Adaptive input shaping for manoeuvring flexible structures using an algebraic identification technique

Input shaping is an efficient feedforward control technique which has motivated a great number of contributions in recent years. Such a technique generates command signals with which manoeuvre flexible structures without exciting their vibration modes. This paper presents a novel adaptive input shaper based on an algebraic non-asymptotic identification. The main characteristic of the algebraic identification in comparison with other identification methods is the short time needed to obtain the system parameters without defining initial conditions. Thus, the proposed adaptive control can update the input shaper during each manoeuvre when large uncertainties are present. Simulations illustrate the performance of the proposed method.     

Experimental control of a single-link flexible robot arm using energy shaping

Flexible-link robotic manipulators are mechanical devices whose control can be rather challenging, among other reasons because of their intrinsic under-actuated nature. This paper presents the application of an energy-based control design methodology (the so-called IDA-PBC, interconnection and damping assignment passivity-based control) to a single-link flexible robotic arm. It is shown that the method is well suited to handle this kind of under-actuated device not only from a theoretical viewpoint but also in practice. A Lyapunov analysis of the closed-loop system stability is given and the design performance is illustrated by means of a set of simulations and laboratory control experiments, comparing the results with those obtained using conventional control schemes for mechanical manipulators.     

Adaptive input shaping for maneuvering flexible structures

In the control of flexible structures many methods are used to reduce residual vibration due to the excitation of flexible modes. Input shaping, a feed-forward method, typically convolves the input with a sequence of impulses that are independent of the system maneuver. While reducing the residual vibration, input shaping extends the duration of the maneuver command by the length of the input shaper. This paper explores the idea of adaptive input shaping which allows a fast input shaper to be used while providing robustness to parameter uncertainty by tuning the shaper to the flexible mode frequency. The adaptive input shaping method presented can adapt between maneuvers or during maneuvers. Analysis yields a large range of convergence that is verified by simulation and shows this method to be less complex than other adaptive approaches.     

Improving an adaptive controller for non-minimum phase plants

This study improves an adaptive controller for linear discrete-time plants in two aspects: (1) a new adaptation law is proposed to reduce the residual and the parameter errors; (2) a new method is proposed to modify the parameter estimates if the estimated model is not controllable. The second improvement is required when the plant is non-minimum phase. It obtains a controllable model from available parameter estimates while minimizing the modification offset. These features enhance closed-loop tracking performance of the adaptive controller when it is applied to non-minimum phase plants.     

Designing feedforward command shapers with multi-objective genetic optimisation for vibration control of a single-link flexible manipulator

This paper presents investigations into the design of a command-shaping technique using multi-objective genetic optimisation process for vibration control of a single-link flexible manipulator. Conventional design of a command shaper requires a priori knowledge of natural frequencies and associated damping ratios of the system, which may not be available for complex flexible systems. Moreover, command shaping in principle causes delay in system's response while it reduces system vibration and in this manner the amount of vibration reduction and the rise time conflict one another. Furthermore, system performance objectives, such as, reduced overshoot, rise time, settling time, and end-point vibration are found in conflict with one another due to the construction and mode of operation of a flexible manipulator. Conventional methods can hardly provide a solution, for a designer-oriented formulation, satisfying several objectives and associated goals as demanded by a practical application due to the competing nature of those objectives. In such cases, multi-objective optimisation can provide a wide range of solutions, which trade-off these conflicting objectives so as to satisfy associated goals. A multi-modal command shaper consists of impulses of different amplitudes at different time locations, which are convolved with one another and then with the desired reference and then used as reference (for closed loop) or applied to system (for open loop) with the view to reduce vibration of the system, mainly at dominant modes. Multi-objective optimisation technique is used to determine a set of solutions for the amplitudes and corresponding time locations of impulses of a multi-modal command shaper. The effectiveness of the proposed technique is assessed both in the time domain and the frequency domain. Moreover, a comparative assessment of the performance of the technique with the system response with unshaped bang–bang input is presented.     

A discrete-time approach to impulse-based adaptive input shaping for motion control without residual vibration

Modifying a command or actuation signal by convolving it with a sequence of impulses is a useful technique for eliminating structural vibration in rest-to-rest motion of mechanical systems. This paper describes an adaptive discrete-time version of this approach where amplitude and timing of impulses are tuned during operation to match the system under control. Solutions giving zero residual vibration are formulated in terms of a quadratic cost function and constructed by iterative operations on measured sets of input–output data. The versatility of the approach is demonstrated by simulated test cases involving (1) amplitude optimization of impulses with fixed timings, (2) timing optimization of impulses with fixed amplitudes and (3) combined timing and amplitude optimization. The approach is model-free and directly applicable to multi-mode systems. Moreover, fast adaptation within a single rest-to-rest maneuver can be achieved.     

Auxiliary signal design for rapid multi-model identification using optimization

Under the assumption that one of several given models is the real underlying model of the system, a proper auxiliary signal is defined as an input signal that allows one to select the correct model. It is assumed that there is no knowledge prior to the beginning of the application of the auxiliary signal and that detection is to be done within a specified detection horizon. Under the assumption that the noise energy is bounded, a method for the computation of the minimal energy auxiliary signal is given. The new algorithm extends previous work in that it can handle more than two models and certain types of nonlinearities.     

Adaptive control based on fast online algebraic identification and GPI control for magnetic levitation systems with time-varying input gain

This paper considers the position tracking problem of a voltage-controlled magnetic levitation system (MLS) in the presence of modelling errors caused by uncertainties in the system’s physical parameters. An adaptive control based on fast online algebraic parameter estimation and generalised proportional integral (GPI) output feedback control is considered as a control scheme candidate. The GPI controller guarantees an asymptotically exponentially stable behaviour of the controlled ball position and the possibilities of carrying out rest-to-rest trajectory tracking tasks. The nature of the control input gain in an MLS is that of a state-dependent time-varying gain, reflecting the nonlinear character of the magnetic force with regard to the distance and the properties of the metallic ball. The system gain has therefore been locally approximated using a periodically updated time polynomial function (of second degree), where the coefficients of the polynomial are estimated during a very short period of time. This estimation is achieved using the recently introduced algebraic online parameter estimation approach. The stability of the closed-loop system is demonstrated under the assumption that no external factors cause changes in the parameter during the time interval in which the stability is analysed. Finally, experimental results are presented for the controlled MLS demonstrating the excellent stabilisation and position tracking performance of the control system designed in the presence of significant nonlinearities and uncertainties of the underlying system.     

Intelligent on-line system identification using a blackboard system

Adaptive control systems have been developed and used for a number of decades. However, there are still some problems with their operation, which limit wider industrial adoption. This paper addresses one aspect of adaptive control, namely the on-line system identification of the time-varying process being controlled. The approach adopted is to use a blackboard system to identify the time-varying process model. The blackboard system contains knowledge sources with, algorithmic, fuzzy-logic and evolutionary reasoning. The paper describes the design of a computer simulation of this approach, concentrating on the fuzzy reasoning used to validate the multiple models, and the evolutionary techniques used to reject poor models and introduce better models. The computer simulation is then evaluated, firstly using simulated plant data and then using real plant data from an experimental hot air dryer. It is concluded that the technique is practical, and worthy of further testing on a pilot plant.     

Adaptive compensation control for special actuator circumstances with input quantization

In this article, considering actuator constraints and possible failures, an adaptive compensation control scheme is developed to realize tracking control for a class of uncertain nonlinear systems with quantized inputs. A new variable is generated to evaluate the effect of actuator saturation and is used in the process of controller design to compensate for the influence of actuator saturation constraint. Moreover, the controller is able to show certain accommodation capability to tolerate possible actuator failures and input quantization error via integrating parameter update process of unknown fault constants into adaption of parametric uncertainties under the backstepping procedure. Specifically, actuator saturation effect and possible actuator failures as well as input quantization error can be dealt with uniformly under the framework of the proposed scheme and the control system has certain robustness to external disturbances. It is proved that all the signals of the closed‐loop system are ensured to be bounded and the tracking error is enabled to converge toward a compact set, which is adjustable by tuning design parameters. Finally, experiments are carried out on an active suspension plant to illustrate the effectiveness of the proposed control scheme.     

Adaptive identification and control algorithms for nonlinear bacterial growth systems

This paper suggests how nonlinear adaptive control of nonlinear bacterial growth systems could be performed. The process is described by a time-varying nonlinear model obtained from material balance equations. Two different control problems are considered: substrate concentration control and production rate control. For each of these cases, an adaptive minimum variance control algorithm is proposed and its effectiveness is shown by simulation experiments. A theoretical proof of convergence of the substrate control algorithm is given. A further advantage of the nonlinear approach of this paper is that the identified parameters (namely the growth rate and a yield coefficient) have a clear physical meaning and can give, in real time, a useful information on the state of the biomass.     

Adaptive output-feedback control for a class of nonlinear systems with actuator failures and input quantisation

In this paper, an adaptive output feedback control technique is proposed for a class of nonlinear systems with unknown parameters, unknown nonlinear functions, quantised input and possible actuator failures up to infinity. A modified backstepping approach is proposed by the use of high-gain K-filters, hyperbolic tangent function property and bound-estimation approach to compensate for the effect of possible number of actuator failures up to infinity, input quantisation and unknown nonlinear functions. It is proved both mathematically and by simulation that with the proposed controller, all the signals of the closed-loop system are globally bounded despite of input quantisation, unknown nonlinear functions and possible number of actuator failures up to infinity.     

Reliability-based robust Pareto design of linear state feedback controllers using a multi-objective uniform-diversity genetic algorithm (MUGA)

In this paper, fuzzy threshold values, instead of crisp threshold values, have been used for optimal reliability-based multi-objective Pareto design of robust state feedback controllers for a single inverted pendulum having parameters with probabilistic uncertainties. The objective functions that have been considered are, namely, the normalized summation of rising time and overshoot of cart (S_RO–C) and the normalized summation of rising time and overshoot of pendulum (S_RO–P) in the deterministic approach. Accordingly, the probabilities of failure of those objective functions are also considered in the reliability-based design optimization (RBDO) approach. A new multi-objective uniform-diversity genetic algorithm (MUGA) is presented and used for Pareto optimum design of linear state feedback controllers for single inverted pendulum problem. In this way, Pareto front of optimum controllers is first obtained for the nominal deterministic single inverted pendulum using the conflicting objective functions in time domain. Such Pareto front is then obtained for single inverted pendulum having probabilistic uncertainties in its parameters using the statistical moments of those objective functions through a Monte Carlo simulation (MCS) approach. It is shown that multi-objective reliability-based Pareto optimization of the robust state feedback controllers using MUGA with fuzzy threshold values includes those that may be obtained by various crisp threshold values of probability of failures and, thus, remove the difficulty of selecting suitable crisp values. Besides, the multi-objective Pareto optimization of such robust feedback controllers using MUGA unveils some very important and informative trade-offs among those objective functions. Consequently, some optimum robust state feedback controllers can be compromisingly chosen from the Pareto frontiers.     

Adaptive neural network control for strict-feedback nonlinear systems using backstepping design

This paper focuses on adaptive control of strict-feedback nonlinear systems using multilayer neural networks (MNNs). By introducing a modified Lyapunov function, a smooth and singularity-free adaptive controller is firstly designed for a first-order plant. Then, an extension is made to high-order nonlinear systems using neural network approximation and adaptive backstepping techniques. The developed control scheme guarantees the uniform ultimate boundedness of the closed-loop adaptive systems. In addition, the relationship between the transient performance and the design parameters is explicitly given to guide the tuning of the controller. One important feature of the proposed NN controller is the highly structural property which makes it particularly suitable for parallel processing in actual implementation. Simulation studies are included to illustrate the effectiveness of the proposed approach.     

Robust adaptive vibration control for an uncertain flexible Timoshenko robotic manipulator with input and output constraints

The problems of the constraints and the vibration suppression are investigated for the flexible Timoshenko robotic manipulator in this paper. Robust adaptive boundary control laws with the disturbance observes are designed to guarantee the convergence of the feedback flexible Timoshenko robotic manipulator system with the uncertain parameters and the states are proven to be uniform bounded. In addition, the proposed boundary controls are verified to be effectiveness by the numeral experiments.     

Proposal and validation of an optimization method using Monte Carlo method for multi-objective functions

Solving optimization problems is essential for many engineering applications and research tools. In a previous report, we proposed a new optimization method, MOST (Monte Carlo Stochastic Optimization), using the Monte Carlo method, and applied it to benchmark problems for optimization methods, and optimization of neural network machine learning. While the proposed method MOST was a single objective, this study is an extension of MOST so that it can be applied to multi-objective functions for the purpose of improving generality. As the verification, it was applied to the optimization problem with the restriction condition first, and it was also applied to the benchmark problem for the multi-objective optimization technique verification, and the validity was confirmed. For comparison, the calculation by genetic algorithm was also carried out, and it was confirmed that MOST was excellent in calculation accuracy and calculation time.     

A new recursive identification algorithm for singularity free adaptive control

Reportedly, guaranteeing the controllability of the estimated system is a crucial problem in adaptive control. In this paper, we introduce a least-squares-based identification algorithm for stochastic SISO systems, which secures the uniform controllability of the estimated system and presents closed-loop identification properties similar to those of the least-squares algorithm. The proposed algorithm is recursive and, therefore, easily implementable. Its use, however, is confined to cases in which the parameter uncertainly is highly structured.     

Adaptive actuator failure compensation for nonlinear MIMO systems with an aircraft control application

A direct adaptive approach is developed for control of a class of multi-input multi-output (MIMO) nonlinear systems in the presence of uncertain failures of redundant actuators. An adaptive failure compensation controller is designed which is capable of accommodating uncertainties in actuator failure time instants, values and patterns. A realistic situation is studied with fixed grouping of actuators and proportional actuation within actuator groups. The adaptive control system is analyzed, to show its desired stability and asymptotic tracking properties in the presence of actuator failure uncertainties. As an application, such an adaptive controller is used for actuator failure compensation of a twin otter aircraft longitudinal model, with design conditions verified and control structure and adaptive laws developed for a nonlinear aircraft dynamic model. The effectiveness of adaptive failure compensation is demonstrated by simulation results.     

Adaptive dynamic surface control using disturbance observer for nonlinear systems with input saturation and output constraints

An adaptive dynamic surface control (DSC) approach using fuzzy approximation and nonlinear disturbance observer (NDO) for uncertain nonlinear systems in the presence of input saturation, output constraint and unknown external disturbances is proposed in this paper. The issue of input saturation is addressed by introducing a lower bound assumption on the approximation function of saturation. The output constraint is handled by introducing an appropriate barried Lyapunov function. The nonlinear disturbance observer (NDO) is employed to estimate the unknown unmatched disturbances. It is manifested that the ultimately bounded convergence of all the variables in the closed-loop system is guaranteed and the tracking error can be made farely small by tuning the design parameters. Finally, two simulation examples illustrate the effectiveness and feasibility of the proposed approach.     

Adaptive Fuzzy Sliding Mode Controller for the Kinematic Variables of an Underwater Vehicle

This paper address the kinematic variables control problem for the low-speed manoeuvring of a low cost and underactuated underwater vehicle. Control of underwater vehicles is not simple, mainly due to the non-linear and coupled character of system equations, the lack of a precise model of vehicle dynamics and parameters, as well as the appearance of internal and external perturbations. The proposed methodology is an approach included in the control areas of non-linear feedback linearization, model-based and uncertainties consideration, making use of a pioneering algorithm in underwater vehicles. It is based on the fusion of a sliding mode controller and an adaptive fuzzy system, including the advantages of both systems. The main advantage of this methodology is that it relaxes the required knowledge of vehicle model, reducing the cost of its design. The described controller is part of a modular and simple 2D guidance and control architecture. The controller makes use of a semi-decoupled non-linear plant model of the Snorkel vehicle and it is compounded by three independent controllers, each one for the three controllable DOFs of the vehicle. The experimental results demonstrate the good performance of the proposed controller, within the constraints of the sensorial system and the uncertainty of vehicle theoretical models.