Perfect Output Tracking Research Articles

Design and Analysis of Data-Driven Learning Control: An Optimization-Based Approach.

Learning to perform perfect tracking tasks based on measurement data is desirable in the controller design of systems operating repetitively. This motivates this article to seek an optimization-based design and analysis approach for data-driven learning control systems by focusing on iterative learning control (ILC) of repetitive systems with unknown nonlinear time-varying dynamics. It is shown that perfect output tracking can be realized with updating inputs, where no explicit model knowledge but only measured input-output data are leveraged. In particular, adaptive updating strategies are proposed to obtain parameter estimations of nonlinearities. A double-dynamics analysis approach is applied to establish ILC convergence, together with boundedness of input, output, and estimated parameters, which benefits from employing properties of nonnegative matrices. Simulations are implemented to verify the validity of our optimization-based adaptive ILC.

Backstepping-Based Adaptive Control of a Class of Uncertain Incommensurate Fractional-Order Nonlinear Systems With External Disturbance

Normally, achieving asymptotic convergence in the presence of unknown arbitrarily bounded external disturbance requires noncontinuous control signals. In this article, an adaptive backstepping controller for a class of incommensurate fractional-order nonlinear systems with parametric uncertainties and external time-varying disturbance is proposed to realize asymptotic perfect output tracking. Appropriate adaptive laws are designed to deal with the uncertainties and unknown bounded disturbance. In the designed adaptive backstepping control scheme, an auxiliary function is adopted to obtain a smooth control signal. It is theoretically shown that asymptotic output tracking to a given reference signal is achieved while ensuring global system stability in the sense that all the closed-loop signals are bounded. Simulation and experimental studies demonstrate the effectiveness of the proposed backstepping control scheme.

Reference tracking controller design for anesthesia

Abstract This paper addresses the problem of tracking a constant BIS reference during anesthesia taking into account control input saturation, multiple time scale dynamics and inter-patient variability. LMIs conditions are proposed to compute a state feedback involving an integral action to ensure a perfect output tracking. These conditions guarantee that the trajectories of the closed-loop system remain in an invariant ellipsoidal set. The theoretical conditions are numerically illustrated on a set of adult patients as a proof of principle.

Deterministic Convergence for Learning Control Systems Over Iteration-Dependent Tracking Intervals.

This brief addresses the iterative learning control (ILC) problems for discrete-time systems subject to iteration-dependent tracking time intervals. A modified class of P-type ILC algorithms is proposed by properly defining an available modified output, for which robust convergence analysis is performed with an inductive approach. It is shown that if a persistent full-learning property is ensured, then a necessary and sufficient convergence condition of ILC can be derived to reach the perfect output tracking objective though the tracking time interval is iteration-dependent. That is, the tracking of ILC for iteration-dependent time intervals can be guaranteed in the same deterministic (not stochastic) convergence way as that of traditional ILC over a fixed time interval. Furthermore, the developed tracking results can be extended to admit iteration-dependent uncertainties in initial state and external disturbances. Simulation tests are also included to demonstrate the effectiveness of the modified P-type ILC.

Robust Iterative Learning Control for Nonrepetitive Uncertain Systems

This technical note proposes a robust iterative learning control (ILC) strategy to regulate iteratively-operated, finite-duration nonrepetitive systems characterized by iteration-varying uncertainties in initial states, external disturbances, plant model matrices and desired reference trajectories. Our convergence analysis exploits results on input-to-state stability of discrete parameterized systems. For a class of multiple-input, multiple-output discrete-time linear systems, with all iteration-varying uncertainties bounded, we give one condition that ensures boundedness of all system trajectories and an additional, second condition that ensures convergence of tracking error. Notably, we do not require the standard ILC contraction mapping requirement to hold at each iteration. Moreover, we show that it is possible to achieve perfect output tracking if the iteration-varying uncertainties all converge with increasing iteration.

Tracking Control of PWM Non-affine Nonlinear Systems via Singular Perturbation Approach

The tracking control problem of nonafine-in-control nonlinear systems is discussed. Filippov's averaging approach is used to get the equivalent continuous-time dynamics of a high-frequency pulse-width modulated (PWM) non-afine-in-control nonlinear system where the resulting equivalent system is both continuous and afine-in-control. The tracking controller is designed for the equivalent system based on singular perturbation method (time-scale separation method) where the controller parameters are selected such that two-time-scale motions are artificially induced in the closed-loop system. Stability conditions imposed on the fast and slow modes and suficiently large mode separation rate between fast and slow modes can ensure that the full-order closed-loop nonlinear system achieves the desired properties in such a way that the almost perfect output tracking and external disturbance rejection are provided. Numerical example and simulation results are presented.

Robust PI based set-point learning control for batch processes subject to time-varying uncertainties and load disturbance

Based on the proportional-integral (PI) closed-loop control widely used in industrial engineering practice, a robust iterative learning control (ILC) method is proposed for industrial batch processes subject to time-varying uncertainties and load disturbance. An important merit is that the proposed ILC design is independent of the PI tuning which maintains the closed-loop system stability, owing to that the ILC updating law is implemented through adjusting the set-point of the closed-loop system and adding a feedforward control signal to the plant input along the batch-to-batch direction. Using the robust H infinity control objective, a robust discrete-time PI tuning algorithm is given in terms of the plant state-space model description with norm-bounded time-varying uncertainties. For the batch-to-batch direction, a robust ILC updating law is developed based on the two-dimensional (2D) control system theory, which is capable of perfect output tracking against repetitive type load disturbance. An illustrative example from the literature is adopted to demonstrate the effectiveness and merits of the proposed ILC method.

Conditional learning control for alignment initial condition

This article tries to handle the alignment initial condition for contraction mapping based iterative learning control, such that the system can operate continuously without any initial condition reset. This goal is achieved for a class of nonlinear systems through the proposed conditional learning control, which has several advantages over the alternative method, adaptive learning control. The conditional learning control guarantees that sufficient knowledge can be learned to update the input and achieve perfect output tracking, despite the non-identical initial conditions. The sufficient conditions of either monotonic or strictly monotonic convergence of the input sequence, and the choice of learning gains are given. The performance of the proposed method is illustrated by simulated examples.

Adaptive Robust Precision Motion Control of Systems With Unknown Input Dead-Zones: A Case Study With Comparative Experiments

In this paper, the recently developed integrated direct/indirect adaptive robust control (DIARC) for a class of nonlinear systems with unknown input dead-zones is combined with the desired compensation strategy to synthesize practical high-performance motion controllers for precision electrical drive systems having unknown dead-zone effects. The effect of measurement noise is alleviated by replacing noisy state feedback signals with the desired state needed for perfect output tracking. Theoretically, certain guaranteed robust transient performance and steady-state tracking accuracy are achieved even when the overall system may be subjected to parametric uncertainties, time-varying disturbances, and other uncertain nonlinearities. Furthermore, zero steady-state output tracking error is achieved when the system is subjected to unknown parameters and unknown dead-zone nonlinearity only. The proposed algorithm is also experimentally tested on a linear motor drive system preceded by a simulated unknown nonsymmetric dead-zone. The comparative experimental results obtained validate the necessity of compensating for unknown dead-zone effects and the high-performance nature of the proposed approach.

Desired Compensation Adaptive Robust Control

A desired compensation adaptive robust control (DCARC) framework is presented for nonlinear systems having both parametric uncertainties and uncertain nonlinearities. The paper first considers a class of higher order nonlinear systems transformable to a normal form with matched model uncertainties. For this class of uncertain systems, the desired values of all states for tracking a known desired trajectory can be predetermined and the usual desired compensation concept can be used to synthesize DCARC laws. The paper then focuses on systems with unmatched model uncertainties, in which the desired values of the intermediate state variables for perfect output tracking of a known desired trajectory cannot be predetermined. A novel way of formulating desired compensation concept is proposed and a DCARC backstepping design is developed to overcome the design difficulties associated with unmatched model uncertainties. The proposed DCARC framework has the unique feature that the adaptive model compensation and the regressor depend on the reference output trajectory and on-line parameter estimates only. Such a structure has several implementation advantages. First, the adaptive model compensation is always bounded when projection type adaption law is used, and thus does not affect the closed-loop system stability. As a result, the interaction between the parameter adaptation and the robust control law is reduced, which may facilitate the controller gain tuning process considerably. Second, the effect of measurement noise on the adaptive model compensation and on the parameter adaptation law is minimized. Consequently, a faster adaptation rate can be chosen in implementation to speed up the transient response and to improve overall tracking performance. These claims have been verified in the comparative experimental studies of several applications.

Two‐Stage Tracking Control Via Output Feedback

ABSTRACTAn 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.

Model output following control based on CGT approach for mimo processes with unmodelled dynamics

This paper is concerned with a design problem of a model output following control (MOFC) system based on static output feedback (SOF) characteristics and command generator tracker (CGT) theorem for multi-input/multi-output (MIMO) processes with unmodelled dynamics. The effect of structured uncertainty is investigated by a modelling method. Further, a design scheme of modelling-based robust parallel compensator (RPC) which makes the MIMO process SOF-able is proposed. The results allow us to explore the role of different tuning parameters for perfect output tracking and also evaluate robust stability of the obtained control system.

Digital tracking control for PWM systems with unacceptable zeros

Perfect output tracking, which requires inversion of the input-output dynamics, is not always a practical control objective. Difficulties are encountered for systems with zeros which are unstable, or stable but lightly damped. When the zeros are unacceptable in the above sense, perfect output tracking would require the control to be either unbounded, or bounded but highly oscillatory. In this paper, an approximate output tracking control design method is introduced for pulsewidth modulated (PWM) systems with unacceptable zeros. The design method is applied to the nonlinear sampled-data model of the PWM system, and is based on output redefinition. Although the new approach leads to approximate rather than perfect output tracking, it guarantees bounded and nonoscillatory responses.