MPC for tracking zone regions

This paper deals with the problem of tracking target sets using a model predictive control (MPC) law. Some MPC applications require a control strategy in which some system outputs are controlled within specified ranges or zones (zone control), while some other variables - possibly including input variables - are steered to fixed target or set-point. In real applications, this problem is often overcome by including and excluding an appropriate penalization for the output errors in the control cost function. In this way, throughout the continuous operation of the process, the control system keeps switching from one controller to another, and even if a stabilizing control law is developed for each of the control configurations, switching among stable controllers not necessarily produces a stable closed loop system. From a theoretical point of view, the control objective of this kind of problem can be seen as a target set (in the output space) instead of a target point, since inside the zones there are no preferences between one point or another. In this work, a stable MPC formulation for constrained linear systems, with several practical properties is developed for this scenario. The concept of distance from a point to a set is exploited to propose an additional cost term, which ensures both, recursive feasibility and local optimality. The performance of the proposed strategy is illustrated by simulation of an ill-conditioned distillation column. (C) 2010 Elsevier Ltd. All rights reserved.

Infinite horizon MPC with non-minimal state space feedback

In the MPC literature, stability is usually assured under the assumption that the state is measured. Since the closed-loop system may be nonlinear because of the constraints, it is not possible to apply the separation principle to prove global stability for the Output feedback case. It is well known that, a nonlinear closed-loop system with the state estimated via an exponentially converging observer combined with a state feedback controller can be unstable even when the controller is stable. One alternative to overcome the state estimation problem is to adopt a non-minimal state space model, in which the states are represented by measured past inputs and outputs [P.C. Young, M.A. Behzadi, C.L. Wang, A. Chotai, Direct digital and adaptative control by input-output, state variable feedback pole assignment, International journal of Control 46 (1987) 1867-1881; C. Wang, P.C. Young, Direct digital control by input-output, state variable feedback: theoretical background, International journal of Control 47 (1988) 97-109]. In this case, no observer is needed since the state variables can be directly measured. However, an important disadvantage of this approach is that the realigned model is not of minimal order, which makes the infinite horizon approach to obtain nominal stability difficult to apply. Here, we propose a method to properly formulate an infinite horizon MPC based on the output-realigned model, which avoids the use of an observer and guarantees the closed loop stability. The simulation results show that, besides providing closed-loop stability for systems with integrating and stable modes, the proposed controller may have a better performance than those MPC controllers that make use of an observer to estimate the current states. (C) 2008 Elsevier Ltd. All rights reserved.

Robust model predictive control with zone control

Model predictive control (MPC) is usually implemented as a control strategy where the system outputs are controlled within specified zones, instead of fixed set points. One strategy to implement the zone control is by means of the selection of different weights for the output error in the control cost function. A disadvantage of this approach is that closed-loop stability cannot be guaranteed, as a different linear controller may be activated at each time step. A way to implement a stable zone control is by means of the use of an infinite horizon cost in which the set point is an additional variable of the control problem. In this case, the set point is restricted to remain inside the output zone and an appropriate output slack variable is included in the optimisation problem to assure the recursive feasibility of the control optimisation problem. Following this approach, a robust MPC is developed for the case of multi-model uncertainty of open-loop stable systems. The controller is devoted to maintain the outputs within their corresponding feasible zone, while reaching the desired optimal input target. Simulation of a process of the oil re. ning industry illustrates the performance of the proposed strategy.

A stable MPC with zone control

Several MPC applications implement a control strategy in which some of the system outputs are controlled within specified ranges or zones, rather than at fixed set points [J.M. Maciejowski, Predictive Control with Constraints, Prentice Hall, New Jersey, 2002]. This means that these outputs will be treated as controlled variables only when the predicted future values lie outside the boundary of their corresponding zones. The zone control is usually implemented by selecting an appropriate weighting matrix for the output error in the control cost function. When an output prediction is inside its zone, the corresponding weight is zeroed, so that the controller ignores this output. When the output prediction lies outside the zone, the error weight is made equal to a specified value and the distance between the output prediction and the boundary of the zone is minimized. The main problem of this approach, as long as stability of the closed loop is concerned, is that each time an output is switched from the status of non-controlled to the status of controlled, or vice versa, a different linear controller is activated. Thus, throughout the continuous operation of the process, the control system keeps switching from one controller to another. Even if a stabilizing control law is developed for each of the control configurations, switching among stable controllers not necessarily produces a stable closed loop system. Here, a stable M PC is developed for the zone control of open-loop stable systems. Focusing on the practical application of the proposed controller, it is assumed that in the control structure of the process system there is an upper optimization layer that defines optimal targets to the system inputs. The performance of the proposed strategy is illustrated by simulation of a subsystem of an industrial FCC system. (C) 2008 Elsevier Ltd. All rights reserved.

A Separation Principle for the Continuous-Time LQ-Problem With Markovian Jump Parameters

In this paper, we devise a separation principle for the finite horizon quadratic optimal control problem of continuous-time Markovian jump linear systems driven by a Wiener process and with partial observations. We assume that the output variable and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time. As in the case with no jumps, we show that an optimal controller can be obtained from two coupled Riccati differential equations, one associated to the optimal control problem when the state variable is available, and the other one associated to the optimal filtering problem. This is a separation principle for the finite horizon quadratic optimal control problem for continuous-time Markovian jump linear systems. For the case in which the matrices are all time-invariant we analyze the asymptotic behavior of the solution of the derived interconnected Riccati differential equations to the solution of the associated set of coupled algebraic Riccati equations as well as the mean square stabilizing property of this limiting solution. When there is only one mode of operation our results coincide with the traditional ones for the LQG control of continuous-time linear systems.

Generation of self-similar Gaussian time series by means of the DWT and DWPT variance maps

Due to the several kinds of services that use the Internet and data networks infra-structures, the present networks are characterized by the diversity of types of traffic that have statistical properties as complex temporal correlation and non-gaussian distribution. The networks complex temporal correlation may be characterized by the Short Range Dependence (SRD) and the Long Range Dependence - (LRD). Models as the fGN (Fractional Gaussian Noise) may capture the LRD but not the SRD. This work presents two methods for traffic generation that synthesize approximate realizations of the self-similar fGN with SRD random process. The first one employs the IDWT (Inverse Discrete Wavelet Transform) and the second the IDWPT (Inverse Discrete Wavelet Packet Transform). It has been developed the variance map concept that allows to associate the LRD and SRD behaviors directly to the wavelet transform coefficients. The developed methods are extremely flexible and allow the generation of Gaussian time series with complex statistical behaviors.

Some remarks on static-feedback linearization for time-varying systems

This work summarizes some results about static state feedback linearization for time-varying systems. Three different necessary and sufficient conditions are stated in this paper. The first condition is the one by [Sluis, W. M. (1993). A necessary condition for dynamic feedback linearization. Systems & Control Letters, 21, 277-283]. The second and the third are the generalizations of known results due respectively to [Aranda-Bricaire, E., Moog, C. H., Pomet, J. B. (1995). A linear algebraic framework for dynamic feedback linearization. IEEE Transactions on Automatic Control, 40, 127-132] and to [Jakubczyk, B., Respondek, W. (1980). On linearization of control systems. Bulletin del` Academie Polonaise des Sciences. Serie des Sciences Mathematiques, 28, 517-522]. The proofs of the second and third conditions are established by showing the equivalence between these three conditions. The results are re-stated in the infinite dimensional geometric approach of [Fliess, M., Levine J., Martin, P., Rouchon, P. (1999). A Lie-Backlund approach to equivalence and flatness of nonlinear systems. IEEE Transactions on Automatic Control, 44(5), 922-937]. (C) 2008 Elsevier Ltd. All rights reserved.

Dynamic positioning systems: An experimental analysis of sliding mode control

Vessel dynamic positioning (DP) systems are based on conventional PID-type controllers and an extended Kalman filter. However, they present a difficult tuning procedure, and the closed-loop performance varies with environmental or loading conditions since the dynamics of the vessel are eminently nonlinear. Gain scheduling is normally used to address the nonlinearity of the system. To overcome these problems, a sliding mode control was evaluated. This controller is robust to variations in environmental and loading conditions, it maintains performance and stability for a large range of conditions, and presents an easy tuning methodology. The performance of the controller was evaluated numerically and experimentally in order to address its effectiveness. The results are compared with those obtained from conventional PID controller. (c) 2010 Elsevier Ltd. All rights reserved.

On state representations of time-varying nonlinear systems

This work considers a nonlinear time-varying system described by a state representation, with input u and state x. A given set of functions v, which is not necessarily the original input u of the system, is the (new) input candidate. The main result provides necessary and sufficient conditions for the existence of a local classical state space representation with input v. These conditions rely on integrability tests that are based on a derived flag. As a byproduct, one obtains a sufficient condition of differential flatness of nonlinear systems. (C) 2009 Elsevier Ltd. All rights reserved.

Closed-loop model re-identification of processes under MPC with zone control

This work deals with a procedure for model re-identification of a process in closed loop with ail already existing commercial MPC. The controller considered here has a two-layer structure where the upper layer performs a target calculation based on a simplified steady-state optimization of the process. Here, it is proposed a methodology where a test signal is introduced in a tuning parameter of the target calculation layer. When the outputs are controlled by zones instead of at fixed set points, the approach allows the continuous operation of the process without an excessive disruption of the operating objectives as process constraints and product specifications remain satisfied during the identification test. The application of the method is illustrated through the simulation of two processes of the oil refining industry. (c) 2008 Elsevier Ltd. All rights reserved.

Environmental impact evaluation using a cooperative model for implementing EMS (ISO 14001) in small and medium-sized enterprises

Certification of an ISO 14001 Environmental Management System (EMS) is currently an important requirement for those enterprises wishing to sell their products in the context of a global market. The system`s structure is based on environmental impact evaluation (EIE). However, if an erroneous or inadequate methodology is applied, the entire process may be jeopardized. Many methodologies have been developed for making of EIEs, some of them are fairly complex and unsuitable for EMS implementation in an organizational context, principally when small and medium size enterprises (SMEs) are involved. The proposed methodology for EIE is part of a model for implementing EMS. The methodological approach used was a qualitative exploratory research method based upon sources of evidence such as document analyses, semi-structured interviews and participant observations. By adopting a cooperative implementation model based on the theory of system engineering, difficulties relating to implementation of the sub-system were overcome thus encouraging SMEs to implement EMS. (C) 2007 Elsevier Ltd. All rights reserved.

Highly integrated and automated high-speed grinding system for printer heads constructed by combination materials

The fabrication of heavy-duty printer heads involves a great deal of grinding work. Previously in the printer manufacturing industry, four grinding procedures were manually conducted in four grinding machines, respectively. The productivity of the whole grinding process was low due to the long loading time. Also, the machine floor space occupation was large because of the four separate grinding machines. The manual operation also caused inconsistent quality. This paper reports the system and process development of a highly integrated and automated high-speed grinding system for printer heads. The developed system, which is believed to be the first of its kind, not only produces printer heads of consistently good quality, but also significantly reduces the cycle time and machine floor space occupation.

Controllability of Volterra-Fredholm type systems in Banach spaces

We show the results in Chalishajar [Controllability of mixed Volterra-Fredholm-type integro-differential systems in Banach space, J. Franklin Inst. 344(1) (2007) 12-21] and Chang and Chalishajar [Controllability of mixed Volterra-Fredholm type integro-differential systems in Banach space, J. Franklin Inst., doi:10.1016/j. jfranklin.2008.02.002] are only valid for ordinary differential control systems. As a result the examples provided cannot be recovered as applications of the abstract results. (C) 2008 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Robust model-order reduction of complex biological processes

This paper addresses robust model-order reduction of a high dimensional nonlinear partial differential equation (PDE) model of a complex biological process. Based on a nonlinear, distributed parameter model of the same process which was validated against experimental data of an existing, pilot-scale BNR activated sludge plant, we developed a state-space model with 154 state variables in this work. A general algorithm for robustly reducing the nonlinear PDE model is presented and based on an investigation of five state-of-the-art model-order reduction techniques, we are able to reduce the original model to a model with only 30 states without incurring pronounced modelling errors. The Singular perturbation approximation balanced truncating technique is found to give the lowest modelling errors in low frequency ranges and hence is deemed most suitable for controller design and other real-time applications. (C) 2002 Elsevier Science Ltd. All rights reserved.

Considerations on the Least Upper Bound for Mixed-Criticality Real-Time Systems

5th Brazilian Symposium on Computing Systems Engineering, SBESC 2015 (SBESC 2015). 3 to 6, Nov, 2015. Foz do Iguaçu, Brasil.