Time‐varying input delay compensation for nonlinear systems with additive disturbance: An output feedback approach

This paper addresses the output feedback tracking control of a class of multiple‐input and multiple‐output nonlinear systems subject to time‐varying input delay and additive bounded disturbances. Based on the backstepping design approach, an output feedback robust controller is proposed by integrating an extended state observer and a novel robust controller, which uses a desired trajectory‐based feedforward term to achieve an improved model compensation and a robust delay compensation feedback term based on the finite integral of the past control values to compensate for the time‐varying input delay. The extended state observer can simultaneously estimate the unmeasurable system states and the additive disturbances only with the output measurement and delayed control input. The proposed controller theoretically guarantees prescribed transient performance and steady‐state tracking accuracy in spite of the presence of time‐varying input delay and additive bounded disturbances based on Lyapunov stability analysis by using a Lyapunov‐Krasovskii functional. A specific study on a 2‐link robot manipulator is performed; based on the system model and the proposed design procedure, a suitable controller is developed, and comparative simulation results are obtained to demonstrate the effectiveness of the developed control scheme.     

A new event‐driven output‐based discrete‐time control for the sporadic MIMO tracking problem

This paper presents a new sporadic control approach to the tracking problem for MIMO closed‐loop systems. An LTI sampled data plant with unmeasurable state affected by external unknown disturbances is considered. The plant is interconnected to an event‐based digital dynamic output‐feedback controller via a network. Both the external reference and the unknown disturbance are assumed to be generated as the free output response of unstable LTI systems. The main feature of the new event‐driven communication logic (CL) is that it works without the strict requirement of a state vector available for measurement. The purpose of the CL is to reduce as much as possible the number of triggered messages along the feedback and feedforward paths with respect to periodic sampling, still preserving internal stability and without appreciably degrading the control system tracking capability. The proposed event‐driven CL is composed of a sensor CL (SCL) and of a controller CL (CCL). The SCL is based on the computation of a quadratic functional of the tracking error and of a corresponding suitably computed time‐varying threshold: a network message from the sensor to the controller is triggered only if the functional equals or exceeds the current value of the threshold. The CCL is directly driven by the SCL: the dynamic output controller sends a feedforward message to the plant only if it has received a message from the sensor at the previous sampled instant. Formulation of the controller in discrete‐time form facilitates its implementation and provides a minimum inter‐event time given by the sampling period. An example taken from the related literature shows the effectiveness of the new approach. The focus of this paper is on the stability and performance loss problems relative to the sporadic nature of the control law. Other topics such as network delay or packets dropout are not considered. Copyright © 2012 John Wiley & Sons, Ltd.     

Optimal grade transition control for liquid‐propylene polymerization reactor

A nonlinear control system integrating an off‐line optimizer and a nonlinear model‐based controller is developed to perform optimal grade transition operations in a continuous pilot plant reactor. A simple black‐box model is developed and used to determine optimal trajectories of inputs and outputs for a series of three polypropylene grades. The simplified model is also used to develop a nonlinear controller. This controller is similar to generic model control; however, the integral action is omitted and an on‐line updating scheme is incorporated to update pre‐specified model parameters using delayed process measurements. The time optimal inputs, which are calculated by the off‐line optimizer, are introduced to the plant in a feedforward manner. At the same time, the deviations from the optimal output are corrected using the feedback nonlinear controller. The simulations on a complex mechanistic model of the process reveal that the nonlinear control scheme performs well for both set point tracking and disturbance rejection. This paper integrates well‐known methodologies, such as the generic‐model control algorithm, parameter update schemes, and off‐line optimization, together to develop an applicable and robust control technique for continuous polymerization reactors. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Output Feedback Stabilization for a Class of Stochastic High‐Order Feedforward Nonlinear Systems with Time‐Varying Delay

This paper considers the output feedback control problem for a class of stochastic high‐order feedforward nonlinear systems with time‐varying delay. Compared with existing works, the features of our system include different bounded time‐varying delays, more general high‐order power and homogeneous feedforward growth conditions. Firstly, we use the adding one power integrator technique to construct an output feedback controller without nonlinearities. Then, by introducing a scaling gain into the controller and choosing an appropriate Lyapunov–Krasovskii functional, the closed‐loop system can be rendered globally asymptotically stable in probability. A simulation example is provided to illustrate the effectiveness of the designed controller.     

Model reference adaptive control of discrete‐time piecewise linear systems

This article presents a switched model reference adaptive controller for discrete‐time piecewise linear systems. In the spirit of the work by Landau in the late seventies, proof of asymptotic stability of the closed‐loop error system is obtained, recasting its dynamics as a feedback system and showing the feedforward and the feedback paths are both passive. The challenge is that both paths can be piecewise linear. Numerical results show excellent performance of the proposed controller even in the face of sudden variations of the plant parameters. Copyright © 2012 John Wiley & Sons, Ltd.     

Multi-objective model-based control for an automotive catalyst

A model-based feedforward/feedback air fuel ratio controller that optimizes the oxygen storage capacity of the three-way catalyst in automotive emission control systems is presented. This work incorporates a simplified dynamic catalyst model that describes the physical behavior of oxygen chemisorption and reversible deactivation in the catalyst system. A novel aspect of this work is the use of the oxygen storage capability of the catalyst not only to minimize vehicle emissions but also to optimize engine performance and fuel economy during transient engine demand. The feedback/feedforward controller is a nonlinear model predictive controller that incorporates catalyst, engine air fuel ratio controller, and fuel system models to determine the optimal air fuel ratio target trajectory. Feedback is provided by a nonlinear moving horizon estimation strategy for the determination of the oxygen storage level of the catalyst based on air fuel ratio sensors.     

Event‐triggered output feedback H∞ control for networked control systems

This paper investigates event‐triggered output feedback H_∞ control for a networked control system. Transmitted through a network under an event‐triggered scheme, the sample outputs of the plant are used to drive the dynamical output feedback controller to generate a new control signal in the discrete‐time domain. The discrete‐time control signals are also transmitted through the network to drive the plant. As a result of two types of transmission delays, the controlled plant and the dynamical output feedback controller are driven by the discrete‐time outputs and control signals at different instants of time. An interval decomposition method is introduced to place the controlled plant and the output feedback controller into the same updated time interval but with updated signals at different instants. Based on a proper Lyapunov‐Krasovskii functional, sufficient conditions are derived to ensure H_∞ performance for the controlled plant. Finally, numerical simulations are used to demonstrate the practical utility of the proposed method.     

A feedforward–feedback controller for infinite‐dimensional systems and regulation of bounded uniformly continuous signals

We design a controller for infinite‐dimensional linear systems (with bounded control, observation and feedthrough operators) which, under certain assumptions, achieves asymptotic tracking of arbitrary bounded uniformly continuous reference signals in the presence of disturbances. The proposed controller is of feedforward–feedback type: The dynamic feedback part is used to stabilize the closed‐loop system consisting of the plant and the controller, whereas the feedforward part is tuned using the regulator equations to achieve the regulation of desired signals. We also completely solve the regulator equations for SISO systems, and we discuss robustness properties of the proposed controller. A useful feature in our design is that the feedforward part of the controller can be designed independently of the feedback part. This automatically leads to a degree of robustness in the stabilizing part of the controller, which is not present in the existing state feedback controllers solving the same output regulation problem. Copyright © 2006 John Wiley & Sons, Ltd.     

A nonlinear state‐feedback state‐feedforward tracking control strategy for a boiler‐turbine unit

A boiler‐turbine unit is a primary module for coal‐fired power plants, and an effective automatic control system is needed for the boiler‐turbine unit to track the load changes with the drum water level kept within an acceptable range. The aim of this paper is to develop a nonlinear tracking controller for the Bell‐Åström boiler‐turbine unit. A Takagi‐Sugeno fuzzy control system is introduced for the nonlinear modeling of the Bell‐Åström boiler‐turbine unit. Based on the Takagi‐Sugeno fuzzy models, a nonlinear tracking controller is developed, and the proposed control law is comprised of a state‐feedforward term and a state‐feedback term. The stability of the closed‐loop control system is analyzed on the basis of Lyapunov stability theory via the linear matrix inequality approach and Schur complement. Moreover, model uncertainties are also considered, and it is proved that with the proposed control law the tracking error converges to zero. To assess the performance of the proposed nonlinear state‐feedback state‐feedforward control strategy, a nonlinear model predictive control strategy and a linear strategy are presented as comparisons. The effectiveness and the advantages of the proposed nonlinear state‐feedback state‐feedforward control strategy are demonstrated by simulations.     

基于反馈控制的迭代学习控制器设计

针对具有不确定项或干扰项的重复非线性时变系统,提出了基于反馈控制的迭代学习控制器,其中迭代学习控制器设计为高阶PD型,它以前馈的形式作用于对象,在满足一定的收敛性条件下,证明了该控制器的跟踪误差界是系统初始状态误差界和系统输出干扰项界的线性函数,同时改变反馈增益可以调整系统的最终跟踪误差界,仿真与实验均表明了该方法的有效性。     

On the design of approximate non‐linear parametric controllers

This paper focuses on the design of non‐linear parametric controllers, around a nominal input/output trajectory of a discrete‐time non‐linear system. The main result provided herein is a relationship between the tracking performance of the closed‐loop control system in the neighbourhood of a nominal trajectory, and some local features (the first‐order linear approximations about the nominal trajectory) of the non‐linear mappings which characterize the plant and the feedback controller. Such a result can be used to predict the dynamic behaviour of the control system, and to reduce the computational complexity of the optimization task associated with the tuning of the parametric feedback controller. Copyright © 2000 John Wiley & Sons, Ltd.     

Robust control of a family of uncertain nonminimum‐phase systems via continuous‐time and sampled‐data output feedback

The problem of global robust stabilization is studied by both continuous‐time and sampled‐data output feedback for a family of nonminimum‐phase nonlinear systems with uncertainty. The uncertain nonlinear system considered in this paper has an interconnect structure consisting of a driving system and a possibly unstable zero dynamics with uncertainty, ie, the uncertain driven system. Under a linear growth condition on the uncertain zero dynamics and a Lipschitz condition on the driving system, we show that it is possible to globally robustly stabilize the family of uncertain nonminimum‐phase systems by a single continuous‐time or a sampled‐data output feedback controller. The sampled‐data output feedback controller is designed by using the emulated versions of a continuous‐time observer and a state feedback controller, ie, by holding the input/output signals constant over each sampling interval. The design of either continuous‐time or sampled‐data output compensator uses only the information of the nominal system of the uncertain controlled plant. In the case of sampled‐data control, global robust stability of the hybrid closed‐loop system with uncertainty is established by means of a feedback domination method together with the robustness of the nominal closed‐loop system if the sampling time is small enough.     

Robust adaptive feedforward control and achievable tracking for systems with time delays

A feedback/feedforward controller architecture is developed that characterises the achievable reference tracking of real time inputs for both minimum phase and non-minimum phase systems with time delays, when there are no modelling errors or external disturbances. This characterisation is obtained by factoring the plant into its minimum phase, non-minimum phase, and time delay components, which are used to design two feedforward controllers that inject signals into two points of the feedback loop. Design constraints are provided that determine both the types of signals that may be achieved, and the feedforward controllers that will generate that output. Of course, in practice, both modelling errors and external disturbances will be present. In this case, we develop robust analysis tools that both guide the feedback controller design process, and provide rigorous robust tracking performance that guarantees for the overall resulting closed-loop system. Robust methods for designing the feedforward controllers are presented, and numerical examples are provided. The performance of this architecture depends strongly on the choice of design parameters, and the accuracy of the plant model used. Hence, the use of adaptation methods is also considered, and it is shown that they can readily be employed to improve the performance of this control methodology.     

Quantized feedback control for nonlinear feedforward systems with unknown output functions and unknown control coefficients

This paper investigates the quantized feedback control for nonlinear feedforward systems with unknown output functions and unknown control coefficients. The unknown output function is Lipschitz continuous but may not be derivable, and the unknown control coefficients are assumed to be bounded. To deal with this challenging quantized control problem, a time‐varying low‐gain observer is designed and a delicate time‐varying scaling transformation is introduced, which can avoid using the derivative information of the output function. Then, based on the well‐known backstepping method and the sector bound approach, a time‐varying quantized feedback controller is designed using the quantized output, which can achieve the boundedness of the closed‐loop system states and the convergence of the original system states. Moreover, a guideline is provided for choosing the parameters of the input and output quantizers such that the closed‐loop system is stable. Finally, two simulation examples are given to show the effectiveness of the control scheme.     

Transient performance for discrete‐time singular systems with actuators saturation via composite nonlinear feedback control

This paper is concerned with the transient performance improvement in tracking control problems for linear multivariable discrete‐time singular systems subject to actuators saturation. A composite nonlinear feedback control strategy is considered, and the resulting controller consists of a linear feedback law and a nonlinear feedback law without any switching element. The nonlinear term leads to a varying damping ratio of the closed‐loop system and yields a small overshoot as the output approaches the target reference, whereas the linear component is designed to achieve a quick response of the closed‐loop system. Two composite nonlinear feedback control laws by both state feedback and measurement output feedback are addressed. An illustrative example is included to show the validity of the obtained results. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive optimal dynamic surface control of strict‐feedback nonlinear systems with output constraints

In this paper, an adaptive optimal control strategy is proposed for a class of strict‐feedback nonlinear systems with output constraints by using dynamic surface control. The controller design procedure is divided into two parts. One is the design of feedforward controller and the other is the design of optimal controller. To guarantee the satisfaction of output constraints in feedforward controller, nonlinear mapping is utilized to transform the constrained system into an unconstrained system. Neural‐network based adaptive dynamic programming algorithm is employed to approximate the optimal cost function and the optimal control law. By theoretical analysis, all the signals in the closed‐loop system are proved to be semi‐globally uniformly ultimately bounded and the output constraints are not violated. A numerical example illustrates the effectiveness of the proposed scheme.     

Observer‐Based Adaptive Output Feedback Fault Tolerant Control for Nonlinear Hydro‐Turbine Governing System with State Delay

This paper focuses on the problem of adaptive output feedback fault tolerant control for a nonlinear hydro‐turbine governing system. A dynamic mathematical model of the system is established, which aims to investigate the dynamic performance of the model under servomotor delay and actuator faults. Then, a fault estimation adaptive observer is proposed to achieve online real‐time diagnosis of system faults. Based on the online fault estimation information, an observer‐based adaptive output feedback fault tolerant controller is designed. Furthermore, under reasonable assumptions, the results demonstrate that the closed‐loop control system can achieve global asymptotic stability by Lyapunov function. Finally, the numerical simulation results are presented to indicate the satisfaction control effectiveness of the proposed scheme.     

DECOUPLING WITH STABILITY: APPLICATION TO THE REAL TIME CONTROL OF A WATER STORING PLANT

In this paper, results on decoupling with stability are applied to the real‐time control of a water storing plant. The conditions of decoupling with stability are verified on the approximate linear model of the system, and a decoupling state feedback providing pole assignment is designed. The state feedback controller achieves input‐output decoupling with stability, allowing controlling the levels of the water in the tanks independently. Simulation and experimental results are also presented showing a good performance of the designed controller.     

Two‐Stage Tracking Control Via Output Feedback

An algorithm is proposed combining a high‐gain control and an internal‐model control for asymptotic output tracking in the presence of non‐decaying external disturbances. The plant output is the only signal used in the feedback loops. The algorithm is divided into two stages: high‐gain control is activated in the transient phase, forcing the output to quickly approach the reference trajectory, and is then taken over by an internal‐model controller in the steady phase so that perfect output tracking can be achieved with moderate gains and smooth control efforts. Smooth transition between the two control laws is ensured through an internal‐model observer, which serves as a relaying mechanism between the high‐gain control and the internal‐model control.     

Two-degree-of-freedom H-infinity control of combustion in diesel engine using a discrete dynamics model

This paper proposes an H-infinity combustion control method for diesel engines. The plant model is the discrete dynamics model developed by Yasuda et al., which is implementable on a real engine control unit. We introduce a two-degree-of-freedom control scheme with a feedback controller and a feedforward controller. This scheme achieves both good feedback properties, such as disturbance suppression and robust stability, and a good transient response. The feedforward controller is designed by taking the inverse of the static plant model, and the feedback controller is designed by the H-infinity control method, which reduces the effect of the trubocharger lag. The effectiveness of the proposed method is evaluated in simulations using the nonlinear discrete dynamics model.