Regulation of Linear Systems with Unknown Additive Sinusoidal Sensor Disturbances

Adaptive regulation for minimum phase systems with unknown relative degree and uncertain exosystems

Given a stabilizable and detectable linear system with additive disturbances and output references generated by a linear exosystem with unknown parameters and unknown order, the problem of designing a global output feedback regulator which asymptotically achieves output regulation and disturbance rejection is considered. The linear system to be regulated is allowed to be a non-minimum phase: its parameters are required to be known. Only an upper bound on the number of the excited frequencies of the exosystem is assumed to be known. A global solution is proposed, which includes asymptotically convergent estimates of the excited unknown frequencies.

SUMMARYThis paper aims to propose an additive‐state‐decomposition‐based tracking control framework, based on which the output feedback tracking problem is solved for a class of nonminimum phase systems with measurable nonlinearities and unknown disturbances. This framework is to ‘additively’ decompose the output feedback tracking problem into two more tractable problems, namely an output feedback tracking problem for a linear time invariant system and a state feedback stabilization problem for a nonlinear system. Then, one can design a controller for each problem respectively using existing methods, and these two designed controllers are combined together to achieve the original control goal. The main contribution of the paper lies on the introduction of an additive state decomposition scheme and its implementation to mitigate the design difficulty of the output feedback tracking control problem for nonminimum phase nonlinear systems. To demonstrate the effectiveness, an illustrative example is given. Copyright © 2013 John Wiley & Sons, Ltd.

Tracking and Regulation in Linear Systems

We look at the stabilization and regulation problems for linear systems subject to both rate and saturation limits. With respect to stabilization we focus on semi-global stabilization. This allows one to use linear compensators. We concentrate on the state feedback, single-input case. However, the results can be extended to the measurement feedback and multi-input case.

This paper studies the tracking control problem for underactuated surface vessel with unknown time-varying disturbances. To avoid the controller singularity problem, the constraints on output tracking errors of underactuated surface vessel are enforced in the control design. With the help of error transformation functions, the constrained tracking control of the vessel is converted into the stabilization of the transformed error systems. To compensate for the effect of the external disturbances, disturbance observers are presented to estimate the unknown time-varying disturbances. Subsequently, disturbance-observer-based tracking control is developed to steer the vessel along a desired reference trajectory with guaranteeing the tracking errors within certain predefined bounds. The performance of the proposed tracking control is demonstrated through simulation results.

In this article, a leader-follower asymptotic consensus control strategy is developed for a class of linear multiagent systems (MASs) with unknown external disturbances and measurement noises. First, the preconditions, the minimum phase condition (MPC) and observer matching condition (OMC), are discussed in detail, and an equivalent result under these two preconditions is given. In this way, the corresponding results from Corless and Tu (1998) are improved. Meanwhile, a reduced-order observer is designed for a constructed augmented system to estimate the system states and noises of each agent. Next, with the help of a traditional interval observer, a novel unknown disturbance reconstruction method is developed, and the reconstruction can converge to the unknown disturbance asymptotically and decouple from the control input. The subsequent asymptotic consensus is accomplished by utilizing an observer-based control scheme, with its design satisfying the so-called separation principle. Finally, two simulation examples are given to verify the effectiveness and show the advantages of the proposed methods.

Three-phase induction motors have been widely used in a variety of industrial applications. Induction motors have been able to incrementally improve energy efficiency to satisfy the requirements of reliability and efficiency, Melfi et al. (2009). There are well known advantages of using induction motors over permanent magnet DCmotors for position control tasks; thus, efforts aimed at improving or simplifying feedback controller design are well justified. There exists a variety of control strategies that depend on difficult to measuremotor parameters while their closed loop behavior is found to be sensitive to their variations. Even adaptive schemes tend to be sensitive to speed-estimation errors, yielding to a poor performance in the flux and torque estimation, especially during low-speed operation, Harnefors & Hinkkanen (2008). Generally speaking, the designed feedback control strategies have to exhibit a certain robustness level in order to guarantee an acceptable performance. It is possible to (on-line or off-line) obtain estimates of the motor parameters, Hasan H Toliyat et al. (2003), but some of them can be subject to variation when the system is undergoing actual operation. Frequent misbehavior is due to external and internal disturbances, such as generated heat, that significantly affect some of the system parameter values. An alternative to overcome this situation is to use robust feedback control techniques which take into account these variations as unknown disturbance inputs that need to be rejected. In this context, sliding mode techniques are a good alternative due to their disturbance rejection capability (see for instance, Utkin et al. (1999)). In this chapter, we consider a two stage control scheme, the first one is devoted to the control of the rotor shaft position. This analog control is performed bymeans of the stator current inputs, in a configuration of an observer based control. Themathematical model of the rotor dynamics is a simplified model including additive, completely unknown, lumping nonlinearities and external disturbances whose effect is to be determined in an on-line fashion by means of linear observers. The gathered knowledge will be used in the appropriate canceling of the assumed perturbations themselves while reducing the underlying control problem to a simple linear feedback control task. The control scheme thus requires a rather reduced set of parameters to be implemented. Sliding Mode Control Design for Induction Motors: An Input-Output Approach 7

SummaryThe rejection of unknown periodic disturbances in the plant output through adaptive feedback has been an active area of research. In most successful efforts, it is assumed that the plant model is a known LTI stable system. In this paper, we relax the assumption of stable known plant and consider the case where the plant model can be unstable with unknown parameters. We do assume, however, that the plant model is minimum phase and use the model reference adaptive control structure to meet the objectives of reference tracking and unknown periodic disturbance rejection without amplifying the effect of broadband noises. The cost of achieving these objectives is the use of overparameterization that adds to the number of computations. The main contribution of this paper is that it shows that the problem of rejecting unknown periodic disturbances can be solved for unstable plants with unknown parameters as long as they are minimum phase. Numerical examples illustrate the effectiveness of the proposed control methodology.

The problem of intermittent fault (IF) detection is studied for a class of linear discrete-time stochastic systems with unknown disturbance under the influence of a class of networked phenomena by using the moving horizon estimation (MHE). Aiming to normalise the transmission of data in network systems, the Round-Robin (RR) protocol is introduced for linear discrete-time stochastic systems, so the system is converted to a linear periodic system. By using the lifting technique and superposition principle, the linear periodic discrete-time system is transformed into a linear discrete time-invariant system. An MHE strategy is developed to cope with unknown disturbance by introducing provisional estimates of external unknown disturbances. By utilizing the moving horizon estimator, a scalar residual decoupled from the unknown disturbance is designed. Finally, the effectiveness of the proposed method is verified by a simulation example.

In this paper, we consider the problem of designing a special type of observer to estimate the state and unknown input disturbance for linear time-invariant positive systems. Although positive observers have been designed for positive systems, they are unable to estimate the states when unknown inputs or disturbances are present in the systems. To realize simultaneous estimation of states and unknown inputs, we first design positive unknown input observers (PUIO) for positive linear systems, which is the main contribution of this paper. Then, we provide a procedure to estimate the unknown disturbance. The PUIO design can be performed with the aid of a positive stabilization scheme via LMI. A critical step in the design process is the requirement of imposing a condition on positivity of the generalized inverse of a certain design matrix. We show that this can easily be accomplished with the aid of a unique result, which makes the design of PUIO possible. An alternative LMI with less restrictive assumption is also included to design PUIO. Finally, theoretical results are supported by numerical examples.

In this paper, two controllers with a compound disturbance observer are proposed for a two-wheeled inverted robot (TWIR) with model uncertainty and unknown input disturbance. First, an equivalent linear model of the TWIR with uncertainty and input disturbance is proposed using the Taylor series expansion for the nonlinear model of the TWIR at an equilibrium point, in which the nonlinear part of the Taylor series and the model uncertainty are combined with unknown input disturbance as compound input disturbance. Then, the compound input disturbance is estimated by using the Newton method and reference model. As the estimated compound disturbance is used to compensate for the compound disturbance, the equivalent linear system becomes closely definite without compound input disturbance. Finally, two controllers are proposed using the equivalent linear system. Stability analysis of the proposed control methods is also given. To illustrate the proposed methods, some simulations for the TWIR are performed and compared with the existing methods. The main contribution of this work includes the following: (i) simple controllers based on compound input disturbance observer for trajectory tracking and balancing of TWIRs with unknown input disturbance and model uncertainty are proposed; (ii) the stability of proposed closed-loop control systems is proved; (iii) our proposed methods are simulated and compared with the existing methods.

This paper addresses the issue of adaptive fixed-time tracking control (FTTC) for a category of parametric nonlinear systems characterized by unknown nonlinear control coefficient (UNCC) and unknown external disturbances (UEDs). To effectively handle unknown parameters and unknown disturbances, the adaptive parameter estimation method is introduced into the control law design. Meanwhile, some parameter adaptive laws are presented to estimate these unknown parameters. To eliminate repeated differentiation of virtual control laws, a class of nonlinear command filters is introduced. Furthermore, the filtering errors are compensated through the designed adaptive compensation control laws. Subsequently, the Nussbaum gain function technique is further used to deal with the UNCC in the system. Leveraging command-filtering backstepping control (BC) and fixed-time control method, an adaptive command filtered FTTC law is final presented to achieve the fixed time tracking. The theoretical analysis results indicate that the designed control law guarantees the convergence of tracking error to a small neighborhood of zero within a fixed time, while ensuring that all signals within the closed-loop system remain bounded. The proposed control law’s effectiveness is demonstrated through three simulation examples.

In this article, a new self-tuning control adaptive system utilizing output tracking error in identification and control instead of the plant output is presented. The output tracking error that is used in the proposed controller works based on the difference between the plant output and its desired value. Thus, in the controller design instead of direct use of model reference of conventional self-tuning controller, another model reference is used for the output tracking error. In contrast to the conventional self-tuning controller, in this approach, dynamic of disturbance does not need to be known a priori and the performance of the control system including robustness against the external disturbance is outstandingly superior to the conventional method. Furthermore, the suggested control structure is simpler with fewer computations and complications. Simulation results demonstrate practicality and effectiveness of the proposed approach in controlling linear systems and locally in nonlinear ones.

This paper presents the design of a linear quadratic analog tracker (LQAT) based on the observer–Kalman-filter identification (OKID) method and the design of a modified functional observer-based equivalent input disturbance (EID) estimator for unknown square–non-square singular analog systems with unknown input and output disturbances. First, an equivalent mathematical model of the singular analog system is presented to simulate the time response of continuous-time linear singular analog systems to arbitrary inputs via the model conversion method. Then, for the unknown singular analog system, it constructs a linear quadratic analog tracker with state feedback and feed-forward gains based on the off-line OKID method. Furthermore, it extends the design methodology of the EID estimator for strictly proper regular systems with unknown matched–mismatched input and output disturbances to proper regular systems. It is important to mention that the newly developed modified functional observer for proper systems is used to estimate the unknown EID of singular analog systems and that the constraints on the dimensions of unknown disturbances can be eliminated by using the newly proposed EID estimation method. The contributions of this paper can be listed as follows: (1) based on both the OKID method and the discrete-to-continuous model conversion, the simulation of the time responses of the continuous-time linear singular models (which are not feasible using existing MATLAB toolboxes) become feasible; (2) for effective control of the unknown singular analog system, an off-line OKID method is proposed to design an LQAT with state feedback and feed-forward gains; and (3) based on the newly developed modified functional observer for the reduced-order proper regular system, the original EID estimator in the literature is newly extended to estimate the EID from the unknown strictly proper singular analog system, without the original dimensional constraints of the disturbances. It is important to mention that the disturbances of interest can be unknown matched–mismatched input and output disturbances.