Showing papers in "International Journal of Control in 1990"

Non-linear system identification using neural networks

Abstract: Multi-layered neural networks offer an exciting alternative for modelling complex non-linear systems. This paper investigates the identification of discrete-time nonlinear systems using neural networks with a single hidden layer. New parameter estimation algorithms are derived for the neural network model based on a prediction error formulation and the application to both simulated and real data is included to demonstrate the effectiveness of the neural network approach.

Practical identification of NARMAX models using radial basis functions

Abstract: A wide class of discrete-time non-linear systems can be represented by the nonlinear autoregressive moving average (NARMAX) model with exogenous inputs. This paper develops a practical algorithm for identifying NARMAX models based on radial basis functions from noise-corrupted data. The algorithm consists of an iterative orthogonal-forward-regression routine coupled with model validity tests. The orthogonal-forward-regression routine selects parsimonious radial-basisTunc-tion models, while the model validity tests measure the quality of fit. The modelling of a liquid level system and an automotive diesel engine are included to demonstrate the effectiveness of the identification procedure.

Robust output tracking for non-linear systems

Abstract: The problem of output tracking for a single-input single-output non-linear system in the presence of uncertainties is studied. The notions relative degree and minimum-phase for non-linear systems are reviewed. Given a bounded desired tracking signal with bounded derivatives, a control law is designed for minimum-phase non-linear systems which results in tracking of this signal by the output. This control law is modified in the presence of uncertainties associated with the model vector fields to reduce the effects of these uncertainties on the tracking errors. Two types of uncertainties are considered: those satisfying a generalized matching condition but otherwise unstructured, and linear parametric uncertainties. It is shown that for systems with the first type of uncertainty, high-gain control laws can result in small tracking errors of O(∊), where e is a small design parameter. An alternative scheme based on variable structure control strategy is shown to yield zero tracking errors. Adaptive control te...

Control of induction motors via feedback linearization with input-output decoupling

Abstract: In induction motor control, power efficiency is an important factor to be considered. We attempt to achieve both high dynamic performance and maximum power efficiency by means of linear decoupling of rotor speed (or motor torque) and rotor flux. The induction motor with our controller possesses the input-output dynamic characteristics of a linear system such that the rotor speed (or motor torque) and the rotor flux are decoupled. The rotor speed responses are not affected by abrupt changes in the rotor flux and vice versa. The rotor flux need not be measured but is estimated by the well known flux simulator. The effect of large variation in the rotor resistance on the control performances is minimized by employing a parameter adaptation method. To illuminate the significance of our work, we present simulation and experimental results as well as mathematical performance analyses. In particular, our experimental work demonstrates that recently developed nonlinear feedback control theories are of practical use.

Mapping non-linear integro-differential equations into the frequency domain

Abstract: A recursive algorithm is derived to compute the generalized frequency response functions for a large class of non-linear integro-differential equations. Applications to Duffing's equation and a modified Van der Pol model are discussed.

Optimal control by dynamic programming using systematic reduction in grid size

Abstract: The use of dynamic programming to solve non-linear optimal control problems resistant to other methods is investigated. The proposed method utilizing a relatively coarse grid followed by systematic...

Parallel recursive prediction error algorithm for training layered neural networks

Abstract: A new recursive prediction error algorithm is derived for the training of feedforward layered neural networks. The algorithm enables the weights in each neuron of the network to be updated in an efficient parallel manner and has better convergence properties than the classical back propagation algorithm. The relationship between this new parallel algorithm and other existing learning algorithms is discussed. Examples taken from the fields of communication channel equalization and nonlinear systems modelling are used to demonstrate the superior performance of the new algorithm compared with the back propagation routine.

Robustness of a minimal controller synthesis algorithm

Abstract: Recently published empirical results (Stoten and Benchoubane 1990) show that a minimal controller synthesis (MCS) adaptive scheme is an extremely effective control strategy. The MCS algorithm appeared to be robust in the face of totally unknown plant dynamics, external disturbances and parameter variations within the plant. Here, an analysis is given of MCS robustness for single-input/single-output and multivariable plants of certain structure.

Two-dimensional model and algorithm analysis for a class of iterative learning control systems

Abstract: The iterative learning control system (ILCS) has attracted considerable research interest in recent years. However the theoretical results on some fundamental properties of the ILCS have not yet been established. One of the common drawbacks shared by current approaches is lack of a suitable mathematical model which can clearly describe both the dynamics of the control system itself and the behaviour of the learning process as well. In this paper, a class of iterative learning control systems is analysed from the point of view of two-dimensional (2-D) system theory. The 2-D model for a class of ILCS is established in the form of‘Roessor's model’, based on which a general type of learning controller is proposed. Analysis of the 2-D error equation shows that the 2-D asymptotic stability of the 2-D model guarantees the learning convergence of an ILCS. Design criteria for a learning controller is also suggested. The learning gain matrices are obtained from a recursive 2-D identifier using the input and output ...

Robust control for the tracking of robot motion

Abstract: In this paper we examine the stability of a proportional derivative (PD) controller for the trajectory-following problem of a robot manipulator. We use Lyapunov's second method to derive a uniform boundness result for the PD controller. We show that if the PD controller gains are chosen greater than a specific bound and if the initial tracking error is zero, the velocity and position tracking errors are uniformly bounded. We then develop two additional controllers that use auxiliary control inputs along with the PD controller. Both of these controllers are shown to yield a uniform ultimate boundness property for the tracking error.

Inherent Observer Property in a Class of Anti-Windup Compensators

Abstract: Owing to the types of non-linearities involved, the analysis and the comparison of different anti-windup compensators that are available in the literature become difficult. Towards achieving a better understanding of the mechanisms of these anti-windup compensators, we here expose the observer property inherent in a class of anti-windup compensators. This observer property allows us to unify these anti-windup compensators as special cases of the generalized anti-windup compensator due to Astrom and Wittenmark (1984), and provides a general framework to investigate their performance.

Squaring down of non-strictly proper systems

Abstract: In an earlier work, a procedure for squaring down proper systems by static and dynamic compensators has been developed. The compensators designed there have the following properties: (a) they are asymptotically stable; (b) the additional finite zeros induced by them are assignable to the open left half complex plane; and (c) they preserve the fundamental properties such as stabilizability, detectability, infinite zero structure and minimum phase nature of the original system. The earlier design procedure is extended to non-strictly proper systems while retaining all the above-mentioned properties.

Empirical studies of an MRAC algorithm with minimal controller synthesis

Abstract: An adaptive control algorithm based upon a well-known model reference adaptive control (MRAC) strategy is described. The main feature of this new algorithm is that minimal synthesis is required to implement the strategy—hence the appellation minimal controller synthesis (MCS). Specifically, no plant model is required (apart from a knowledge of the state dimension) and no controller gains have to be calculated. We also present two implementation studies and one simulation study of the MCS strategy to demonstrate the robustness and excellence of control that can be achieved. Robustness proofs are left to sequels of this paper.

Stabilization of discrete-event processes

Abstract: Discrete-event processes are modelled by state-machines in the Ramadge-Wonham framework with control by a feedback event disablement mechanism. In this paper concepts of stabilization of discrete-event processes are defined and investigated. We examine the possibility of driving a process (under control) from arbitrary initial states to a prescribed subset of the state set and then keeping it there indefinitely. This stabilization property is studied also with respect to ‘open-loop’ processes (i.e. uncontrolled processes) and their asymptotic behaviour is characterized. To this end, such well known classical concepts of dynamics as invariant sets and attractors are redefined and characterized in the discrete-event control framework. We provide polynomial time algorithms for verifying various types of attraction and for the. synthesis of attractors.

Application of dynamic programming to high-dimensional non-linear optimal control problems

Abstract: In using dynamic programming, by taking only accessible states for the x-grid and using an iterative procedure employing region contraction, only a small number of grid points are required at each ...

Review of wind turbine control

Abstract: The literature on the design of control sysems for medium- and large-scale wind turbine generators is reviewed. The vast majority of relevant literature is concerned with the control of horizontal-axis machines. Emphasis is given to public-utility service machines with power outputs in the range hundreds to thousands of kilowatts. This work was prompted by the need to determine specific objectives for the turbine control system. The control system is an integral part of the wind turbine; it is stochastic and non-linear and the different wind-turbine configurations pose a variety of design goals. The review highlights the lack of a clear consensus on the role of the control system and an inadequate treatment of dynamic and stochastic issues. Wind-turbine control is an application area with an interesting set of problems for control engineering. These problems have not been adequately solved and continue to pose challenges to the control community. Wind-turbine control issues are therefore important, since ...

Robust trajectory following of robots using computed torque structure with VSS

Abstract: A control approach is proposed for robust accurate trajectory tracking of manipulators based on the computed torque technique and variable-structure systems (VSS) theory. The computed torque structure of the control scheme, most importantly, provides greater insight to the control of manipulators and serves as a unifying framework for control law development. Looking at the control structure from a computed torque perspective also enables the extension of the technique from joint space to direct end-effector control of both non-redundant and redundant robots in task or operational space. The technique, perhaps, may be further augmented to incorporate force control to achieve hybrid force/position control. The use of sliding modes in the control scheme, in its idealized form, ensures accurate tracking while achieving insensitivity to parameter variations/uncertainties and bounded disturbances. In the development of the control laws, some useful properties of the robot dynamics, viz., positive definiteness ...

Spectral factorization and LQ-optimal regulation for multivariable distributed systems

Abstract: A necessary and sufficient condition is proved for the existence of a bistable spectral factor (with entries in the distributed proper-stable transfer function algebra 𝒜-) in the context of distributed multivariable convolution systems with no delays; a by-product is the existence of a normalized coprime fraction of the transfer function of such a possibly unstable system (with entries in the algebra ℬ of fractions over 𝒜-). We next study semigroup state-space systems SGB with bounded sensing and control (having a transfer function with entries in ℬ) and consider its standard LQ-optimal regulation problem having an optimal state feedback operator K0. For a system SGB, a formula is given relating any spectral factor of a (transfer function) coprime fraction power spectral density to K0; a by-product is the description of any normalized coprime fraction of the transfer function in terms of K0. Finally, we describe an alternative way of finding the solution operator K0 of the LQ-problem using spectral factor...

Controllability of multi-input positive discrete-time systems

Abstract: Linear discrete-time positive systems arise in various fields of science, such as economic modelling, behavioural science, stochastic processes, etc. Recently, some authors have examined the problem of the controllability of such systems for the single-input case. This paper provides necessary and sufficient conditions for characterizing the controllability properties of multi-input systems. The results here developed show that only a narrow class of these systems enjoys the properties of reachability and controllability.

Robust stabilizability of normalized coprime factors: The infinite-dimensional case

Abstract: The problem of robustly stabilizing a linear system subject to H∞-bounded perturbations in the numerator and the denominator of its normalized left coprime factorization is considered for a class of infinite-dimensional systems. This class has possible unbounded, finite-rank input and output operators, which include many delay and distributed systems. The optimal stability margin is expressed in terms of the solutions of the control and filter algebraic Riccati equations.

Self-tuning control of non-linear ARMAX models

Abstract: A control-weighted self-tuning minimum-variance controller with a non-linear difference equation structure is described. An extended recursive least-squares estimation algorithm is employed to provide the adaptiveness. Performance analysis of the controller is discussed in terms of a cumulative loss function and high-order correlation functions of the system input, output and residual sequences. Simulation results from an experiment using a model identified from a real system are also provided.

QSVD approach to on- and off-line state-space identification

Abstract: Moonen et al. (1989 a), presented an SVD-based identification scheme for computing state-space models for multivariable linear time-invariant systems. In the present paper, this identification procedure is reformulated making use of the quotient singular value decomposition (QSVD). Here the input-output error co-variance matrix can be taken into account explicitly, thus extending the applicability of the identification scheme to the case were the input and output data are corrupted by coloured noise. It turns out that in practice, due to the use of various pre-filtering techniques (anti-aliasing, etc.), this latter case is most often encountered. The extended identification scheme explicitly compensates for the filter characteristics and the consistency of the identification results follows from the consistency results for the QSVD. The usefulness of this generalization is demonstrated. The development is largely inspired by recent progress in total least-squares solution techniques (Van Huffel 1989) for ...

Interpretation of non-linear frequency response functions

Abstract: Analytical and graphical methods of interpreting generalised frequency response functions for non-linear systems are derived. It is shown that non-linear phenomena can be classified into intra-kernel and inter-kernel interference and that worst-case responses can be computed. The results are illustrated using several discrete- and continuous-time non-linear systems.

Sliding-mode controller design of a single-link flexible manipulator under gravity

Abstract: This is follow-up research of the regulator design for a single-link flexible manipulator using the sliding-mode technique (Yeung and Chen 1989). In this paper, we have extended the controller design for the regulation problem to that for the tracking problem when the single-link manipulator is moving on a horizontal plane. In addition, by placing strain gauges along the flexible arm (Hastings and Book 1985) we can substitute strain measurements for the need to estimate modal functions, which is a step close to implementational reality. Extension of the controller design is also carried out to the regulation of a flexible arm under gravity. A PID compensation is needed to compensate for the steady-state offset due to gravity. The controller design presented is simple and requires no inertia matrix inversion, no modal estimation and no payload forecast. Simulation studies demonstrate the robustness of the control against input disturbance and payload variations

Phase margins for multivariable control systems

Abstract: This paper presents a new definition for the phase margin of multivariable systems. The properties of the phase margin are such that a stable closed-loop multi-input multi-output system will remain stable for all unitary perturbations in the feedback path whose phases are less than the phase margin of the system. It is also shown that the definition of phase margin is invariant under unitary transformations of the system.

Generalized multirate-output controllers

Abstract: This paper studies controllers employing multirate sampling of the plant output (Hagiwara and Araki 1988 a). Specifically, it is shown that arbitrary pole assignment is possible by a multirate output sampling mechanism with smaller output multiplicities if a multiframe control law is introduced. We refer to the new control law as the generalized multirate-output controller. It is also shown that type-1 robust servo controllers with two degrees of freedom can be designed and strong stabilization with loop transfer reovery is possible. The relation of the generalized multirate-output controllers to the two-delay output controllers (Mita et al. 1987, Mita and Chida 1988) is also discussed.

Almost exact modelling assumption in adaptive linear control

Abstract: Modem adaptive controllers are known to give bounded solutions when the system ‘normalized’ unmodelled effects are bounded by a small constant. This paper studies this unusual characterization of uncertainties. We show it encompasses more classical approaches. We discuss how feedback and by-passing may allow this assumption to be satisfied. We conclude by proposing the notion of almost exactly linearly modelled systems.

Control and stabilization of a flexible beam attached to a rigid body

Abstract: We consider a flexible spacecraft modelled as a rigid body rotating in inertial space; a light flexible beam is clamped to the rigid body at one end and is free at the other. The equations of motion are obtained by using free-body diagrams. It is shown that suitable boundary controls applied to the free end of the beam and a control torque applied to the rigid body stabilize the system. The proof is obtained by using the energy of the system as a Lyapunov functional.

Adaptive force control of robot manipulators

Abstract: An adaptive controller that achieves a pure tracking force objective for n-link robot manipulators is presented in this paper. The main features of the proposed algorithm are: (i) the dynamic parameters of the robot are assumed to be unknown, (ii) object stiffness is unknown, (iii) only position, velocity and interaction force measurements are required. Under the practical assumption of a constant inertia matrix, the scheme is shown to be globally convergent to zero-force tracking error. This assumption can be removed for single link devices, thus providing the first proof of the global convergence of an adaptive force controller that includes estimation of both manipulator and environment dynamics

Necessary and sufficient conditions for stability of symmetric interval matrices

Abstract: It is shown that a family of symmetric interval matrices is Schur if and only if the vertex matrices are Schur. This result is also applicable to Hurwitz stability and aperiodic properties of linear systems.