A review of methods for input/output selection <s> Right half-plane zeros <s> Control structure (strategy) selection consists of the selection and pairing of manipulated and measured variables. This article outlines a procedure that uses such tools as the existence of right half plane (RHP) transmission zeros, the relative gain array, the performance relative gain array, and the closed-loop disturbance gain. The regulatory control system for the fluid catalytic cracking process is used as an example. Several authors found the Kurihara control structure to be preferable to the conventional control structure. The reason is that RHP transmission zeros limit the achievable bandwidth for the conventional control structure. Two other control structures, however, have better controllability characteristics than both the conventional and the Kurihara control structures. The sensitivity of the measurement selection and variable pairing with respect to changes in the operating point and parametric uncertainty is examined, as well as the general objectives of the regulatory control level and its interaction with the higher levels in the control hierarchy. <s> BIB001 </s> A review of methods for input/output selection <s> Right half-plane zeros <s> The nonrational transfer function of an important component of a flexible structure, the beam, is analyzed. The true pattern of zeros of that transfer function is investigated as a function of sensor and actuator separation. Translational displacement sensors are used for two cases in which a force input and a moment input are separately applied at one end of the beam. Contrary to general opinion, zeros do not simply approach the origin along the real axis of the s plane as the sensor is moved away from the point of force/moment application. When the displacement sensor is located at a certain point, the first pair of zeros on the real axis of the s plane arrive at the origin and cancel the rigid-body mode. The location of the translational displacement sensor on the beam at which the rigid-body mode of the beam is unobservable is analyzed as the center of percussion and is uniquely located for each case. If the sensor is moved beyond such a point, a pair of zeros appear on the imaginary axis and move away from the origin along the imaginary axis of the s plane. Finally, the zero migration associated with an angular displacement sensor is briefly considered and compared with the zero migration associated with the translational displacement sensor. <s> BIB002 </s> A review of methods for input/output selection <s> Right half-plane zeros <s> This paper explores the application of recent techniques to the problem of structure selection and robust multivariable controller design for a high performance gas turbine engine. The engine under consideration is a Rolls Royce: 2-spool reheated turbofan, used to power modern military aircraft. Efficient and effective tools for control structure design are described and applied to the problem at hand. It is stressed that a good structure selection is very important, it results in simpler controllers, and in general, a simpler design exercise. A 2-DOF H/sub infinity / controller design is presented. Work is currently in progress on gain scheduling of such controllers. <s> BIB003 </s> A review of methods for input/output selection <s> Right half-plane zeros <s> From the Publisher: ::: This is a book on practical feedback control and not on system theory in general. Feedback is used in control systems to change the dynamics of the system and to reduce the sensitivity of the system to both signal and model uncertainty. The book presents a rigorous, yet easily readable, introduction to the analysis and design of robust multivariable control systems. It provides the reader with insights into the opportunities and limitations of feedback control. Its objective is to enable the engineer to design real control systems. Important topics are: extensions and classical frequency-domain methods to multivariable systems, analysis of directions using the singular value decomposition, performance limitations and input-output controllability analysis, model uncertainty and robustness including the structured singular value, control structure design, and methods for controller synthesis and model reduction. Numerous worked examples, exercises and case studies, which make frequent use of MATLAB, are included. MATLAB files for examples and figures, solutions to selected exercises, extra problems and linear state-space models for the case studies are available on the Internet. <s> BIB004
Distinct IO sets may give rise to distinct numbers and distinct locations of (multivariable) system zeros, as de-"ned in, e.g., Zhou et al. (1996, Section 3.11) . Considering plant (2)}(3), the zeros can be interpreted as those values of s where the rank of the corresponding transfer function matrix (TFM) P(s) : "C(sI!A)\B#D from u to y is smaller than its normal rank, i.e., its maximally possible rank for at least one value of s. In general, the zeros of P(s) have no direct relation with the zeros of the individual elements of P GH (s). Zeros in the right half-plane (RHP) limit the closedloop performance. For instance, for SISO systems as in Fig. 2 the performance speci"cation is often in terms of a magnitude bound on the sensitivity de"ned as In case of tracking (r) or disturbance (d) rejection, "S( j )" is required small for low frequencies. The bandwidth is desirably large, but RHP zeros impose an upper bound. For a stable plant with a single RHP zero, this bound is smaller if the RHP zero is closer to the origin (Skogestad & Postlethwaite, 1996, Section 5.6 ). For a stable MIMO plant, the implications of RHP zeros are similar to those for stable SISO plants BIB004 , Section 6.5). For an unstable plant, the restrictions due to RHP zeros are even more severe. Performance limitations due to RHP zeros are extensively discussed by, e.g., Freudenberg and Looze (1985, SISO) , Havre and Skogestad (1996, MIMO) , Sidi (1997, SISO) , Skogestad and Postlethwaite (1996, Chapters 5 (SISO) and 6 (MIMO)), and Zhou et al. (1996, Chapter 6 (MIMO) ). If magnitude bounds are imposed on u and y,  show that RHP zeros of the individual elements of P(s) may be detrimental, in contrast to the case without these requirements. Goodwin and Seron (1995) initiate e!orts towards quantifying performance limitations due tò RHP zerosa in nonlinear systems. Though zeros in the left half-plane do not impose fundamental limitations on control, they may cause practical problems if they are close to the origin BIB004 , Section 5.6). A guideline for IO selection in the set-up of Fig. 2 is to reject IO sets which introduce RHP zeros with magnitudes below the desired bandwidth. This is employed by, e.g.,  , BIB001 , BIB003 , and Wol!,  . For unstable plants, also IO sets should be avoided with RHP zeros close to RHP poles. Exact cancellation of RHP poles and zeros causes the unstable modes to become uncontrollable and/or unobservable and so a stabilizing controller does not exist. BIB002 show that a sensible placement of single actuators and sensors along a #exible beam is important to avoid cancellation of zeros and poles in the origin.