Abstract: It is shown that the Hilbert-Schmidt-Hankel norm (HSH-norm) of a transfer function of a stable system is equal, up to a constant factor, to the square root of the area enclosed by the oriented Nyquist diagram of the transfer function (multiplicities included) A generalization is presented for the case of systems which have no poles on the stability boundary, but otherwise have no restrictions on the pole locations >

Abstract: A method to synthesize a transfer function from experimentally obtained gain and phase data is presented. The least squares technique discussed minimizes the error between the inverse transfer function and the inverse of the experimental frequency response data. The relevant formulas are derived in a straightforward manner so that undergraduate students can follow the development. The inverse formulation appears to give a better fit to the data than the previous approaches. This is most likely due to the fact that the technique biases the error with the numerator rather than the denominator of the derived transfer function. There is, however, no guarantee that a minimum phase transfer function will result from this technique. The user of this technique must preselect the numerator and denominator orders. The formulation assumes that there are no zeros at the origin. A modification to the basic scheme is presented for this case. >

Abstract: The problem of minimizing the 2-norm of one transfer function subject to an ∞-norm bound on another transfer function is examined for increased order controllers. It is shown that, unlike controllers under full-state availability, output feedback controllers are unable to achieve the global minimum 2-norm while simultaneously meeting the ∞-norm constraint for certain levels of γ, regardless of compensator order. The solution to the mixed H2/H∞, problem is shown to lie on the boundary of the ∞-norm constraint in the increased order case for this same range of γ's. Also, it is shown that the optimal compensator order for the mixed problem is greater than the order of the plant under certain conditions. A numerical example is given.

Abstract: One of the main open problems in linear system theory is to determine the minimum order q of a dynamic compensator that can arbitrarily assign the closed loop poles of a generic real m-input, p-output system of McMillan degree n. The authors prove that the generic system has arbitrary pole assignability if q max(m,p)+mp>n. >

Abstract: This paper is concerned with the placement of the closed-loop poles of distributed parameter heat exchangers having no finite open-loop poles via a linear feedback control law. To use eigen function expansion technique, the system is applied a simple output feedback which yields countable finite poles. Modal control is used to place the poles at assigned locations without moving the rest of poles.

Abstract: The pole assignment problem for distributed parameter systems governed by analytic semigroups is discussed. Introducing unbounded feedback operators, we can solve the problem under a weaker restriction on the separation of the open-loop and the closed-loop poles. These types of feedback systems inherit the spectrum determined growth assumption of the open-loop systems. We first present a characteristic equation whose roots are the poles of the closed-loop system. Next we give a feedback element which realizes the desired pole assignment of the closed-loop system. We show an interesting result that an infinite number of the open-loop poles can be uniformly moved by means of a suitable linear feedback. We apply the results -to a heat system and a flexible structure for the cases of distributed controls and boundary controls.

Abstract: A strategy for the design of a single-input and single-output self-tuning controller for reference signal tracking is described. An already existing algorithm for shifting the closed-loop poles radially toward the origin in the z-domain for regulation has been used for reference signal tracking by combining it with a well-known control law. The use of a self-searching pole-shifting technique increases the flexibility when applied to varying operating conditions encountered in various industrial applications. It also eliminates the necessity of choosing the closed-loop pole locations and still possesses the quality of robustness of pole assignment and ease of reference signal tracking. Digital simulation results are compared with those of two other algorithms. >

Abstract: Stability analysis is presented for discrete time pole placement adaptive control systems with input rate saturation constraints in this paper. It is shown that with appropriate controller design, the robust adaptive control system is stable for a class of stable minimum phase plants in the sense that all the signals in the loop remain bounded in the presence of modelling uncertainties and disturbances. It is also shown that if the plant is free from modelling uncertainties and disturbances and the control input rate remains unsaturated for a period of time, then the closed loop adaptive control system will asymptotically be characterized by the desired closed loop poles within this time period.

Abstract: A quasi-elliptic transfer function with a maximum possible number of ripples in the stopband is synthesized. The double poles of these functions, with adequately reduced Q factors, produce twice as few ripples in the passband in comparison with the elliptic function of the same order. In contrast to other known functions with low Q factors of the dominant poles, the design of the proposed filter function is simple. >

Abstract: This paper is concerned with a synthesis method for a robust pole placement compensator. The compensator is robust with respect to plant parameter variations. To reduce conservativeness of considering the coefficents of the plant transfer function numerator and denominator polynomials only as interval1 parameters, it is assumed that these are related by an affine function to a primary parameter vector, which in general contain physical quantities [ l ] and is supposed to vary within known bounds. This approach thus takes into account interdependency of the plant transfer function coefficients. The robustness of the closed loop system is achieved by minimizing the sensitivities of the closed loop poles with respect to small variations of the primary parameter vector.

Abstract: Outlines a design methodology for synthesizing control systems for a class of SISO (single-input single-output) systems to guarantee a nonovershooting nominal step response in addition to satisfying standard feedback requirements such as robust stability, disturbance rejection, and sensitivity reduction. Compensators can be synthesized for SISO, stable, and minimum-phase plants with significant plant variations. The basic idea of the technique is to appropriately locate the closed-loop poles with respect to fixed and added zeros. An example illustrating the design procedure is presented. >

Abstract: The problem of pole placement or eigenvalue assignment by state or output feedback is very well studied. Provided the locations of closed-loop poles are known, it is always possible under certain conditions to determine the feedback compensator. However, the selection of closed-loop pole location is based on heuristics and the designers' experience. In this paper, it is shown that by specifying the desired impulse response of the closed-loop system, the optimal closed-loop characteristic polynomial, and therefore, the optimal locations for the closed-loop poles can be determined.

Abstract: This paper describes the feedback limitations caused by the presence of right half-plane poles and zeros in the plant and compensator when bounds on the size of the plant input are imposed. It is shown that nonminimum phase zeros of the plant and unstable poles of the compensator constrain the magnitude of the closed loop transfer function relating the plant input and exogenous signals. A new result shows the distinct role played by unstable poles of the compensator and nonminimum Phase zeros of the plant. This characterization that is lost when the closed loop feedback properties are expressed solely in terms of the loop transfer function. It is shown that if an unstable compensator is used then constraining the size of the plant input may result in peaks of the sensitivity function.

Abstract: A problem of practical and theoretical interest in control is the synthesis of a compensator that results in a closed loop system response with no overshoot. In this short paper we present an approach for synthesizing such compensators for SISO, minimum phase plants. The essential idea of the technique is to appropriately locate the closed loop poles with respect to fixed and added zeros. Admissible pole-zero locations are characterized by two sufficiency theorems.