Optimal utilization of fixed-capacity channels in feedback control

The performance limitations on the linear control of a linear plant, due to the presence of a feedback channel with finite information capacity, are considered in this paper. This situation may arise in such diverse applications as (a) the remote control of a plant, using a digital data link for feedback, (b) where quantization errors and bit errors of a digital controller may be modelled as occurring in a noisy digital channel in cascade with an ideal controller, and (c) in human-operator modelling, where the sensory feedback channels are characterized by fixed information capacity due to neural noise. The principle result obtained is that, given the state-dimension n of the plant and the channel capacity ?, reliability function E(R), and block encoding time $\text{T> >}\text{1}\text{C}$, the optimum data-rate R satisfies the equation 2R=nE(R). This rate provides the optimum tradeoff between the effects of quantization errors and message errors. It is seen that R_opt→C as n becomes large, but that good channel performance is retained provided that $\text{> >}\text{n}\text{T}$.     

Non-linear generalized minimum variance feedback, feedforward and tracking control

A generalized minimum variance control law is derived for the control of nonlinear, possibly time-varying, multi-variable systems. The solution for the tracking and feedback/feedforward control law was obtained in the time-domain using a nonlinear operator representation of the process. The cost index involves both error and control signal costing terms and is normally quadratic but may also involve nonlinear functions. The feedback controller obtained is simple to implement and includes an internal model of the process. The tracking controller can include future reference change information, providing a predictive control capability. In one form the compensator might be considered a nonlinear version of the Smith Predictor that has feedforward action.     

Depth control of the INFANTE AUV using gain-scheduled reduced order output feedback

The paper addresses the problem of autonomous underwater vehicle (AUV) control in the absence of full state information. An application is made to the control of a prototype AUV in the vertical plane. The methodology adopted for controller design is nonlinear gain-scheduling control, whereby a set of linear, dynamic, reduced order output feedback controllers are designed and scheduled on the vehicle's forward speed. The paper summarizes the controller design steps, describes a technique for its practical implementation, and presents experimental results obtained with the INFANTE AUV during tests at sea.     

On the stability of convolution feedback systems with dynamical feedback

This paper considers distributed n-inputn-output convolution feedback systems characterized by $\text{y = G}{}_1\text{1e}$, $\text{z = G}{}_2\text{1y}$ and e = u ? z, where the forward path transfer function $\text{G}\text{?}{}_1$ and the feedback path transfer function $\text{G}\text{?}{}_2$ both contain a real single unstable pole at different locations. Theorem 1 gives necessary and sufficient conditions for both input-error and input-output stability. In addition to usual conditions that guarantee input-error stability a new condition is found which results in the fact that input-error stability will guarantee input-output stability. These conditions require to investigate only the open-loop characteristics. A basic device is the consideration of the residues of different transfer functions at the open-loop unstable poles. An example is given.     

Nonlinear stabilizability via encoded feedback: The case of integral ISS systems

In this note we observe how, using the same arguments of Liberzon and Hespanha [(2005). Stabilization of nonlinear systems with limited information feedback, IEEE Transactions on Automatic Control, 50, 910-915] , integral input-to-state stabilizability with respect to measurement errors is enough to prove stabilizability of nonlinear systems with limited information. The utility of the remark lies on the fact that, under a requirement on the data rate analogous to the one in the paper by Liberzon and Hespanha, the stabilizability result is proven for a larger class of systems.     

Iterative learning feedback control of human limbs via functional electrical stimulation

A high-order iterative learning controller (ILC) is proposed for the tracking control of an electrically stimulated human limb that is repeatedly required to perform a given task. The limb is actuated by the muscles, which are out of the control of the central nerve systems (CNS), through functional electrical stimulation (FES) or functional neuromuscular stimulation (FNS). By using the proposed discrete-time high-order P-type ILC updating law and the PD-type feedback controller, it is shown that the proposed control strategy, which learns from repetitions, provides strong robustness in tracking control of the uncertain time-varying FES systems, which is essential for the adaptation and customization of FES applications. The effectiveness of the proposed control scheme is demonstrated by simulation results on a one-segment planar system. Some experimental results are also presented to validate the proposed control method.     

Output feedback control of a class of nonminimum‐phase nonlinear systems

The problem of global stabilization by output feedback is investigated in this paper for a class of nonminimum‐phase nonlinear systems. The system under consideration has a cascade configuration that consists of a driven system known as the inverse dynamics and a driving system. It is proved that although the zero dynamics may be unstable, there is an output feedback controller, globally stabilizing the nonminimum‐phase system if both driven and driving systems have a lower‐triangular form and satisfy a Lipschitz‐like condition, and the inverse dynamics satisfy a stronger version of input‐to‐state stabilizability condition. A design procedure is provided for the construction of an n‐dimensional dynamic output feedback compensator. Examples and simulations are also given to validate the effectiveness of the proposed output feedback controller. Copyright © 2016 John Wiley & Sons, Ltd.     

The strong stabilization of a one-dimensional wave equation by non-collocated dynamic boundary feedback control

The stabilization of a one-dimensional wave equation with non-collocated observation at its unstable free end and control at another end is considered. The controller comprises a state estimator which is designed in the case where the velocity is not available. The method of “backstepping” is adopted in our design of the feedback law. We use the theory of C₀-semigroups and Lyapunov functionals to prove the strong stability of the resulting closed-loop system.     

Stabilization with data-rate-limited feedback: tightest attainable bounds

This paper investigates the stabilizability of a linear, discrete-time plant with a real-valued output when the controller, which may be nonlinear, receives observation data at a known rate. It is first shown that, under a finite horizon cost equal to the mth output moment, the problem reduces to quantizing the initial output. Asymptotic quantization theory is then applied to directly obtain the limiting coding and control scheme as the horizon approaches infinity. This is proven to minimize a particular infinite horizon cost, the value of which is derived. A necessary and sufficient condition then follows for there to exist a coding and control scheme with the specified data rate that takes the mth output moment to zero asymptotically with time. If the open-loop plant is finite-dimensional and time-invariant, this condition simplifies to an inequality involving the data rate and the unstable plant pole with greatest magnitude. Analagous results automatically hold for the related problem of state estimation with a finite data rate.     

PID controller design of TITO system based on ideal decoupler

The proposed method for designing multivariable controller is based on ideal decoupler D(s) and PID controller optimization under constraints on the robustness and sensitivity to measurement noise. The high closed-loop system performance and robustness are obtained using the same controller in all loops. The method is effective despite the values and positions of the right half plane zeros and dead-times in the process transfer function matrix G_p(s). The validity of the proposed multivariable control system design and tuning method is confirmed using a test batch consisting of Two-Input Two-Output (TITO) stable, integrating and unstable processes, and one Three-Input Three-Output (TITO) stable process.     

带执行器饱和的N 连杆机械臂输出反馈动态面控制

针对带执行器饱和的多关节刚性机械臂系统,提出一种基于RBF神经网络补偿的输出反馈动态面控制.通过观测器实现角速度的观测,采用RBF网络实现执行器饱和的补偿;通过Lyapunov方法证明闭环系统的稳定性,实现高精度的角度和角速度跟踪.仿真结果表明,所提出的方法能够有效补偿系统存在的执行器饱和,显著减小跟踪误差,并且对于外界干扰具有一定的鲁棒性.     

State feedback tracking control for indirect field-oriented induction motor using fuzzy approach

This paper deals with the synthesis of fuzzy controller applied to the induction motor with a guaranteed model reference tracking performance. First, the Takagi-Sugeno (T-S) fuzzy model is used to approximate the nonlinear system in the synchronous d-q frame rotating with field-oriented control strategy. Then, a fuzzy state feedback controller is designed to reduce the tracking error by minimizing the disturbance level. The proposed controller is based on a T-S reference model in which the desired trajectory has been specified. The inaccessible rotor flux is estimated by a T-S fuzzy observer. The developed approach for the controller design is based on the synthesis of an augmented fuzzy model which regroups the model of induction machine, fuzzy observer, and reference model. The gains of the observer and controller are obtained by solving a set of linear matrix inequalities (LMIs). Finally, simulation and experimental results are given to show the performance of the observer-based tracking controller.     

A new calculation method of feedback controller gain for bilinear paper-making process with disturbance

This paper presents a new method to calculate the feedback control gain for a class of multivariable bilinear system, and also applied this method on the control of two sections of paper-making process with disturbance. The robust H∞ control problem is to design a state feedback controller such that the robust stability and a prescribed H∞ performance of the resulting closed-loop system are ensured. The controller turns out to be robust with respect to the disturbance in the plant. Utilizing the Schur complement and some variable transformations, the stability conditions of the multivariable bilinear systems are formulated in terms of Lyapunov function via the form of linear matrix inequality (LMI). The gain of controller will be calculated via LMI. Finally, the application examples of a headbox section and a dryer section of paper-making process are used to illustrate the applicability of the proposed method.     

H2/H∞ Control of discrete singularly perturbed systems: the state feedback case

The design of a mixed H₂/H_∞ linear state variable feedback suboptimal controller for a discrete-time singularly perturbed system using reduced order slow and fast subsystems is described. It is shown that the designed controller based on reduced order models and the corresponding performance index both are O(ε) close to those synthesized using the full order system.     

A new extended LMI-based robust gain scheduled state feedback <Emphasis Type="Italic">H</Emphasis><Subscript>2</Subscript> controller design

This paper proposes an improved robust H ₂ state feedback control synthesis for the Linear Parameter Varying (LPV) systems by attaining the affine quadratic stability. In place of standard H ₂ computation in the literature, a new H ₂ computation based on extended Linear Matrix Inequality (LMI) is improved by means of the slack variable, where it is obtained by separation Lyapunov matrix from system matrix. State feedback H ₂ synthesis is improved for the systems, and is more effective and less conservative than the common ones in the literature. Therefore, the less conservative results are obtained for gain scheduling controller design for LPV systems. The numerical examples are presented to show the superiority of the proposed controller design.     

Output feedback variable structure control for linear systems with uncertainties and disturbances

This paper proposes a dynamic output feedback variable structure controller for linear MIMO systems with mismatched and matched norm-bounded uncertainties and matched nonlinear disturbances. The proposed controller consists of nonlinear and linear parts, similar to the unit vector type of controller. The nonlinear part of the new controller takes care only of matched uncertainties and disturbances and, on the other hand, the linear part with full dynamics completely handles mismatched uncertainties. Designing such a linear part leads to use a Lyapunov function associated with the full states, which achieves the global stability against the mismatched uncertainties. The resulting criteria are, furthermore, converted into solvable ones, by using the so-called cone complementary linearization algorithm for bi-convex problems.     

Robust feedback model predictive control of constrained uncertain systems

We propose a novel procedure for the solution to the problem of robust model predictive control (RMPC) of linear discrete time systems involving bounded disturbances and model-uncertainties along with hard constraints on the input and state. The RMPC (outer) controller – responsible for steering the uncertain system state to a designed invariant (terminal) set – has a mixed structure consisting of a state-feedback component as well as a control-perturbation. Both components are explicitly considered as decision variables in the online optimization and the nonlinearities commonly associated with such a state-feedback parameterization are avoided by adopting a sequential approach in the formulation. The RMPC controller minimizes an upper bound on an H₂/H_∞-based cost function. Moreover, the proposed algorithm does not require any offline calculation of (feasible) feedback gains for the computation of the RMPC controller. The optimal Robust Positively invariant set and the inner controller – responsible for keeping the state within the invariant set – are both computed in one step as solutions to an LMI optimization problem. We also provide conditions which guarantee the Lyapunov stability of the closed-loop system. Numerical examples, taken from the literature, demonstrate the advantages of the proposed scheme.     

Reduced-order controllers for the H∞ control problem with unstable invariant zeros

This paper addresses the existence and design methods of reduced-order controllers for the H_∞ control problem with unstable invariant zeros in the state-space realization of the transfer function matrix from the control input to the controlled error or from the exogenous input to the observation output, where the realization is induced from a stabilizable and detectable realization of the generalized plant. This paper presents a new controller degree bound for the H_∞ control problem in terms of the minimal rank of the system matrix pencils of these two transfer function matrices in the unstable region. When the unstable invariant zero exists, this paper shows that reduced-order controllers with orders strictly less than that of the generalized plant exist if the H_∞ control problem is solvable. Moreover, this paper shows that the computational problem of finding the controllers with the new degree bound is convex by providing two linear matrix inequality-based design methods (algorithms) for constructing the reduced-order controllers. The results developed in this paper are valid both for the continuous- and discrete-time H_∞ control problems.     

Making a polynomial Hurwitz-invariant by choice of feedback gains†

An integrated design procedure is developed for a modified Smith predictor and associated controller for linear time-delay systems having transfer functions of the form k ₁, A exp (—sT)/B, where A and B are monic polynomials in s of degree n — l and n, respectively. A is Hurwitz and B has a single right-half-plane root at s = λ. For l=1,2,3, an augmented PI controller guarantees asymptotic stability for λT less than an l-dependent limit. The procedure for l = 3 is extended to l = 4 with the introduction of derivative action into the controller. Design arguments are on root locus topology, and on Nyquist analysis applied to an auxiliary system.     

Master‐slave synchronization for delayed Lur'e systems using time‐delay feedback control

This paper deals with the problem of designing delayed feedback controllers of master‐slave synchronization for Lur'e systems with time‐variant delay (0≤τ₀≤τ(t)≤τ_m). Through partitioning the intervals [0, τ₀] and [τ₀, τ_m], respectively, and choosing two augmented Lyapunov‐Krasovskii functionals(LKFs), two delay‐dependent synchronization criteria are formulated in the form of linear matrix inequalities (LMIs), in which the conservatism can be greatly reduced by thinning the partitioning of delay intervals and employing convex combination. Thus the sufficient conditions can be derived for the existence of delayed feedback controllers, and the controller gain matrices can be achieved by solving the established LMIs. Finally, three numerical examples are given to illustrate the presented synchronization schemes. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society