Global tracking of nonlinear systems with simultaneous unknown time‐varying state and input delays

This paper presents the design of a robust control law for a class of nonlinear dynamical systems subjected to parametric uncertainty and simultaneous unknown, variable state and input delays. A novel controller is developed, which consists of a filtered tracking error and the integral of previous values of control input where the limits of integration are dependent on the known bound of the input delay. Lyapunov‐Krasovskii functionals–based stability analysis guarantees a global uniformly ultimately bounded tracking result where sufficient conditions on controller gains and maximum allowable delay are derived. The performance and robustness of the controller are evaluated by simulation on a two‐link robot manipulator for different combinations of time‐varying state and input delays.     

Anti‐windup design of active disturbance rejection control for sampled systems with input delay

A novel anti‐windup design of active disturbance rejection control (ADRC) is proposed for industrial sampled systems with input delay and saturation. By using a generalized predictor to estimate the delay‐free system output, a modified extended state observer is designed to simultaneously estimate the system state and disturbance, which could become an anti‐windup compensator when the input saturation occurs. Accordingly, a feedback controller is analytically designed for disturbance rejection. By proposing the desired closed‐loop transfer function for the set‐point tracking, a prefilter is designed to tune the tracking performance while guaranteeing no steady‐state output tracking error. A sufficient condition for the closed‐loop system stability is established with proof for practical application subject to the input delay variation. Illustrative examples from the literature are used to demonstrate the effectiveness and merit of the proposed control design.     

A STABLE ON‐LINE SELF‐TUNING OPTIMAL PID CONTROLLER FOR A CLASS OF UNKNOWN SYSTEMS

In this paper, a novel self‐tuning method of optimal PID control laws is proposed for both continuous‐time systems and discrete‐time systems. The controlled plant is assumed to be unknown except the system order (or system delay) and the direction of transmitting control input. Through the minimization of PID gains subject to the Lyapunov stability based reaching condition, the tuning of the three PID control gains is transformed to solve the inequality constraint optimization problem. An unknown SISO nonlinear system subject to a unit step input, and the tracking control problem of the piezoelectric actuator (PZA) with unknown dynamics are simulated. The simulation results show that the excellent tracking performance can be achieved.     

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.     

Adaptive Friction Compensation: Modular Design with Passive Identifier

For a second‐order mechanical system incorporating Coulomb frictional effect, a nonlinear adaptive control that achieves a controller‐identifier separation is designed. This modularity is made possible by the strong input‐to‐state stability (ISS) property of the ISS controller with respect to the parameter estimation error as input. This input is independently guaranteed to be bounded by the passive identifier. We use two types of passive identifiers: z‐scheme passive identifier and x‐scheme passive identifier. These designs are more flexible than the Lyapunov‐based design and lead to lower control effort. In addition, the advantages and disadvantages of z‐scheme and x‐scheme are presented. Transient performance of the system is enhanced with a trajectory initialization technique. The validity and effectiveness of the proposed friction compensator is verified by simulation for position tracking control under the influence of Coulomb friction.     

Output feedback tracking control by additive state decomposition for a class of uncertain systems

Besides parametric uncertainties and disturbances, unmodelled dynamics and time delay at the input are often present in practical systems, and cannot always be ignored. This paper aims to solve the problem of output feedback tracking control for a class of non-linear uncertain systems subject to unmodelled high-frequency gains and time delay in the input. By additive state decomposition, the uncertain system is transformed to an uncertainty-free system, in which the uncertainties, disturbances and effects of unmodelled dynamics along with time delay are lumped into a new disturbance at the output. Subsequently, additive state decomposition is used to decompose the transformed system to simplify the tracking controller design. The proposed control scheme is applied to three benchmark examples to demonstrate its effectiveness.     

Finite‐time angular velocity observers for rigid‐body attitude tracking with bounded inputs

The attitude tracking of a rigid body without angular velocity measurements is addressed. A continuous angular velocity observer with fractional power functions is proposed to estimate the angular velocity via quaternion attitude information. The fractional power gains can be properly tuned according to a homogeneous method such that the estimation error system is uniformly almost globally finite‐time stable, irrespective of control inputs. To achieve output feedback attitude tracking control, a quaternion‐based nonlinear proportional‐derivative controller using full‐state feedback is designed first, yielding uniformly almost globally finite‐time stable of the attitude tracking system as well as bounded control torques a priori. It is then shown that the certainty equivalent combination of the observer and nonlinear proportional‐derivative controller ensures finite‐time convergence of the attitude tracking error for almost all initial conditions. The proposed methods not only avoid high‐gain injection, as opposed to the semi‐global results, but also overcome the unwinding problem associated with some quaternion‐based observers and/or controllers. Numerical simulations are presented to verify the effectiveness of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd.     

姿态变化一致有界的姿态稳定控制器设计

针对航天器姿态稳定控制问题, 设计一种迭代学习姿态控制器. 将连续非周期运动的姿态跟踪过程分解为队列重复运动, 采用前一周期的姿态跟踪误差修正后一周期的控制输入, 分别对未知参数和干扰构建有界迭代学习律, 给出航天器姿态稳定控制器, 并从理论上分析了闭环系统的渐近稳定性和姿态跟踪误差的一致有界性. 通过在轨捕获非合作目标过程中航天器姿态跟踪控制问题的数值仿真, 验证了迭代学习控制器的鲁棒性和强抗干扰性.

     

Design of UDE‐based controllers from their two‐degree‐of‐freedom nature

The control algorithm based on the uncertainty and disturbance estimator (UDE) is a robust control strategy and has received wide attention in recent years. In this paper, the two‐degree‐of‐freedom nature of UDE‐based controllers is revealed. The set‐point tracking response is determined by the reference model, whereas the disturbance response and robustness are determined by the error feedback gain and the filter introduced to estimate the uncertainty and disturbances. It is also revealed that the error dynamics of the system is determined by two filters, of which one is determined by the error feedback gain and the other is determined by the filter introduced to estimate the uncertainty and disturbances. The design of these two filters are decoupled in the frequency domain. Moreover, after introducing the UDE‐based control, the Laplace transform can be applied to some time‐varying systems for analysis and design because all the time‐varying parts are lumped into a signal. It has been shown that, in addition to the known advantages over the time‐delay control, the UDE‐based control also brings better performance than the time‐delay control under the same conditions. Design examples and simulation results are given to demonstrate the findings. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive NN state error PCH trajectory tracking control for unmanned surface vessel with uncertainties and input saturation

A novel robust state error port controlled Hamiltonian (PCH) trajectory tracking controller of an unmanned surface vessel (USV) subject to time-varying disturbances, dynamic uncertainties and control input saturation is presented. The proposed control scheme combines the advantages of the high robustness and energy minimization of the state error PCH approach and the approximation capability of adaptive radial basis function neural networks (RBFNNs). Adaptive RBFNNs are used to the time-varying disturbances of the environment and unknown dynamics uncertainties of the USV model. The state error PCH control approach is designed such that the system can optimize energy consumption, and the state error PCH technique makes the designed trajectory tracking controller be easy to implement in practice. To handle the effect of the control input saturation, a Gaussian error function model is employed. It has been demonstrated that the proposed approach can maintain the USV's trajectory at the desired trajectory, while the closed-loop control system can guarantee the uniformly ultimate boundedness. The energy consumption model of the USV is constructed to reveal to the energy consumption. Simulation results demonstrate the effectiveness of the proposed controller.     

Immersion and Invariance Based Robust Adaptive Control of High‐Speed Train with Guaranteed Prescribed Performance Bounds

This paper proposes a novel robust adaptive algorithm for train tracking control with guaranteed prescribed transient and steady‐state performance. As speed increases, the inherent time‐varying uncertainties and unmodeled dynamics in the longitudinal dynamics of a high‐speed train seriously impacts the tracking performance of automatic train operation. To improve train operation performance, an estimator based on immersion and invariance technology is developed to recover the unknown and time‐varying plant parameters, and it renders the estimation error converging to a bounded residual set exponentially while providing more freedom for the controller. After certain error transformation, the prescribed tracking performance is introduced into the controller design. Then, an input‐to‐stable stable controller is developed through the backstepping technique, and it is proven that stabilization of the transformed system is sufficient to guarantee the prescribed performance. Rigorous theoretical analysis for the presented algorithm is provided, and a series of simulation studies also are given to verify the effectiveness of it.     

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.     

Reaction wheel pendulum control using fourth‐order discontinuous integral algorithm

The fourth‐order model of the reaction wheel pendulum is considered and a fourth‐order discontinuous integral algorithm is used for stabilization and tracking of the system, using a continuous control signal. The states reach the origin or a reference signal in finite‐time, even in presence of uncertain control coefficient and a kind of matched and unmatched uncertainties/disturbances. A homogeneous Lyapunov function is designed to ensure local finite‐time stability of the system, which can be used for designing the controller gains. Simulations and experimental results illustrate the performance and advantages of the presented algorithm.     

Fuzzy‐Neuron Intelligent Coordination Control Fora Unit Power Plant

A novel fuzzy‐neuron intelligent coordination control method for a unit power plant is proposed in this paper. Based on the complementarity between a fuzzy controller and a neuron model‐free controller, a fuzzy‐neuron compound control method for Single‐In‐Single‐Out (SISO) systems is presented to enhance the robustness and precision of the control system. In this new intelligent control system, the fuzzy logic controller is used to speed up the transient response, and the adaptive neuron controller is used to eliminate the steady state error of the system. For the multivariable control system, the multivariable controlled plant is decoupled statically, and then the fuzzy‐neuron intelligent controller is used in each input‐output path of the decoupled plant. To the complex unit power plant, the structure of this new intelligent coordination controller is very simple and the simulation test results show that good performances such as strong robustness and adaptability, etc. are obtained. One of the outstanding advantages is that the proposed method can separate the controller design procedure and control signals from the plant model. It can be used in practice very conveniently.     

Low‐complexity adaptive tracking control of MIMO nonlinear systems with unknown control directions

This paper is concerned with the tracking control problem for a class of multiple‐input–multiple‐output systems with unmatched disturbances and the unknown additive and multiplicative nonlinearities. The objective is to provide a low‐complexity control solution in the sense that (i) approximating structures are not involved, despite unknown nonlinearities and (ii) iterative calculations of command derivatives are avoided in the backstepping design. A robust adaptive control strategy is proposed to fulfill the task. In the control design, a new‐type adaptive law is first developed to update Nussbaum gains to handle control direction uncertainties, while ensuring Nussbaum gains bounded. Then, the potential robustness of error constraint techniques is exploited to counteract the effects of unknown nonlinearities and disturbances and achieve predefined transient and steady‐state tracking performance. Finally, simulation results are given to illustrate the above theoretical findings.     

Input‐to‐state stability of min‐max MPC scheme for nonlinear time‐varying delay systems

This paper studies the robustness problem of the min–max model predictive control (MPC) scheme for constrained nonlinear time‐varying delay systems subject to bounded disturbances. The notion of the input‐to‐state stability (ISS) of nonlinear time‐delay systems is introduced. Then by using the Lyapunov–Krasovskii method, a delay‐dependent sufficient condition is derived to guarantee input‐to‐state practical stability (ISpS) of the closed‐loop system by way of nonlinear matrix inequalities (NLMI). In order to lessen the online computational demand, the non‐convex min‐max optimization problem is then converted to a minimization problem with linear matrix inequality (LMI) constraints and a suboptimal MPC algorithm is provided. Finally, an example of a truck‐trailer is used to illustrate the effectiveness of the proposed results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

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.     

Design of Preview Controller for Linear Continuous-time Systems with Input Delay

This paper makes it possible to design a preview controller for linear continuous-time systems with input delay, which expands the preview control theory. An augmented error system is established. And a variable substitution is used to transform the delay preview control system into a delay-free one whose preview controller uses the future value of the augmented state vector. The future value of the augmented state vector is estimated by the information of the current state vector, the control input on the past time window, and the reference signal on the future time window. Under the assumption of zero initial conditions, a simplified controller with both delay compensation and preview compensation is obtained for the original system. In addition, a preview controller with full-order observer is offered. Finally, simulation results are presented to illustrate the effectiveness and robustness of the controller.     

AN ALGORITHM FOR DIGITAL IMPLEMENTATION OF TRAJECTORY TRACKING CONTROLLERS

In this work, we study the problem of the digital implementation of continuous‐time solutions to the trajectory tracking control problem for nonlinear systems. We exhibit an example that shows that, in general, no proper behavior of the tracking error can be expected when these solutions are implemented via the Sampling and Zero Order Hold technique. Inspired in some constructions developed in the context of Positional Games, we present a sampled‐data controller that, based on a continuous‐time solution of the tracking problem, assures semiglobal practical stability of the tracking error, with final error arbitrarily small if we choose a suitable sampling period. The controller is robust with respect to small external disturbances and small errors in the measurements.