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.     

Robust MPC for tracking zone regions based on nominal predictions

This paper deals with the problem of robust tracking of target sets using a model predictive control (MPC) law. Real industries applications often require a control strategy in which some system outputs are controlled within specified ranges or zones (zone control), while some others variables – possibly including input variables – are steered to fixed target or setpoint. 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. This problem is particularly interesting in case of additive disturbances which might push the outputs out of the zones. In this work, a stable robust MPC formulation for constrained linear systems, based on nominal predictions is presented. The main features of this controller are the use of nominal predictions, restricted constraints and the concept of distance from a point to a set as offset cost function. The controller ensures both recursive feasibility and local optimality. The properties of the controller are shown in a simulation test, in which we consider a subsystem of an industrial FCC system.     

Closed-loop stable model predictive control of integrating systems with dead time

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.     

Stability of model predictive control with mixed constraints

We derive stability conditions for model predictive control (MPC) with hard constraints on the inputs and “soft” constraints on the outputs for an infinitely long output horizon. We show that with state feedback, MPC is globally asymptotically stabilizing if and only if all the eigenvalues of the open loop system are in the closed unit disk. With output feedback, we show that the results hold if all the eigenvalues are strictly inside the unit circle. The online optimization problem defining MPC can be posed as a finite dimensional quadratic program even though the output constraints are specified over an infinite horizon     

Globally Stable Adaptive Tracking Control for Uncertain Strict‐Feedback Systems Based on Neural Network Approximation

This paper addresses the problem of globally stable adaptive neural tracking control for a class of strict‐feedback nonlinear systems. Compared with the existing works, the salient properties of the proposed scheme are given as follows. First, a novel switching controller is developed, which consists of a traditional adaptive neural controller and an extra robust controller to pull back the transient outside of the approximation domain. Second, only two adaptive parameters need to be tuned online, and the computational burden is considerably alleviated in practice. Third, to design the desired switching controller via the backstepping technique, a novel switching function, which has continuous derivatives up to the nth order, is constructed. It is shown that the system output converges to a small neighborhood of the reference signal and the closed‐loop system is globally stable. Finally, an example is provided to verify the effectiveness of the proposed control method.     

Almost output regulation of switched linear dynamics with switched exosignals

For systems with switched linear dynamics and affected by persistent switched exosignals, we propose a new hybrid control approach to achieve not only closed‐loop stability but also tracking and/or rejection of persistent references/disturbances generated by multiple exosystems, namely, output regulation. It is assumed that both controlled plant and exosystem are described by switched linear models. The proposed hybrid controller/output regulator is specified as a switching impulsive system, where the controller states will undergo impulsive jumps at each switching instant. Based on the average dwell time switching technique, it has been shown how to completely reduce the synthesis problem of the hybrid controller to a set of linear matrix equations and linear matrix inequalities. Both continuous‐time and discrete‐time cases are discussed. To demonstrate its usefulness, the proposed hybrid control method has been applied to solve the output regulation problem for a mechanical system. Copyright © 2017 John Wiley & Sons, Ltd.     

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.     

Model based approach to closed loop control of 1-D engine simulation models

1-D engine simulation models are widely used for the analysis and verification of air-path design concepts to assess performance and therefore determine suitable hardware. The transient response is a key driver in the selection process which in most cases requires closed loop control of the model to ensure operation within prescribed physical limits and tracking of reference signals. Since the controller effects the system performance a systematic procedure which achieves close-to-optimal performance is desired, if the full potential of a given hardware configuration is to be properly assessed. For this purpose a particular implementation of Model Predictive Control (MPC) based on a corresponding Mean Value Engine Model (MVEM) is reported here. The MVEM is linearised on-line at each operating point to allow for the formulation of quadratic programming (QP) problems, which are solved as the part of the proposed MPC algorithm. The MPC output is used to control a 1-D engine model. The closed loop performance of such a system is benchmarked against the solution of a related optimal control problem (OCP). The system is also tested for operation at high altitude conditions to demonstrate the ability of the controller to respect specified physical constraints. As an example this study is focused on the transient response of a light-duty automotive Diesel engine. For the cases examined the proposed controller design gives a more systematic procedure than other ad hoc approaches that require considerable tuning effort.     

Stability and robust position control of hysteretic systems

Position control of a wide class of hysteretic systems, which includes those described by a Preisach model, is considered. The main focus of this paper is stability, tracking and the trajectories of a hysteretic system controlled by a PI controller. The system output (not its derivative) is measured and controlled. It is shown that, for arbitrary reference signals, the closed‐loop system is bounded‐input–bounded‐output‐stable with a finite gain of one. Furthermore, the absolute value of the error decreases monotonically for a constant reference signal. In this case, provided that the desired output is within the limits of the system output, zero steady‐state error is guaranteed. A bound on the time required to achieve a specified error is obtained. Only a simple condition on the controller parameters is required. The results imply that stability and position control are guaranteed, even if large errors in the model exist. Copyright © 2009 John Wiley & Sons, Ltd.     

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 an 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.     

Zone model predictive control for pressure management of water distribution network

In the water distribution network (WDN), although the water demand of the node is changing constantly, the water quantity and water pressure of the node need to be met at each moment. To realize energy saving and consumption reduction, it is proposed to control the nodal water head of WDN in an appropriate narrow range. The frequent large fluctuation of the water demand, which may lead the water pressure exceed the expected range, increases the difficulty of the zone control. To realize optimized WND control, a novel zone predictive control is proposed, where two switching cases are considered. The switching condition is whether there are feasible solutions to keep the pressure within the expected region over the prediction horizon. When the condition is satisfied, the controller minimizes the variation of inputs with constraints of pressure range for ensuring the tank level staying within the expected zone and obtaining optimal economic cost. When the current pressure is out of the expected region or the condition is not satisfied due to the large variation of water demand, a reference trajectory of outputs is introduced, which is combined with the inputs as an optimization variable, and the constraints of expected zone are moved from the output to the introduced reference trajectory. Through minimizing the distance between reference trajectory and output, the controller will keep the tank level from deviating too far from the expected zone and will drive the tank level rapidly into the expected zone once the tank level exceeds the expected range. An application of the proposed zone MPC to WDN in Shinan District of Shanghai is given to illustrate its effectiveness.     

Decentralized stabilization of Markovian jump interconnected systems with unknown interconnections and measurement errors

This paper investigates the decentralized output feedback control problem for Markovian jump interconnected systems with unknown interconnections and measurement errors. Different from some existing results, the global operation modes of all subsystems are not required to be completely accessible for the decentralized control system. A decentralized dynamic output feedback controller is constructed using neighboring mode information and local outputs, where the measurement errors between actual and measured outputs are considered. Subsequently, a new design method is developed such that the resultant closed‐loop system is stochastically stable and satisfying an L_∞‐norm constraint. Sufficient conditions are formulated by linear matrix inequalities, and the controller gains are characterized in terms of the solution of a convex optimization problem. Finally, an example is given to illustrate the effectiveness of the proposed theoretical results.     

Fault diagnosis and accommodation of nonlinear systems based on multiple-model adaptive unscented Kalman filter and switched MPC and H-infinity loop-shaping controller

In this paper, a new active fault tolerant control (AFTC) methodology is proposed based on a state estimation scheme for fault detection and identification (FDI) to deal with the potential problems due to possible fault scenarios. A bank of adaptive unscented Kalman filters (AUKFs) is used as a core of FDI module. The AUKF approach alleviates the inflexibility of the conventional UKF due to constant covariance set up, leading to probable divergence. A fuzzy-based decision making (FDM) algorithm is introduced to diagnose sensor and/or actuator faults. The proposed FDI approach is utilized to recursively correct the measurement vector and the model used for both state estimation and output prediction in a model predictive control (MPC) formulation. Robustness of the proposed FTC system, H_∞ optimal robust controller and MPC are combined via a fuzzy switch that is used for switching between MPC and robust controller such that FTC system is able to maintain the offset free behavior in the face of abrupt changes in model parameters and unmeasured disturbances. This methodology is applied on benchmark three-tank system; the proposed FTC approach facilitates recovery of the closed loop performance after the faults have been isolated leading to an offset free behavior in the presence of sensor/actuator faults that can be either abrupt or drift change in biases. Analysis of the simulation results reveals that the proposed approach provides an effective method for treating faults (biases/drifts in sensors/actuators, changes in model parameters and unmeasured disturbances) under the unified framework of robust fault tolerant control.     

Robust output feedback model predictive control of constrained linear systems: Time varying case

The problem of output feedback model predictive control of discrete time systems in the presence of additive but bounded state and output disturbances is considered. The overall controller consists of two components, a stable state estimator and a tube based, robustly stabilizing model predictive controller. Earlier results are extended by allowing the estimator to be time varying. The proposed robust output feedback controller requires the online solution of a standard quadratic program. The closed loop system renders a specified invariant set robustly exponentially stable.     

Robust control and fault detection for continuous‐time switched systems subject to a dwell time constraint

This paper is concerned with the simultaneous robust control and fault detection problem for continuous‐time switched systems subject to a dwell time constraint. To meet the control and detection objectives under the constraint, the controller/detectors matching different time intervals are first constructed in an output feedback framework. A state‐dependent switching law that obeys the dwell time constraint is then designed such that the closed‐loop switched system is asymptotically stable and also with the robust and detection performance. Further, the proposed switching law is dependent only on the partial measurable states of the closed‐loop system, which is applicable when the states of system mode are fully unavailable. Thus, our result extends the existing ones in state‐dependent switching and state‐feedback frameworks. Finally, a numerical example is given to illustrate the effectiveness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

Delay‐dependent anti‐windup strategy for linear systems with saturating inputs and delayed outputs

This paper addresses the problem of the determination of stability regions for linear systems with delayed outputs and subject to input saturation, through anti‐windup strategies. A method for synthesizing anti‐windup gains aiming at maximizing a region of admissible states, for which the closed‐loop asymptotic stability and the given controlled output constraints are respected, is proposed. Based on the modelling of the closed‐loop system resulting from the controller plus the anti‐windup loop as a linear time‐delay system with a dead‐zone nonlinearity, constructive delay‐dependent stability conditions are formulated by using both quadratic and Lure Lyapunov–Krasovskii functionals. Numerical procedures based on the solution of some convex optimization problems with LMI constraints are proposed for computing the anti‐windup gain that leads to the maximization of an associated stability region. The effectiveness of the proposed technique is illustrated by some numerical examples. Copyright © 2004 John Wiley & Sons, Ltd.     

An inverse dynamics control strategy for tip position tracking of flexible multi-link manipulators

In this article, we present an inverse dynamics control strategy to achieve small tracking errors for a class of multi-link structurally flexible manipulators. This is done by defining new outputs near the end points of the arms as well as by augmenting the control inputs by terms that ensure stable operation of the closed loop system under specific conditions. The controller is designed in a two-step process. First, a new output is defined such that the zero dynamics of the original system are stabilized. Next, to ensure stable asymptotic tracking, the control input is modified such that stable asymptotic tracking of the new output or approximate tracking of the actual output may be achieved. This is illustrated for the case of single- and two-link flexible manipulators. ©1997 John Wiley & Sons, Inc.     

一类非线性多变量系统的多模型自适应控制

针对一类不确定的非线性多变量离散时间动态系统,提出了一种基于切换的多模型自适应控制方法.该控制方法的特点在于以下两个方面:首先,引入一个高阶差分算子使得非线性系统的非线性项的限制条件不再要求全局有界;其次,提出的控制方法由线性自适应控制器、神经网络非线性自适应控制器以及切换机构组成:线性控制器用来保证闭环系统的输入输出信号有界,神经网络非线性控制器用来改善闭环系统的性能,基于性能指标的切换机构在每一时刻选择性能指标较好的控制器对系统进行控制.理论分析和仿真实验说明了提出的多模型自适应控制方法的有效性.     

Disturbance modeling for offset-free linear model predictive control

An offset-free controller is one that drives controlled outputs to their desired targets at steady state. In the linear model predictive control (MPC) framework, offset-free control is usually achieved by adding step disturbances to the process model. The most widely-used industrial MPC implementations assume a constant output disturbance that can lead to sluggish rejection of disturbances that enter the process elsewhere. This paper presents a general disturbance model that accommodates unmeasured disturbances entering through the process input, state, or output. Conditions that guarantee detectability of the augmented system model are provided, and a steady-state target calculation is constructed to remove the effects of estimated disturbances. Conditions for which offset-free control is possible are stated for the combined estimator, steady-state target calculation, and dynamic controller. Simulation examples are provided to illustrate trade-offs in disturbance model design.     

Distributed model predictive control for constrained linear systems

We address the distributed model predictive control (MPC) for a set of linear local systems with decoupled dynamics and a coupled global cost function. By the decomposition of the global cost function, the distributed control problem is converted to the MPC for each local system associated with a cost involving neighboring system states and inputs. For each local controller, the infinite horizon control moves are parameterized as N free control moves followed by a single state feedback law. An interacting compatibility condition is derived, disassembled and incorporated into the design of each local control so as to achieve the stability of the global closed‐loop system. Each local system exchanges with its neighbors the current states and the previous optimal control strategies. The global closed‐loop system is shown to be exponentially stable provided that all the local optimizers are feasible at the initial time. Copyright © 2009 John Wiley & Sons, Ltd.