Output Error Feedback Research Articles

Motion-Tracking Control of Mobile Manipulation Robotic Systems Using Artificial Neural Networks for Manufacturing Applications

Robotic systems have experienced exponential growth in their utilization for manufacturing applications over recent decades. Control systems responsible for executing desired robot motion planning face increasingly stringent performance requirements. These demands encompass high precision, efficiency, stability, robustness, ease of use, and simplicity of the user interface. Furthermore, diverse modern manufacturing applications primarily employ robotic systems within disturbed operating scenarios. This paper presents a novel neural motion-tracking control scheme for mobile manipulation robotic systems. Dynamic position output error feedback and B–Spline artificial neural networks are integrated in the design process of the introduced adaptive robust control strategy to perform efficient and robust tracking of motion-planning trajectories in robotic systems. Integration of artificial neural networks demonstrates performance improvements in the control scheme while effectively addressing common issues encountered in manufacturing environments. Parametric uncertainty, unmodeled dynamics, and unknown disturbance torque terms represent some adverse influences to be compensated for by the robust control scheme. Several case studies prove the robustness of the adaptive neural control scheme in highly coupled nonlinear six-degree-of-freedom mobile manipulation robotic systems. Case studies provide valuable insights and validate the efficacy of the proposed adaptive multivariable control scheme in manufacturing applications.

Attractivity of unstable equilibria for a controlled Chen system via small output feedback

We present an output feedback controller for a single-input single-output variant of the Chen dynamical system that renders an unstable equilibrium point of the unforced system attractive using small control signals. The controller first exploits ergodicity of the unforced dynamics to asymptotically estimate the system’s state vector. Then, based on the proximity of the estimate to the desired equilibrium and a computable minimum wait time, a second stage begins applying static output error feedback. Attractivity is proven using interconnected system theory and Lyapunov analysis.

PI-generalizing saturated repetitive learning control for a class of nonlinear uncertain systems: Robustness w.r.t. relative degree zero or one

The class of single-input, single-output, nonlinear, time-invariant systems with unknown output-dependent nonlinearities, unknown parameters and relative degree ρ ∈ { 0 , 1 } is considered. A priori knowledge of the system includes globally Lipschitz nature of the nonlinearities and positive sign of the high-frequency gain, besides the minimum-phase property. Single-input, single-output, observable, minimum phase, linear, time-invariant systems are included as a very special case. The aim is to track, via the output error feedback only, periodic output reference signals with known period. Here we originally show that the same saturated repetitive learning control that constitutes the most natural generalization of the PI (Proportional–Integral) control, concurrently ensures the following properties for any initial condition of the system: asymptotic convergence to zero of the output tracking error is guaranteed if ρ = 1 ; exponential convergence to zero is achieved for both the output and the input tracking errors if ρ = 0 .

Experimental Application of Robust and Converse Dynamic Control for Rotary Flexible Joint Manipulator System

Performance evaluation of trajectory tracking for a rotary flexible joint system is demonstrated in this paper. The robust and converse dynamic (RCD) technique is proposed and implemented for this evaluation. This control methodology is of the left inversion type, i.e., the control inputs are obtained by means of plant output error feedback. RCD control encompasses the baseline inverse (BI) control and sliding mode control-based discontinuous control element. The baseline inverse controller enforces the prescribed servo (virtual) constraints that represent the control objectives. The control objectives of the baseline inverse controller are enclosed in the form of servo (virtual) constraints which are inverted using Moore–Penrose Generalized Inverse (MPGI) to solve for the baseline control law. To boost the robust attributes against parametric uncertainties and disturbances, a discontinuous control function is augmented with baseline controller such that semiglobal practical stability is guaranteed in the sense of Lyapunov. To exhibit the effectiveness of RCD control in terms of tracking performance, computer simulations are conducted in Simulink/Matlab environment. Furthermore, the practical implementation is also investigated through a real-time experiment on Quanser’s rotary flexible joint manipulator system. The experimental results obtained by RCD are compared to the conventional sliding mode and fractional-order control techniques.

Hybrid observer with finite-memory output error correction for linear systems under intrinsic impulsive feedback

A novel hybrid observer that estimates the states of an oscillating system composed of a linear chain structure and an intrinsic pulse-modulated feedback is considered. This particular type of plant model appears in e.g. endocrine systems with pulsatile hormone secretion. The observer reconstructs the continuous states of the model as well as the firing times and weights of the feedback impulses. Since the pulse-modulated feedback is intrinsic, no measurements of the discrete part of the plant are available to the observer. For a periodical plant solution, to reconstruct the hybrid state, the impulses in the observer have to be synchronized with those in the plant. The observer is equipped with two feedback loops driven by the output estimation error. One of these is utilized to correct the estimates of the continuous states. In contrast with previous observer designs, the estimate of the next impulse firing time is implemented by means of a finite-memory convolution operator. A pointwise mapping capturing the propagation of the continuous plant and observer states through the discrete cumulative sequence of the feedback firing instants is derived. Local stability properties of the synchronous mode are related to the spectral radius of the Jacobian of the pointwise mapping. The observer design is based on assigning a guaranteed convergence rate to the local dynamics of a synchronous mode through the output error feedback gains to the continuous and discrete part of the observer. The observation of a stable m-cycle in the plant is treated to establish a general scenario, whereas the special case of 1-cycle is worked out in detail as the most common one. A numerical example illustrates the observer performance in the case of periodic modes of low multiplicity in an impulsive model of testosterone regulation in the male. Despite the local nature of the design approach, convergence to a synchronous mode is observed for a wide range of initial conditions for the discrete state estimate in the observer.

Output tracking for a non-minimum phase robotic manipulator

We exploit a recently developed funnel control methodology for linear non-minimum phase systems to design an output error feedback controller for a nonlinear robotic manipulator, which is not minimum phase. We illustrate the novel control design by a numerical case study where we simulate end-effector output tracking of the robotic manipulator.

DC Motor Identification Based on Artificial Neural Networks Implementation in a Microcontroller

In the last few decades neural networks have been involved in many fields of researches and their application was restricted to be embedded on a computer. This paper describes implementing of artificial neural network (ANN) based on a low cost microcontroller to identify a DC motor mode. The identifier will act as path for the output error feedback in Model Reference Adaptive Controller or to build an inverse controller. To reduce the size of the proposed system, the DC Motor is controlled conventionally using the method of Pulse Width Modulation technique on the same microcontroller. The proposed neural network is a multilayer feed-forward network which is of three layers (1-3-1) structure. The training technique used the back propagation algorithm by using C program. Identification process has been implemented successfully in the microcontroller and validated with different randomly picked data with least mean square error of 0.0007.

Stabilization of Switched Nonlinear Systems by Adaptive Observer-Based Dynamic Surface Control with Nonlinear Virtual and Output Feedback

This paper presents a new nonlinear output and virtual error feedback control technique for stabilization of switched uncertain nonlinear systems using a continuous differentiable nonlinear feedback function (NFF). The merits of the proposed method are threefold: (i) there is no assumption that the switching signals must satisfy the (average) dwell time, (ii) the feedback amplitude self-adjusts under different state levels to guarantee better dynamic performance using the NFF, and (iii) the number of parameters that needs online tuning is 1, i.e., the proposed control method is computationally inexpensive. Moreover, the closed-loop signals are kept bounded using the rigorously proved Lyapunov and Invariant-set theorems, and the output signal converges to a sufficiently small region around zero by choosing proper design parameters. Finally, simulation and comparative results are given to demonstrate the effectiveness of the proposed method.

Output and error feedback regulator designs for linear infinite-dimensional systems

This manuscript addresses the output regulation problem for linear distributed parameter systems (DPSs) with bounded input and unbounded output operators. We introduce novel methods for the design of the output feedback and error feedback regulators. In the output feedback regulator design, the measurements available for the regulator do not belong to the set of controlled outputs. The proposed output feedback regulator with the injection of the measurement ym(t) and reference yr(t) can realize both the plant and the exosystem states estimation, disturbance rejection and reference signal tracking, simultaneously. Moreover, new design approach provides an alternative choice for seeking the output injection gain in a traditional error feedback regulator design. The regulator parameters are easily configured to solve the output regulation problems, and to ensure the stability of the closed-loop systems. The results are demonstrated via computer simulation in two types of representative systems: the parabolic partial differential equation (PDE) system and the first order hyperbolic PDE system.

Trajectory planning and tracking control for the temperature distribution in a deep drawing tool

The deep drawing process and the resulting product quality essentially rely on the temperature distribution inside the tool. For temperature manipulation and control a flatness-based design technique for thermal trajectory planning and feedforward control for a deep drawing tool is developed based on a distributed parameter system description. Heating cartridges, that are embedded into the tool structure, serve as actuators to insert energy into the system with the desire to transfer the spatial-temporal temperature distribution from an initial to a desired final stationary profile. To address the complex-shaped geometry of the tool a high-order finite element (FE) approximation is deduced and combined with model-order reduction techniques to determine a sufficiently low order system representation that is applicable for optimal actuator placement. For this, a mixed-integer optimization problem is formulated based on a particular reduced-order formulation of the controllability Gramian. The resulting actuator configuration is exploited for flatness-based trajectory planning by constructing a virtual output that differentially parametrizes any system state and input. This implies a particularly intuitive approach to solve the thermal trajectory planning problem. Convergence of the differential parametrization is analyzed in the continuous limit as the finite element approximation approaches the continuum model. Re-summation techniques are integrated into the design to enhance the domain of applicability of the approach. The feedforward control is combined with industry-standardized proportional-integral-derivative (PID) output error feedback control within the so-called two-degree-of-freedom (2DOF) control concept. Simulation and experimental results obtained for a fully equipped forming tool are presented and confirm the applicability of the proposed design technique and the tracking performance. In addition, the results of this paper present a first experimental validation of flatness-based trajectory planning for thermal systems with three-dimensional spatial domain.

Zero dynamics and funnel control of general linear differential-algebraic systems

We study linear differential-algebraic multi-input multi-output systems which are not necessarily regular and investigate the zero dynamics and tracking control. We introduce and characterize the concept of autonomous zero dynamics as an important system theoretic tool for the analysis of differential-algebraic systems. We use the autonomous zero dynamics and ( E, A, B )-invariant subspaces to derive the so called zero dynamics form – which decouples the zero dynamics of the system – and exploit it for the characterization of system invertibility and asymptotic stability of the zero dynamics. A refinement of the zero dynamics form is then used to show that the funnel controller (that is a static nonlinear output error feedback) achieves – for a special class of right-invertible systems with asymptotically stable zero dynamics – tracking of a reference signal by the output signal within a pre-specified performance funnel. It is shown that the results can be applied to a class of passive electrical networks.

Transients in output feedback adaptive systems with observer‐like reference models

This note presents analysis and quantification of transient dynamics in Model Reference Adaptive Control MRAC with output feedback and observer-like reference models. A practical design methodology for this class of systems was first introduced in , where an output error feedback was added to the reference model dynamics. Here, this design is complemented with an analysis of the corresponding transients. Specifically, it is shown that employing observer-like reference models in MRAC leads to a trade-off between achieving fast transient dynamics and using large error feedback gains in the modified reference model. For clarity sake, only systems with matched uncertainties are analyzed, yet the reported results can be extended to a broader class of uncertainties by utilizing MRAC modifications for robustness . The note ends with a summary of the derived results and a discussion on practical design guidelines for adaptive output feedback controllers with observer-like reference models. Copyright © 2015John Wiley & Sons, Ltd.

Robust Nonlinear Control of an Innovative Engine Cooling System

In this paper, a robust nonlinear control of an engine cooling system for vehicles is presented, where an electrically driven radiator fan serves as the control input. A simplified control-oriented model of the engine cooling system is derived using the first law of thermodynamics. The control design is based on an integral sliding mode approach and aims at tracking of desired trajectories for the engine outlet temperature. A gain-scheduled modified Utkin sliding mode observer, which uses both a switching term and an output error feedback, is employed to estimate unknown heat ows acting as system disturbances. The estimated heat ows are used in the control structure for a disturbance compensation. An experimental analysis highlights the effectiveness of the integral sliding mode control strategy in combination with the gain-scheduled sliding mode observer.

Linear repetitive learning controls for nonlinear systems by Padé approximants

SummaryWe discuss the use of [m,m]‐Padé approximants in the implementation of repetitive learning controls solving the output tracking problem (via output error feedback) in the presence of uncertain periodic reference and/or disturbance signals with known common period. The aim is to address the stability issues concerning those approximants when a linear learning controller—designed through a detailed stability proof (involving the use of a suitable Lyapunov‐like function) and described by a transfer function exhibiting all its poles with negative real part—is to be obtained as well as to evaluate the corresponding closed‐loop performances: robustness (for instance with respect to additive disturbance noises due to unmodeled sensor dynamics) is consequently achieved with improvements in the output tracking errors appearing as the approximation order m increases. Even though the case of any relative degree may be explicitly addressed, in this paper, for the sake of clarity, we restrict our attention to the learning problem for the class of single‐input, single‐output, minimum phase, time‐invariant systems with known relative degree ρ = 2, uncertain parameters and uncertain output‐dependent nonlinearities. Numerical simulation results illustrate the theoretical derivations. Copyright © 2014 John Wiley & Sons, Ltd.

Trajectory Planning For a Deep Drawing Tool

Model-based trajectory planning is addressed for the realization of desired temperature trajectories for a deep drawing tool. Based on the distributed-parameter system description of the tool a finite element approximation is deduced which serves as basis for a systematic flatness-based design of a feedforward control. Trajectory assignment is considered by taking into account the minimization of a process-related objective function. Simulation and experimental data obtained from a fully equipped forming tool are presented for pure feedforward control and a two-degree-of-freedom control concept amending the feedforward part by an output error feedback controller. These confirm the applicability of the design technique and the tracking performance.

Funnel Control for Linear DAEs

AbstractWe study funnel control for linear differential‐algebraic multi‐input multi‐output systems which are not necessarily regular. We show that the funnel controller (that is a static nonlinear output error feedback) achieves ‐ for a special class of right‐invertible systems with asymptotically stable zero dynamics ‐ tracking of a reference signal by the output signal within a pre‐specified performance funnel. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Zero dynamics and funnel control of linear differential-algebraic systems

We study the class of linear differential-algebraic m-input m-output systems which have a transfer function with proper inverse. A sufficient condition for the transfer function to have proper inverse is that the system has ‘strict and non-positive relative degree’. We present two main results: first, a so-called ‘zero dynamics form’ is derived; this form is—within the class of system equivalence—a simple form of the DAE; it is a counterpart to the well-known Byrnes–Isidori form for ODE systems with strictly proper transfer function. The ‘zero dynamics form’ is exploited to characterize structural properties such as asymptotically stable zero dynamics, minimum phase, and high-gain stabilizability. The zero dynamics are characterized by (A, E, B)-invariant subspaces. Secondly, it is shown that the ‘funnel controller’ (that is a static non-linear output error feedback) achieves, for all DAE systems with asymptotically stable zero dynamics and transfer function with proper inverse, tracking of a reference signal by the output signal within a pre-specified funnel. This funnel determines the transient behaviour.

Nonlinear PI control of fed-batch processes for growth rate regulation

This paper deals with the regulation of the biomass specific growth rate, which is an important goal in many fed-batch fermentation processes. The proposed control system is based on the minimal model paradigm, requiring only biomass and volume measurement along with some bounds on the reaction rate. The controller has the structure of a partial state feed-back with adjustable gain. An integral-proportional control algorithm is designed to adjust this gain. It is inspired in concepts of invariant control and system immersion. First, a nonlinear integral action that makes invariant a goal manifold defined by a reference model dynamics is developed. Then, a proportional output error feed-back is incorporated to the control law with the aim of fastening convergence. Stability is investigated in detail using Lyapunov functions. To implement the control law, an estimation of the growth rate is required like any other PI-like controller. Because of its strong convergence properties, a sliding observer that requires the same process information as the controller is used for this task, although conventional continuous observers can alternatively be used provided they are fast enough to preserve stability. Simulation results showing the transient response and robustness features of the controller under nominal and perturbed scenarios are presented.

Output-feedback lag-synchronization of time-delayed chaotic systems in the presence of external disturbances subjected to input nonlinearity

In this paper, an adaptive output error feedback control scheme is proposed for the lag-synchronization of two time-delayed chaotic systems in the presence of channel time-delay, external disturbances and input nonlinearity. Using the Lyapunov theory, stability of the proposed adaptive controller is proved. Lyapunov-Krasovskii approach is used to deal with the existence of time-delay in the system dynamics. Finally, two numerical simulations are presented to illustrate the effectiveness of the developed method.

An adaptive learning regulator for uncertain minimum phase systems with undermodeled unknown exosystems

The design of an adaptive learning regulator is addressed for uncertain minimum phase linear systems (with known bounds, known upper bound on system order, known relative degree, known high frequency gain sign) and for unknown exosystems (with unknown order, uncertain frequencies). On the basis of a known bound on system uncertainties and a known bound on the modeled exosystem frequencies, a new adaptive output error feedback control algorithm is proposed which guarantees exponential convergence of both the output and the control input errors into residual bounds which decrease as the exosystem modeling error decreases. Exponential convergence of both errors to zero is obtained when the regulator exactly models all exosystem excited frequencies, while asymptotic convergence of both errors to zero is achieved when the actual exosystem is overmodeled by the regulator. The new algorithm generalizes existing learning controllers since, in the case of periodic references and/or disturbances, the knowledge of the period is not required.