Suchin Arunsawatwong

Computation of peak output for inputs satisfying many bounding conditions on magnitude and slope

The evaluation of peak outputs is an essential component of control systems design in which the outputs are required to remain within their prescribed bounds in the presence of all possible inputs. Characterising a possible set with many bounding conditions can reduce conservatism, thereby yielding a better design. However, this gives rise to difficulty in computing the peak outputs using analytical techniques. This article develops a practical method for computing the peak outputs of linear time-invariant systems for a class of possible sets characterised with many bounding conditions on the two- and/or the infinity-norms of the inputs and their slopes. The original infinite-dimensional convex optimisation problem is approximated as a large-scale convex programme defined in a Euclidean space with sparse matrices, which can be solved efficiently in practice. A case study of control design for a building subject to seismic disturbances is reinvestigated, where three bounding conditions are used. The numerical results show that the design so obtained is better than the previous one.

Critical Control of Building under Seismic Disturbance

The control of a building subject to a seismic disturbance is critical in the sense that the drift in each interstorey is required to remain strictly within a prescribed bound, despite any earthquake excitation. This is because any violation of the bound can lead to the collapse of the building. This chapter describes the design of such a control system using the principle of matching and the method of inequalities, where all earthquakes supposed to be possible to happen are explicitly taken into account and are modelled as functions such that the two norms of the magnitude and rate of change are uniformly bounded by respective constants. As a result, one can ensure that (provided a design solution is found) the building is tolerant to all the earthquakes that can be modelled in this way. A design is carried out for the case of a six storey laboratory-scaled building. The numerical results demonstrate that the design framework employed here gives a realistic formulation of the design problem and therefore is suitable for designing critical systems in practice.

Stability of ZakianI MN recursions for linear delay differential equations

Long sequences of linear delay differential equations (DDEs) frequently occur in the design of control systems with delays using iterative-numerical methods, such as the method of inequalities. ZakianIMN recursions for DDEs are suitable for solving this class of problems, since they are reliable and provide results to the desired accuracy, economically even if the systems are stiff. This paper investigates the numerical stability property of theIMN recursions with respect to Barwells concept ofP-stability. The result shows that the recursions using full gradeIMN approximants areP-stable if, and only if,N−2≤M≤N−1.

Design of Uncertain Nonlinear Feedback Systems with Inputs and Outputs Satisfying Bounding Conditions

Abstract This paper develops a computational method for designing a feedback control system where the plant is an uncertain linear time-invariant convolution subsystem with a static memoryless input nonlinearity. The main design objective is to determine a controller ensuring that the error and the controller output are always within respective bounds for all uncertainties and for all inputs having bounded magnitude and slope. First, using Schauder fixed point theorem, we show that (if exists) a design solution for an uncertain linear system obtained by replacing the nonlinearity with a gain and a bounded disturbance is also a solution for the original problem. Then, by extending a known theory and applying it to the so-obtained linear problem, we derive design inequalities that can readily be solved in practice. The usefulness of the developed method is illustrated by a design example of an uncertain heat-conduction process.

Design of nonlinear feedback systems with inputs and outputs satisfying bounding conditions

This paper develops a method for designing a feedback system comprising a static memoryless nonlinearity and linear time-invariant convolution subsystems so as to ensure that the error and the controller output stay within prescribed bounds for all time and for all inputs having bounded magnitude and bounded slope. Since the original design criteria are computationally intractable, we derive practical sufficient conditions for ensuring them. The conditions provide surrogate design criteria that are in keeping with the method of inequalities. Essentially, the nonlinearity is replaced with a fixed gain and an equivalent disturbance; thus, the nominal system used during the design process becomes linear and the associated performance measures are readily obtainable by known methods. To illustrate the usefulness of the method, a design example of a hydraulic force control system is given.

Stability and Stabilization of Retarded Fractional Delay Differential Systems

Abstract The main objective of this paper is twofold. First, we devise a stability test for determining whether a linear retarded fractional delay differential system has no characteristic roots in a specified right half of the complex plane. Second, we develop a practical method for computing the abscissa of stability (defined as the largest of the real parts of the characteristic roots) for this type of system. The method is based on a known technique which makes repeated use of a stability test, thereby avoiding the calculation of all the roots. The stability test and the method for computing the abscissa of stability provide useful computational tools for the design of fractional differential systems using the method of inequalities as well as other numerical optimization approaches. Numerical examples are also given.

Design of Fractional PI Controllers for a Binary Distillation Column with Disturbances Restricted in Magnitude and Slope

Abstract This paper designs fractional PI controllers for a binary distillation column, where all disturbances that can happen or are likely to happen in practice are explicitly taken into account in the design formulation and modeled as functions having bounded magnitude and bounded slope. The design objective considered is to ensure that the top product, the bottom product, the reflux rate and the reboiler rate deviate within their prescribed bounds for all time and for all the disturbances. To this end, the performance measures called the peak outputs are used and, according to the multi-objective nature of the problem, the design criteria are expressed as a set of inequalities that can be solved. Satisfactory controllers are obtained by searching in the space of design parameters. The numerical results show that the obtained fractional PI controller enhances the quality of the control system in comparison with the conventional controller.

Design of decentralized load frequency regulator for two-area power systems subject to bounded persistent disturbances

This paper presents the design of decentralized load frequency regulator for two-area power systems in which each areas disturbance is bounded persistent change in load demand. In the formulation of the design problem, all of such disturbances that happen or are likely to happen in practice are treated explicitly as signals having uniform bounds on magnitude and slope. The design problem is solved by using two known principles: namely, the principle of matching and the method of inequalities. Once a design solution is found, one can ensure that the frequency deviations and the tie-line power deviation always remain within prescribed bounds in the presence of all possible disturbances. The numerical results show that the framework adopted here is suitable and effective, thereby giving a realistic formulation for the load frequency control problem with persistent disturbances.

Design of compensators for power systems operating under load voltage fluctuation satisfying bounding conditions

In power systems generation and control, the load variation has a great influence directly on the systems stability and dynamic performances. This paper describes the design of a compensator for a power system subject to random load voltage fluctuation, where the voltage fluctuations are treated as persistent functions satisfying bounding conditions. For stable operation and good performances of power systems, the rotor angle, the terminal voltage and the speed deviation of the generator are required to remain within their prescribed bounds, despite any change in the load voltage. Any violation of the bounds may lead to the systems instability and hence unacceptable consequences. The numerical results illustrate that the proposed design method provides a realistic formulation and therefore is effective for designing power system compensators.

Design of load frequency regulator for power systems subject to bounded persistent disturbance considering generation rate constraint

This paper presents the design of load frequency regulator for power systems that are subject to persistent disturbance, in which all possible disturbances are treated as signals having uniform bounds on their magnitude and slope. The design objective is to determine a controller which maximizes the absolute value of the rate of change of the systems load (thereby maximizing the size of the possible set in some sense) while keeping the frequency deviation within its prescribed bound for all possible disturbances. In conjunction with the notion of conditionally linear model, the generation rate is required to stay within its linear range of operation for all possible disturbances. Consequently, the linear models of the systems are ensured to exist and, more importantly, theories for linear systems can be conveniently utilized. Using the known design framework consisting of the method of inequalities and the principle of matching, the design specifications are expressed as a set of distinct inequalities that can be solved in practice. The numerical results clearly illustrates the effectiveness and the usefulness of the framework adopted here.