-varying system. A sequence of feedback gains is determined by solving off-line a series of optimal control optimization problems. A sequence of nested corresponding robustly positive invariant set, which is either ellipsoidal or polyhedral set, is then constructed. At each sampling time, the smallest invariant set containing the current state is determined. If the current invariant set is the innermost set, the pre-computed gain associated with the innermost set is applied. If otherwise, a feedback gain is variable and determined by a linear interpolation of the pre-computed gains. The proposed algorithms are illustrated with case studies of a two-tank system. The simulation results showed that the proposed interpolation techniques significantly improve control performance of off-line robust model predictive control without much sacrificing on-line computational ...

Implementation of Model Predictive Control in Industrial Gasoline Desulfurization Process

Abstract Sulfur is an important pollutant that can severely prevent an implementation of all major pollution control strategies. Thus, to reduce air pollution and to comply with strict environmental regulations, sulfur content in all types of fuel produced is required to be lowered to a certain level. A selective desulfurization process is used to reduce sulfur content of fluidized catalytic cracked (FCC) naphtha, which is a blending component for gasoline product. Though, the desulfurization process can considerably lower sulfur content of the naphtha. Some undesirable olefin saturation reactions are also occurred, resulting in octane loss of the gasoline product. The octane loss depressingly influences economic performances of the plant. Thus, optimizing the operation in order to minimize the octane loss while still complying with sulfur specification and other process constraints is necessary. The operation optimization can be accomplished by implementing model predictive control (MPC). In this work, we focus on the implementation of MPC in the selective desulfurization process in order to strictly control sulfur content in the gasoline product while minimizing octane loss. A soft-sensor for on-line estimating sulfur content in gasoline product was designed and implemented. A series of step tests were performed to build empirical dynamic models. The models obtained were validated and used in MPC design. Analysis of benefit was performed with data collected before and after MPC implementation. The results showed that after MPC implementation, the control performances were improved by shifting mean of sulfur content in product close to the high limit operation. Thus, energy consumption was significantly decreased.

Off-Line Tube-Based Robust Model Predictive Control for Uncertain and Highly Exothermic Polymerization Processes

Abstract Polymerization processes usually contain some uncertain parameters such as those in kinetic rate constants and heat transfer coefficients. An inefficient handling of these uncertain parameters may lead to unexpected thermal runaway of the reaction. In this paper, off-line tube-based robust model predictive control (MPC) is developed. The trajectories of uncertain systems are restricted to lie in a sequence of tubes so robust stability and constraint satisfaction are guaranteed in the presence of both uncertain parameters and disturbances. All of the optimization problems are solved off-line so the proposed algorithm is applicable to fast dynamic polymerization processes. The proposed algorithm is applied to an illustrative example of continuous stirred tank reactor where highly exothermic polymerization reactions occur. The results show that robust stability and constraint satisfaction are guaranteed.