Katrina Lau

Undershoot and settling time tradeoffs for nonminimum phase systems

It has been known for some time that real nonminimum phase zeros imply undershoot in the step response of linear systems. Bounds on such undershoot depend on the settling time demanded and the zero locations. In this note, we review such constraints for linear time invariant systems and provide new stronger bounds that consider simultaneously the effect of two real nonminimum phase zeros. Using the concept of zero dynamics, we extend these results to a class of nonlinear systems.

Properties of modulated and demodulated systems with implications to feedback limitations

It is well known that the poles, zeros and delay of a system play an important role in determining the associated feedback performance limitations. In this paper, we first derive an approximate transfer function for a modulated and demodulated system of a particular form. We next analyse the behaviour of the poles, zeros and delay of this transfer function when the modulation frequency is varied. Some implications of these results are also briefly discussed.

Switched Integrator Control Schemes for Integrating Plants

In this paper, we compare and analyse three switched integrator control schemes for integrating plants. The schemes attempt to circumvent a fundamental limitation of linear time invariant (LTI) control, namely, that the closed loop response to a step change in the reference must overshoot if both the controller and the plant contain an integrator. We show that, for a simple example, the switched schemes all have significantly less overshoot than their LTI counterpart. The stability properties of the schemes are also studied. It is first shown that bounded input bounded state stability is guaranteed. Sufficient frequency domain conditions for asymptotic stability are then derived using passivity analysis.

Linear and nonlinear decoupling for inner loop power control in 3G mobile communications

Abstract Inner loop power control is a crucial part of the operation of 3G mobile communication systems. This is necessary to deal with the, so called, ‘near-far’ problem and to combat the effects of time variations in the channel gain. In practice, power control is dealt with in a decentralized fashion, i.e., using one SISO control loop for each user. However, significant multivariable coupling occurs due to the fact that each user is a source of interference to every other user. This means that the actual performance is significantly degraded relative to the idealized SISO case. In this paper, we describe a novel nonlinear decoupling algorithm for the uplink of the WCDMA 3G cellular system which effectively compensates for the MIMO interactions. We also develop a simplified linearized form of the algorithm. We explore the relative merits of the scheme for typical mobile communication scenarios incorporating grant changes, fading and quantization. Our simulations show that, in all cases, the decoupling strategies lead to significant performance gains relative to the use of decentralized strategies in common use.

Application of Non-stationary EIV Methods to Transient Electromagnetic Mineral Exploration

In this paper, we apply a non-stationary errors-in-variables model estimation technique to a problem arising in transient electromagnetic mineral exploration. The proposed technique is used to estimate a model which is deployed for noise cancellation. Alternative methods for noise cancellation in these systems rely on specific signal characteristics, and are thus not readily transferable to other applications. The proposed technique produces an estimated model that agrees well with those obtained using alternative methods, and achieves noise reduction levels similar to those achieved via the alternative methods. This is shown by performance comparisons on experimental data. An advantage of the proposed technique is that it is more readily transferable to other applications.

Conjectures and counterexamples on optimal L/sub 2/ disturbance attenuation in nonlinear systems

This paper considers the problem of optimal L/sub 2/ disturbance attenuation with global asymptotic stability for strict feedback nonlinear systems. It is known from previous results that this problem cannot be solved with an arbitrary level of disturbance attenuation (almost disturbance decoupling) if the disturbance input drives unstable zero dynamics of the system. In this case, the problem can only be solved to achieve a level of disturbance attenuation above a nonzero optimal bound. An explicit expression of this lowest optimal bound is known for linear systems, and an approximate bound exists for a special subclass of nonlinear systems with second order zero dynamics. A more general expression for the lowest bound remains unknown. In this paper we provide background to the problem, and discuss the feasibility of obtaining such a general expression by presenting a series of conjectures, examples and counterexamples. We first present a conjecture that might appear as a natural generalisation of the linear expression but that, as we show by means of a counterexample, is generally false. Finally, we present a second conjecture, which holds generally for the linear case, and also for a class of scalar nonlinear systems. A general proof, or a counterexample, to this conjecture are still questions open to further research.

On the use of switching control for systems with bounded disturbances

It has been known for some time that there are limits to the achievable performance in a linear time invariant feedback control system. Some of these limitations, however, may be ameliorated by the use of nonlinear and/or time varying feedback. Recently, there has been some interest in the use of switching control to improve the control performance for linear integrating plants with bounded input disturbances. In this paper we study asymptotic and bounded-input bounded-state stability properties of a class of switching feedback systems, and also examine one form of optimal control for such systems.

Brief paper: An errors-in-variables method for non-stationary data with application to mineral exploration

In this paper, an errors-in-variables (EIV) method is applied to the problem of model estimation for noise cancellation in transient electromagnetic mineral exploration. The algorithm exploits the non-stationary nature of the data. Alternative methods for noise cancellation in these systems rely on specific signal characteristics, and are thus less readily transferable to other applications. The proposed method produces a model that agrees well with those obtained by alternative methods and has similar noise cancellation performance. This is shown by performance comparisons on experimental data.

Uplink Load Based Scheduling for CDMA Systems

Cellular third-generation wideband code division multiple access (WCDMA) systems must meet interference constraints to maintain coverage when uplink traffic is scheduled. The interference constraints can be expressed in the form of load factor constraints but current scheduling algorithms are typically not formulated in terms of these variables. The current paper shows how a cost function for the scheduling problem can be expressed directly in terms of load factors. A near optimal solution is developed for the resulting problem.

Control with communication constraints

An emerging area of importance in control science is that of networked control. Within this framework one considers the impact of communication constraints on the performance of feedback control systems. The topic bridges the traditional areas of control, communications and information theory. In this paper we will focus on the practical application of these ideas. Perhaps unsurprisingly, a major area of application arises in the control of communication systems themselves since, here, the control commands and measurements are invariably sent over the same communication channels as are used for data. These channels are subject to imperfections including quantization, lost packets, random delays and decentralized architectures. Hence the associated control problems are quintessential examples of control subject to communication constraints. The paper will review several of these problems and point to future research challenges.