Steve Daley

Novel adaptive repetitive algorithm for active vibration control of a variable-speed rotor

The paper describes experimental work that demonstrates the use of repetitive control to attenuate radial vibrations of a variable speed-rotor. The experiments were performed on a rotor test rig having a 3-kg rotor supported by journal bearings. The first bending resonance of the rotor shaft (i.e. the critical speed) was approximately 50 Hz. The objective was to control the radial response at the rotor midpoint by using an actuator located outside the bearing span. A novel aspect of the controller design is that the length of the control output vector of the repetitive controller was updated as a function of the speed of rotation. The speed of rotation determined the required delay time and the repetitive filter length that approximately matches with the delay time. The results obtained were comparable to those achieved in earlier studies with feedforward compensation methods. The best results were achieved when the frequency of rotation enables an integer ratio between disturbance period and sample rate.

Robust gradient iterative learning control: time and frequency domain conditions

This paper considers the use of matrix models and the robustness of a gradient-based iterative learning control (ILC) algorithm using fixed learning gains to ensure monotonic convergence with respect to the mean square value (Euclidean norm) of the error time series. The paper provides a complete and rigorous analysis for the systematic use of matrix models in ILC. They provide necessary and sufficient conditions for robust monotonic convergence and permit the construction of sufficient frequency domain conditions for robust monotonic convergence on finite time intervals for both causal and non-causal controller dynamics.

Limit sets and switching strategies in parameter-optimal iterative learning control

This paper characterizes the existence and form of the possible limit error signals in typical parameter-optimal iterative learning control. The set of limit errors has attracting and repelling components and the behaviour of the algorithm in the vicinity of these sets can be associated with the undesirable properties of apparent (but in fact temporary) convergence or permanent slow convergence properties in practice. The avoidance of these behaviours in practice is investigated using novel switching strategies. Deterministic strategies are analysed to prove the feasibility of the concept by proving that each of a number of such strategies is guaranteed to produce global convergence of errors to zero independent of the details of plant dynamics. For practical applications a random switching strategy is proposed to replace these approaches and shown, by example, to produce substantial potential improvements when compared with the non-switching case. The work described in this paper is covered by pending patent applications in the UK and elsewhere.

A geometric design approach to the broadband control of remotely located vibration

Over the past three decades, a wide variety of active control methods have been proposed for controlling problematic vibration. The vast majority of approaches make the implicit assumption that sensors can be located in the region where vibration attenuation is required. However, for many large scale structures or where the system environment is harsh, this is either not feasible or prohibitively expensive. As a result, the optimal control of local vibration may lead to enhancement at remote locations. Motivated by such problems in marine system environments, a geometric methodology that provides an approach for defining the design freedom available for reducing vibration both at local and remote locations has been proposed by the authors in a previous paper. The results are then used to develop design procedures for discrete frequency control. In this paper, design procedures for broadband control are developed. Particularly it is shown that the broadband control problem along with the convex optimization over LMI can be cast into this geometric framework. A numerical example is given with the broadband attenuation of rotor blade vibration to illustrate the design procedure.

Adjoint multivariable repetitive control algorithm for active control of vibration

Abstract In this paper a well-known adjoint SISO Repetitive Control algorithm is extended to the multivariable case and its convergence properties are analysed. The new adjoint algorithm is validated using a simulation of an experimental facility consisting of a passive Naval vibration isolation mount that is combined with six active control channels located in a Stewart platform style arrangement. The algorithm utilises a multivariable FIR system description that is derived from frequency response function measurements. The adjoint repetitive control algorithm is used to eliminate a harmonic disturbance where the first harmonic coincides with the fundamental mount resonance of the passive component. The simulation results show that the repetitive control algorithm ultimately achieves good vibration isolation but due to the wide spread of system eigenvalues at the harmonic frequency, convergence is slow. Copyright

The "Smart Spring" mounting system: A new active control approach for isolating marine machinery vibration 1

Abstract A major problem, in isolating large marine machinery rafts, is how best to isolate excited resonances. These generate large forces on the hull and create a major vibration problem. The design of such mounts typically represents a compromise between providing good vibration isolation and good machinery alignment under seaway motion. This paper describes a completely new approach to the problem of isolating marine machinery by making use of digitally controlled actuators that ignore local displacements while controlling the response of the structures rigid body modes. The paper describes how this is accomplished and gives some preliminary experimental results.

Experimental validation of a geometric method for the design of stable and broadband vibration controllers using a propeller blade test rig

A systematic geometric design methodology to generate a stable controller for simultaneous local and remote attenuation that was previously proposed is experimentally validated on a structure. The local control path transfer function for this experimental system is non-minimum phase due to which the original broadband controller design would yield an unstable controller. Here a modified procedure for systems with local non-minimum phase dynamics is used to generate a stable controller. According to this method, reduction in vibration at local and remote points on a structure can be parameterised in terms of the available design freedom and a controller is realised in terms of the optimal selection of this using the minimum phase counterpart of the local control path transfer function. The modified method results in a controller that is both stable and stabilizing and which achieves the desired vibration attenuation at the local and remote points on the structure. An experimental facility that replicates the vibration transmission through the shaft of a propeller blade rig system is used to demonstrate the method. Vibration for excitation near the first bending mode frequency of the resonating part of this structure is attenuated at the non-resonating part of the system without deteriorating vibration at the resonating end.

Active control of a frequency varying tonal disturbance by a nonlinear optimal controller with frequency tracking

Abstract In this paper a method for suppressing frequency varying tonal disturbances is presented. In most of such processes additional components are required to be installed within the process to measure the disturbance frequency. The proposed nonlinear optimal controller is combined with an RLS-based frequency tracking algorithm. The resulting controller is adaptive in terms of the disturbance frequency and can act as a stand-alone solution for the suppression of tonal disturbances, requiring only measurements from the process output. The performance of the resulting controller is validated by implementation on a process emulating the problem of isolating vibration using flexible raft structures.

Proportional difference type iterative learning control algorithm based on parameter optimization

In order to enhance learning efficiency and obtain more accuracy transient tracking performances in iterative domain, a proposition difference type operator constructed ldquofive termsrdquo parameter optimal iterative learning control algorithm based on norm performance index is proposed. The convergence condition and necessary theoretic proof is given. And the reasons why the algorithm has better learning efficiency and monotone convergence performance are discussed in detail. Finally, a class of parameter optimal iterative learning control algorithm tracking performances with different structure is compared. Simulation show that the tracking error of the proposed algorithm in this paper converges monotonically and faster than other similar algorithms.

Stability and convergence analysis for different harmonic control algorithm implementations

In many engineering systems there is a common requirement to isolate the supporting foundation from low frequency periodic machinery vibration sources. In such cases the vibration is mainly transmitted at the fundamental excitation frequency and its multiple harmonics. It is well known that passive approaches have poor performance at low frequencies and for this reason a number of active control technologies have been developed. For discrete frequencies disturbance rejection Harmonic Control (HC) techniques provide excellent performance. In the general case of variable speed engines or motors, the disturbance frequency changes with time, following the rotational speed of the engine or motor. For such applications, an important requirement for the control system is to converge to the optimal solution as rapidly as possible for all variations without altering the systems stability. For a variety of applications this may be difficult to achieve, especially when the disturbance frequency is close to a resonance peak and a small value of convergence gain is usually preferred to ensure closed-loop stability. This can lead to poor vibration isolation performance and long convergence times. In this paper, the performance of two recently developed HC algorithms are compared (in terms of both closed-loop stability and speed of convergence) in a vibration control application and for the case when the disturbance frequency is close to a resonant frequency. In earlier work it has been shown that both frequency domain HC algorithms can be represented by Linear Time Invariant (LTI) feedback compensators each designed to operate at the disturbance frequency. As a result, the convergence and stability analysis can be performed using the LTI representations with any suitable method from the LTI framework. For the example mentioned above, the speed of convergence provided by each algorithm is compared by determining the locations of the dominant closed-loop poles and stability analysis is performed using the open-loop frequency responses and the Nyquist criterion. The theoretical findings are validated through simulations and experimental analysis.