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 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.