The Lambert W function is defined as the multivalued inverse of the function w→wew=z. It has been applied to stability analysis of a class of fractional delay systems whose transcendental characteristic equation (TCE) can be remodelled in the form (as+b)ecs+d=0. The approach of using the Lambert W function to time-domain analysis of a class of feedback fractional-order time-delay systems is extended. It should be noted that, owing to the multivaluedness of a transfer function of fractional order, the approach has two pitfalls that must be circumvented with care. Because remodelling the TCE of a feedback fractional delay system to allow for the Lambert W function representation of roots introduces superfluous poles to the original TCE, a clarification of the relationship between the roots of the remodelled TCEs and the poles of the system is provided. As a result, the time response function of the system can be approximated by a finite series of eigenmodes written in terms of Lambert W functions. As the singularities of a fractional-order system include both the poles and the branch cut(s) of the transfer function, the neglect of the response portion contributed by the branch cut(s) incurs a significant transient response error. In order to compensate for such a transient response error, three schemes of optimal approximation with specified poles are developed. Simulation results show that the proposed approaches to time-domain analysis of feedback fractional delay systems can indeed enlarge the application scope of the emerging Lambert W function.
Tracking ground moving targets with ground moving target indicator and high resolution range (HRR) measurements is becoming increasingly important for many military and civilian applications. We first propose a new HRR information exploitation method using the technique of mixture density estimation. With this technique, features extracted from HRR profiles include not only peak locations and magnitudes, but also the information regarding how energy spreads around peaks. Therefore it is expected to increase significantly the feature discrimination power. We then develop a feature-aided tracking (FAT) algorithm that combines HRR features with traditional kinematic measurements in a probabilistic way. The algorithm does not require any a priori knowledge of target identifications. Simulation results are presented for both the HRR feature extraction method and the FAT algorithm.
A robust recurrent-neural-network (RRNN) sliding-mode control is proposed for a biaxial motion mechanism to allow reference contour tracking. The biaxial motion mechanism is a X-Y table of a computer numerical control machine that is driven by two field-oriented control permanent-magnet synchronous motors. The single-axis motion dynamics are derived in terms of a lumped uncertainty that includes cross-coupled interference between the two-axes. A RRNN sliding-mode control system is proposed based on the derived motion dynamics to approximate the control obtained by using sliding-mode control and the motions at the X-axis and Y-axis are controlled separately. The motion tracking performance is significantly improved using the proposed control technique and robustness to parameter variations, external disturbances, cross-coupled interference and frictional torque can be obtained as well. Experimental results on circular, four-leaf, window and star reference contours are provided to show that the dynamic behaviour of the proposed control system is robust with regard to uncertainties.
The problem of flow control in fast connection-oriented communication networks supporting traffic generated by multiple sources is addressed. The network is modelled as a dynamic system with different delay times. A nonlinear strategy governing the behaviour of the sources is proposed. The strategy combines Smith's principle with a conventional relay controller. It ensures full bottleneck link utilisation and no cell loss in the controlled network, even if the round-trip times of the connections contributing to the bottleneck link queue are not known exactly, but can only be estimated within a certain level of accuracy. Furthermore, a modified strategy with extra feed-forward compensation is proposed. This strategy also guarantees no cell loss and full bottleneck link utilisation. Moreover, it helps to achieve a favourable quality of service in the controlled network.
The issue of globally robust asymptotic stability with norm-bounded parameter uncertainties is studied for delayed Cohen-Grossberg neural networks. By constructing a suitable Lyapunov functional, several sufficient conditions are obtained guaranteeing the global robust convergence of the equilibrium point. The obtained conditions are given in the form of matrix and linear matrix inequalities that can be checked numerically and very efficiently by resorting to the recently developed interior-point method. Finally, an illustrative numerical example is provided to demonstrate the effectiveness of the obtained results.
A new method is presented for the design of simply structured multivariable controllers that can explicitly meet mixed sensitivity robust performance and robust stability criteria. Currently, most established robust controller design methods are synthesis-based and produce controllers that are often of much higher order than the plant. Based on the technique of diagonal dominance, this method proposes a novel means of directly 'designing' a robust controller, which among others, has the benefit that its order can be determined by the designer. By using elementary algebra, it is shown that the Gershgorin disks of a matrix may also be used to bind its singular values in addition to the eigenvalues. This fact is then exploited to create simple envelopes that bind the singular values of the sensitivity and complementary sensitivity functions, which are subsequently used in the design of the diagonal dominance-based controller such that the mixed criteria on the loop transfer function sensitivities may be met. As with other mixed sensitivity design techniques, this method does not guarantee that a controller is feasible for any set of arbitrary specifications. The method is applied to design a mixed-sensitivity controller for a mathematical model of the Rolls-Royce gas-turbine engine.
A survey on networked control systems (NCSs), published in a previous paper, is updated and extended. A simple framework and some general formulations for the study of NCSs are proposed. In addition to the survey on NCSs, the impact of NCSs on traditional large-scale system control methodologies with a related application is also reviewed.
The use of Fourier analysis as a step in building a model of a linear dynamic system involves end effects which introduce bias and variance in estimates. The source of these errors is considered, and their detailed form is estimated. This leads to a significant improvement in the accuracy of the final model. Simulation results are included.
The framework of supervisory control of discrete event systems (DESs) is applied to agent-based power protection systems for achieving high reliability and selectivity. The DES-based supervisory control uses feedback information of events occurring in systems to achieve the set of desired event sequences. The large-scale and complex power systems need systematic tools for protection and control on a more abstract level. The supervisory control technique on the event-based abstract level can be used as a formal method for protection of large-scale power systems. Specifically, a design procedure of a supervisor that coordinates the behaviour of relay agents to isolate fault areas through the minimum operations of circuit breakers is presented.
Treasure et al. (2004) recently proposed a new subspace-monitoring technique, based on the N4SID algorithm, within the multivariate statistical process control framework. This dynamic-monitoring method requires considerably fewer variables to be analysed when compared with dynamic principal component analysis (PCA). The contribution charts and variable reconstruction, traditionally employed for static PCA, are analysed in a dynamic context. The contribution charts and variable reconstruction may be affected by the ratio of the number of retained components to the total number of analysed variables. Particular problems arise if this ratio is large and a new reconstruction chart is introduced to overcome these. The utility of such a dynamic contribution chart and variable reconstruction is shown in a simulation and by application to industrial data from a distillation unit.
A new technique is presented based on genetic algorithms (GAs) for designing a multivariable PID controller. The considered application is a gasifier benchmark problem, for which a number of performance and robustness requirements are defined. In addition, actuator constraints are also considered. The proposed design procedure allows the optimisation of both controller parameters and structure. An advantage of the proposed technique over standard optimal control techniques (H-2 and H-infinity methods) is its ability to take non-linear constraints and dynamics into account in the design algorithm in a straightforward manner. A disadvantage of the proposed technique is the potentially large computation time required by GA. To overcome this problem, the optimisation is performed over several stages. First the structure is optimised, then basic controllers are designed (only PI terms) and finally a derivative term is added if needed. Simulation results on the gasifier problem have confirmed the superiority of the proposed technique in terms of achieved performance and robustness; moreover, the computation time of the overall design procedure is significantly reduced when compared with a standard GA approach. A controller that meets all design objectives under all operating conditions, and satisfies all input-output constraints, is presented.
The singularly perturbed system is easily analysed by two time-scale systems, each of which with a lower dimension than the original system. However, if uncertainties are added, then the analysis is very difficult because uncertainties change the slow manifold, the boundary layer model and the reduced model of the nominal system. Robust stability analysis of nonlinear singularly perturbed systems with vanishing uncertainties, of which the upper norm bounds only are available, is presented. The stability condition, under which the zero state equilibrium of the singularly perturbed system is exponentially stable for the sufficiently small perturbation parameter ε, is found and a stabilising controller is proposed.
The position tracking control problem for rigid n-link robot manipulators operating under unknown external disturbances and stochastic perturbations is addressed. The robot model is considered to be completely uncertain and therefore the proposed controller uses suitable neural network designs and adaptive bounding algorithms for the approximation of all the unknown non-linear uncertainties and the deterministic and stochastic disturbances while effectively penalises the position tracking error. Stability analysis based on Lyapunov functions proves that all the error variables are bounded in probability; simultaneously, the mean square tracking error enters in finite time in an arbitrarily selected small region around the origin wherein it remains thereafter. The controller performance is evaluated by two representative examples: a two-link and a three-link robot manipulator. An excellent tracking response is verified while the effective approximation achieved by the adaptive neural design is clearly demonstrated.
A new approach implementing the sliding-mode controller is proposed for dc-do converters. The equivalent control input is used as the system control input, which results in a duty cycle regulation control system. As designed, equivalent control input is maintained at a value between 0 and 1, similar to the desired duty cycle value. Thus, constant switching frequency can be achieved under changes of state conditions. Two sliding-mode controllers based on this method are designed for positive output elementary Luo converter. Traditional small-signal analysis is applied to study the close-loop system performance under proposed approach. Audio-susceptibility, control-to-output transfer functions and output impedance are derived on the basis of the small-signal model. It is shown that the proposed sliding-mode control approach retains the advantages of traditional sliding-mode control, as well as achieve constant switching frequency, which is decided by the input saw-tooth waveform. Results of the experiment are reported for both controllers and they verify the theoretical analysis.
Multivariable proportional-integral-plus (PIP) control methods are applied to the nonlinear ALSTOM Benchmark Challenge II. The approach utilises a data-based combined model reduction and linearisation step, which plays an essential role in satisfying the design specifications. The discrete-time transfer function models obtained in this manner are represented in a non-minimum state space form suitable for PIP control system design. Here, full state variable feedback control can be implemented directly from the measured input and output signals of the controlled process, without resorting to the design and implementation of a deterministic state reconstructor or a stochastic Kalman filter. Furthermore, the non-minimal formulation provides more design freedom than the equivalent minimal case, a characteristic that proves particularly useful in tuning the algorithm to meet the Benchmark specifications. The latter requirements are comfortably met for all three operating conditions by using a straightforward to implement, fixed gain, linear PIP algorithm.
A new Gersgorin-type result on the location of the eigenvalues of a given matrix has been proved. On the basis of the inclusions there established, in this paper a new method is proposed for analyzing the stability of a class of uncertain linear systems, characterized by an interval family of dynamical matrices. As a result a new bound to the real parts (moduli) of the eigenvalues of matrices in the interval family are obtained. This bound immediately provides a sufficient condition of stability and a way to compute an estimate of the stability margin, i.e. of the minimal destabilizing perturbation for the uncertain system. A huge number of numerical experiments have been carried out to compare the method here proposed to others based on Gersgorin-type regions. The results show that in several cases it gives less conservative estimates than the other ones, thus suggesting that it may be a useful tool for the analysis of uncertain systems
The design of a double-loop robust digital control algorithm for a wind turbine (WT) containing a doubly-fed induction machine is presented. The operating zone considered is that obtained when the rotational speed is limited to its rated value and the generated electricity has not reached its corresponding rated value. It is not particularly easy to find descriptions of controllers for this working zone in the existing literature. The rotational sampling effect may produce drive-train torque oscillations when a WT operates at constant speed. Consequently, its control system, which consists of two levels of control loops, has to be able to address these oscillations and be able to minimise flicker emission and dynamical loads in the drive train. These specifications, along with the robustness of the synthesised controller, lead to a reduced cost for the generated electricity and to a higher power quality, compared to those obtained using more classical WT control strategies that do not account for the peculiarities of the considered operation zone. The inner control loops govern the machine electromagnetic torque. The outer control-loop is synthesised using the discrete pole-placement with sensitivity function shaping method, to keep the rotational speed at its rated value and to reduce electromagnetic torque oscillations. The designed and synthesised control algorithms are tested on a simulation model validated using field data. Simulation results show that the proposed regulator reduces both flicker emission and dynamical drive-train loads, when compared to a classical PI regulator tuned to show an identical cut-off frequency and integral action.
Model predictive control (MPC) has become the first choice of control strategy in many cases especially in the process industry because it is intuitive and can explicitly handle MIMO (multiple input multiple output) systems with input and output constraints. The authors implemented a simple MPC algorithm based on the state space formulation to control the ALSTOM gasifier. Among three operating conditions of the plant, 0% load condition is identified as the worst case. A linearised state space model at 0% load condition of the non-linear plant is adopted as the internal model for performance prediction. Because of this choice, the control system comfortably achieves performance requirements at the most difficult load condition. Meanwhile, the case study shows that the model is also adequate to pass all tests under other load conditions specified in the benchmark problem. The MPC algorithm uses standard formulation and off-the-shelf software with a few tunable parameters. Thus, it is easy to implement and to tune to achieve satisfactory performance.
This note studies the robust stabilisation problem of a linear time-invariant singularly perturbed system with nonlinear uncertainties, where the only information available for system uncertainties is their norm upper bounds, and no matching conditions are assumed. A linear stabilising control law is presented which can be determined by the solutions of two independent Lyapunov equations. The system stability bound can then be obtained by using the existing methods. Finally, a numerical example is given to illustrate the applications of the proposed results, and future work on this subject is also discussed.
