On-line identification scheme using adaptive filters

An on-line scheme for identifying a linear process is proposed which consists of a linear time-varying filter and a parameter update algorithm. The disturbances affecting the process, its input and its output, belong to a general class of signals which are a mixture of stochastic and deterministic signal processes generated by some linear time-invariant system excited by white noise and the Dirac delta function, respectively. The process and the disturbance signal models are not restricted to be asymptotically stable. Either a probing input signal or a normal operating input signal can be employed. The probing signal consists of a finite number of sinusoidal signals (exponentially increasing sinusoidal signals for unstable processes) of distinct frequencies. When a normal operating signal is used, an adaptive scheme is employed to tune the parameters of the filters to the distinct frequency components of the signal. The convergence of the parameter estimates to their true value is established.     

Closed-loop persistent identification of linear systems with unmodeled dynamics and stochastic disturbances

The essential issues of time complexity and probing signal selection are studied for persistent identification of linear time-invariant systems in a closed-loop setting. By establishing both upper and lower bounds on identification accuracy as functions of the length of observation, size of unmodeled dynamics, and stochastic disturbances, we demonstrate the inherent impact of unmodeled dynamics on identification accuracy, reduction of time complexity by stochastic averaging on disturbances, and probing capability of full rank periodic signals for closed-loop persistent identification. These findings indicate that the mixed formulation, in which deterministic uncertainty of system dynamics is blended with random disturbances, is beneficial to reduction of identification complexity.     

Robust observer-based optimal linear quadratic tracker for five-degree-of-freedom sampled-data active magnetic bearing system

This paper presents three observer/Kalman filter identification (OKID) approaches and develops a robust observer-based optimal linear quadratic digital tracker (LQDT) for the five-degree-of-freedom (five-DOF) sampled-data active magnetic bearing (AMB) system with various disturbances. The more detailed objectives are: (i) to construct both an equivalent linear time-invariant discrete-time model and its state estimator via the proposed OKID approaches for the AMB system, which might be an unknown nonlinear time-varying unstable system with both a specified rotation speed and a sampling rate; (ii) to provide an adaptive disturbance estimation scheme, which establishes an equivalent input disturbance (EID) estimator for the AMB system with unexpected disturbances; and (iii) to develop a robust observer-based optimal LQDT for the sampled-data AMB system with both a pre-specified time-varying speed and unexpected disturbances. The developed LQDT is able to recover the displacement of the rotor to the pre-specified trajectory position whenever it deviates from such trajectory.     

Uniting bounded control and MPC for stabilization of constrained linear systems

In this work, a hybrid control scheme, uniting bounded control with model predictive control (MPC), is proposed for the stabilization of linear time-invariant systems with input constraints. The scheme is predicated upon the idea of switching between a model predictive controller, that minimizes a given performance objective subject to constraints, and a bounded controller, for which the region of constrained closed-loop stability is explicitly characterized. Switching laws, implemented by a logic-based supervisor that constantly monitors the plant, are derived to orchestrate the transition between the two controllers in a way that safeguards against any possible instability or infeasibility under MPC, reconciles the stability and optimality properties of both controllers, and guarantees asymptotic closed-loop stability for all initial conditions within the stability region of the bounded controller. The hybrid control scheme is shown to provide, irrespective of the chosen MPC formulation, a safety net for the practical implementation of MPC, for open-loop unstable plants, by providing a priori knowledge, through off-line computations, of a large set of initial conditions for which closed-loop stability is guaranteed. The implementation of the proposed approach is illustrated, through numerical simulations, for an exponentially unstable linear system.     

System identification using Kautz models

In this paper, the problem of approximating a linear time-invariant stable system by a finite weighted sum of given exponentials is considered. System identification schemes using Laguerre models are extended and generalized to Kautz models, which correspond to representations using several different possible complex exponentials. In particular, linear regression methods to estimate this sort of model from measured data are analyzed. The advantages of the proposed approach are the simplicity of the resulting identification scheme and the capability of modeling resonant systems using few parameters. The subsequent analysis is based on the result that the corresponding linear regression normal equations have a block Toeplitz structure. Several results on transfer function estimation are extended to discrete Kautz models, for example, asymptotic frequency domain variance expressions     

Stabilization of second-order LTI switched systems

This paper studies and solves the problem of asymptotic stabilization of switched systems consisting of unstable secondorder linear time-invariant (LTI) subsystems. Necessary and sufficient conditions for asymptotic stabilizability are first obtained. If a switched system is asymptotically stabilizable, then the conic switching laws proposed in the paper are used to construct a switching law that asymptotically stabilizes the system. Switched systems consisting of two subsystems with unstable foci are studied first and then the results are extended to switched systems with unstable nodes and saddle points. The results are applicable to switched systems that consist of more than two subsystems.     

A stable indirect adaptive control scheme for first-order plantswith no prior knowledge on the parameters

An indirect adaptive control scheme for a first-order linear time-invariant plant with unknown parameters is presented and analyzed. The scheme requires a priori knowledge of the sign or bounds of the plant parameters. A discontinuous control law, involving the use of probing, is utilized to avoid any singularities caused by the lack of stabilizability of the estimated model. The scheme guarantees signal boundedness and zero residual tracking error     

On-line frequency-and time-domain identification of a linear multivariable system

A method for the on-line identification of a linear multivariable plant subject to both deterministic and stochastic disturbances is proposed. The identification scheme rests on the use of a sum of sinusoids of distinct frequencies as probing-signal inputs and on the employment of linear time-varying filters to filter the plant inputs and the plant outputs. The time-varying filters are essentially banks of narrow-band filters tuned to the probing-signal frequencies. The filtered plant inputs and the filtered plant outputs yield an estimate of the plant transfer function matrix at the probing-signal frequencies. The filtered data are further processed using a recursive least-squares algorithm and a time-domain model estimate is obtained in terms of the coefficients of the difference equation relating each input-output pair. The identification algorithm is decoupled in the sense that the estimate of the transfer function or difference equation between the ith input and jth output is unaffected by other inputs or outputs. Simulation results on the performance of the time-varying filter and the identification scheme are given.     

The output control of linear time-invariant multivariable systems with unmeasurable arbitrary disturbances

Necessary and sufficient conditions are derived for a minimal order linear time-invariant differential feedback control system to exist for a linear time-invariant multivariable system with unmeasurable arbitrary disturbances of a given class occurring in it, such that the outputs of the system asymptotically become equal to preassigned functions of a given class of outputs, independent of the disturbances occurring in the system, and such that the closed-loop system is controllable. The feedback gains of the control system are obtained so that the dynamic behavior of the closed-loop system is specified by using either an integral quadratic optimal control approach or a pole assignment approach. The result may be interpreted as being a generalization of the single-input, single-output servomechanism problem to multivariable systems or as being a solution to the asymptotic decoupling problem.     

基于量化控制信号的线性系统的跟踪性能极限

研究基于量化控制信号的线性系统的跟踪性能极限. 所研究的被控对象是稳定的线性时不变(LTI)系统, 参考跟踪信号是阶跃信号. 跟踪性能通过对象输出与参考信号之差的能量来衡量. 为了达到渐近跟踪, 提出了一个新的量化方案. 方案包括两部分: 一部分是在初始时刻将控制信号的稳态值通过网络传输给被控对象并且存储在其输入端; 另一部分则是通过对数量化器, 对控制信号的瞬态部分(即控制信号与其稳态值之差)进行量化, 然后传输给被控对象. 最后该量化信号与稳态控制信号相加后作用于被控对象. 这里, 假设对数量化误差是     

Optimal asymptotic identification under bounded disturbances

The intrinsic limitation of worst-case identification of linear time-invariant systems using data corrupted by bounded disturbances, when the unknown plant is known to belong to a given model set, is studied. This is done by analyzing the optimal worst-case asymptotic error achievable by performing experiments using any bounded input and estimating the plant using any identification algorithm. It is shown that under some topological conditions on the model set, there is an identification algorithm which is asymptotically optimal for any input, and the optimal asymptotic error is characterized as a function of the inputs. These results, which hold for any error metric and disturbance norm, are applied to three specific identification problems: identification of stable systems in the l₁ norm, identification of stable rational systems in the H_∞ norm and identification of unstable rational systems in the gap metric. For each of these problems, the general characterization of optimal asymptotic error is used to find near-optimal inputs to minimize the error     

不确定时滞系统增益型故障的检测与估计

针对一类不确定连续线性定常时滞系统,提出了一种执行器、传感器增益故障的鲁棒检测与估计策略。该类系统含有多状态与输出时滞,状态和输出方程上同时作用有非结构有界未知扰动。在Trunov和Polycarpou方法的基础上,设计了一种新的时滞系统自适应观测器用于检测并估计突变或缓变的增益故障。与Wang等针对线性无时滞不合输出扰动系统的工作相比,该结论更具一般性。理论分析表明,该方法对于未知扰动鲁棒,能够保证故障的估计,状态与输出估计偏差一致有界。数值仿真验证了方法的有效性。     

Asymptotic recovery for discrete-time systems

An asymptotic recovery design procedure is proposed for square, discrete-time, linear, time-invariant multivariable systems, which allows a state-feedback design to be approximately recovered by a dynamic output feedback scheme. Both the case of negligible processing time (compared to the sampling interval) and of significant processing time are discussed. In the former case, it is possible to obtain perfect recovery if the plant is minimum-phase and has the smallest possible number of zeros at infinity. In other cases good recovery is frequently possible. New conditions are found which ensure that the return-ratio being recovered exhibits good robustness properties.     

Robust attitude tracking control of small-scale unmanned helicopter

Robust attitude control problem for small-scale unmanned helicopters is investigated to improve attitude control performances of roll and pitch channels under both small and large amplitude manoeuvre flight conditions. The model of the roll or pitch angular dynamics is regarded as a nominal single-input single-output linear system with equivalent disturbances which contain nonlinear uncertainties, coupling-effects, parameter perturbations, and external disturbances. Based on the signal compensation method, a robust controller is designed with two parts: a proportional-derivative controller and a robust compensator. The designed controller is linear and time-invariant, so it can be easily realised. The robust properties of the closed-loop system are proven. According to the ADS-33E-PRF military rotorcraft standard, the controller can achieve top control performances. Experimental results demonstrate the effectiveness of the proposed control strategy.     

大系统的动态递阶伺服控制

本文针对大系统的伺服控制问题,提出了动态递阶伺服控制这一新的伺服控制方案,给出了动态递阶伺服控制器的结构及动态递阶伺服控制问题可解的条件。研究结果表明,这种伺服控制方案可用来解决有不稳定分散固定模的大系统的伺服控制问题。     

A novel narrow band digital filter and its application to multivariable system identification

A novel narrow band time-varying digital filter is proposed, which has desirable properties such as global asymptotic stability, asymptotic noise annihilation and asymptotic signal tracking. It is shown that the proposed filter is comparable to the Kalman filter in performance, but with substantial computational simplicity; no Ricatti equation is involved. It is basically a Fourier analysis method but the Fourier coefficients are found recursively. The application of the proposed filter for on-line identification of a linear multivariable system subject to both deterministic and stochastic disturbances is presented; simulation results are given.     

Adaptive output rejection of unmatched input disturbances

To adaptively reject the effect of certain unmatched input disturbances on the output of a linear time-invariant system, a transfer function matching condition is needed. A lemma which presents a novel basic property of linear systems is derived to characterize system conditions for such transfer function matching. An adaptive disturbance rejection control scheme is developed for such systems with uncertain dynamics parameters and disturbance parameters. This adaptive control technique is applicable to control of systems with actuator failures whose failure values, failure time instants, and failure patterns are unknown. A solution is presented to this adaptive actuator failure compensation problem, which ensures closed-loop stability and asymptotic output tracking, in the presence of any up to m−1 uncertain failures of the total m actuators. Desired adaptive system performance is verified by simulation results.     

Observation and output adaptive tracking for a class of nonlinear non-minimum phase systems

ABSTRACT

In this paper, the output tracking problem for a class of systems with unstable zero dynamics is addressed. The state is assumed not measurable. The output of the dynamical system to be controlled has to track a signal, which is the sum of a known number of sinusoids with unknown frequencies, amplitudes and phases. The non-minimum phase nature of the considered systems prevents the direct tracking by standard sliding mode methods, which are known to generate unstable behaviours of the internal dynamics. The proposed method relies on the availability of a flat output and its time derivatives which are functions of the unavailable state; therefore, a nonlinear observer is needed. Due to the uncertainty in the frequencies and in the parameters defining the relationship between the output of the system and the flat states, adaptive indirect methods are applied.     

Stable adaptive regulation of arbitrary nth-order plants

This paper presents an algorithm for adaptively stabilizing and asymptotically regulating an arbitrary single-input single-output linear time-invariant plant, which is controllable and observable, of known ordern, and has unknown parameters. No further assumptions are made. No external probing signal is required.     

Observer-based fault detection and isolation filter design for linear time-invariant systems

In this paper we consider a model-based fault detection and isolation problem for linear time-invariant dynamic systems subject to faults and disturbances. We use a state observer scheme that cancels the system dynamics and defines a residual vector signal that is sensitive only to faults and disturbances. We then design a stable fault detection and isolation filter such that the ?_∞-norm of the transfer matrix function from disturbances to the residual is minimised (for fault detection) subject to the constraint that the transfer matrix function from faults to residual is equal to a pre-assigned diagonal transfer matrix (for isolation of possibly simultaneous occurring faults). Our solution is given in the form of linear matrix inequalities using state-space techniques, as well as a model matching problem using matrix factorisation techniques. A numerical example is given to illustrate the efficiency of the fault detection and isolation filter.