Abstract: The iterative feedback tuning (IFT) is a data-based method for the tuning of restricted-complexity controllers. In the classical formulation, the IFT aims at minimizing a certain model-reference criterion in which the reference-model is chosen by the user. This minimization is based on signal information only. In this paper we formulate a new criterion for the IFT method. In the new criterion, some freedom is given to the reference-model in order to let it reproduce the features of the unknown plant (i.e. the delay and non-minimum phase zeros) which the controller should not attempt to change. It is shown that using the new criterion corresponds to giving more emphasis to the placement of the closed loop poles.

Abstract: A parameterization of continuous-time passive systems (positive real transfer functions) with given poles is proposed. This parameterization has a minimum number of parameters and is suited to convex optimization, especially for semidefinite programming. As an example, we show how to find the best approximation of a stable transfer function with a positive real one, with the same poles.

Abstract: Necessary and sufficient conditions for the transfer function of a passive linear stationary scattering (or resistance) system are found ensuring that minimal systems in this class are determined by their transfer functions up to similarity. The criteria are stated in terms of a Hankel operator the symbol of which is a contractive operator-valued function defined by the transfer function and having the meaning of the inner scattering suboperator of a simple conservative scattering (respectively, resistance) system with the transfer function in question. A connection between the similarity criterion and the corona theorem and its matrix generalizations is revealed.

Abstract: This paper proposes a noniterative method to fit a rational transfer function to a specified frequency response. A method using a smoothing of width-modulated pulses of the phase asymptotic-diagram is modified to provide an exact algebraic method. This is then used to synthesize a robust controller and a nonrational transfer function with a fractional differentiation order.

Abstract: This paper develops a first principles approach to constructing parameterized transfer function models for an abstraction of admission control, the M/M/1/K queueing system. We linearize this system using the first order model y(k+1)=ay(k)+bu(k), where y is the output (e.g., number in system) and u is the buffer size. The pole a is estimated as the lag 1 autocorrelation of y at steady state, and b is estimated using dy/du. With these analytic models for a and b, we study the effects of workload (i.e., arrival and service rates) and sample times. We show that a and b move in opposite directions at large utilizations, an effect that can have significant. implications on closed loop poles. Further, the DC gain for response time and number in system drops to 0 as buffer size increases, and the DC gain of number in system converges to 0.5 as workload intensity becomes large. These insights may aid in designing robust and/or adaptive controllers for computing systems. Finally, our models provide insight into why the integral control of a Lotus Notes e-mail server has an oscillatory response to a change in reference value.

Abstract: The problem of optimal zero locations of continuous-time systems with distinct poles tracking first-order step responses, is considered in this paper. The step response deviation from a given first-order step response is minimized, resulting in an explicit and easily computable solution for the transfer function numerator coefficients.

Abstract: To attenuate the effects of phase noise and input jitter introduced in the reference frequency of the PLL, the zeros of the forward path transfer function are removed. As a result, the forward path does not amplify any phase noise or input jitter appearing in the reference frequency. However, overall loop stability is maintained by placing the zeros in the feedback path of the PLL. A discriminator may be placed in the feedback path to introduce the zero in the loop gain transfer function and provide stability.

Abstract: This paper presents the application of genetic algorithms (GAs) to the robust pole placement for LTI systems with parameter uncertainties. The robust pole placement approach is firstly converted to a constrained optimization problem. The objective of the optimization is to derive the most robust state-feedback gain matrix K with respect to parametric plant uncertainties. Then, GAs are introduced as efficient optimization tools to solve the problem. The search of the GA is done within the linear bounded domain in the space of parameters in matrix K. The resulting system guarantees the closed-loop poles to remain in a prescribed region in the complex plane despite of the greatest possible uncertainty in plant parameters. Finally, this method is applied to design the longitudinal stability augmentation system (SAS) for a static unsteady airship. Simulation results show that the designed system not only stabilizes the longitudinal motion of the airship, but also reduces the sensitivity to parameter uncertainties.

Abstract: Dynamic behavior and each performance index of a control system depend on the positions of the poles in the system at some extent; therefore, one target of synthesis of system is to take a group of desirable poles on the s plane The pole-placement namely is to make poles of closed loop of system just at positions of a group of desirable poles by selecting state feedback matrix The theorem of poles-placement answered the question that what is the condition to place poles at will just only by means of state feedback At meanwhile, it can be seen that different state gain matrix can be gotten by applying different solution method for a certain question of pole-placement of state feedback This shows the solution of pole-placement of state feedback is not exclusiveBecause the solution method of poles-placement of state feedback has quite deep of theorization and also has a lot of calculation workload, it often can not be applied very well in the practice This paper provides a method that binomial theorem applied in the algebra can change the matrix calculation of state feedback抯 poles-placement into algebra computation for the control systems such as boiler super-heater temperature control because of the controlled objects having the trait of higher-order inertia link The method given by this paper is not only simple but also practicable, at the same time having specific project meaning Simulation test proves that this algorithm is effective

Abstract: Given the pole-zero configuration of a stable and rational transfer function it is trivial to determine the normalized covariances and Markov parameters. It is nontrivial and was recently shown that for finite windows of these parameters there corresponds a unique minimal and stable rational transfer function. Furthermore, small changes in the parameters corresponds to small changes of the transfer function, which makes the method robust. However, the proof was non-constructive and no algorithm for determining the inverse map was known. An efficient algorithm for determining the pole-zero configuration of the interpolating transfer function is the main contribution of this paper. As a corollary a novel and simplified approach to the minimal stochastic realization problem is obtained. Using an example from speech processing it is shown how this realization theory result can be used for identification of time series.

Abstract: A robust pole placement design method is given that satisfies given specified closed loop performance for a motion control system with uncertain process parameters. Complex plane specifications on the nominal closed loop poles are calculated from maximum trajectory deviations and maximum amplitude on the sensitivity function. The design problem is solved by calculating bounds on the control parameters that satisfies the complex plane specification for the closed loop system, for all vertices of the uncertain parameter space.

Abstract: A discretization processing method for transforming a transfer function in continuous time systems to a transfer function in discrete time systems is disclosed. To obtain the new transfer function, angular frequency ωa of the original transfer function in continuous time systems is transformed to angular frequency ωc using the bilinear z-transform of the inverse characteristic. In the discretion processing result, the equivalent characteristics of the original transfer function in continuous time systems can be obtained by performing the bilinear z-transform against the new transfer function in continuous time systems having been obtained by the angular frequency transformation of inverse characteristic.

Abstract: This chapter considers the problem of estimation of the transfer function of a continuous-time dynamic system in the presence of colored noise. Whereas parameter estimation can be made by means of a discrete-time maximum-likelihood algorithm, an operator transformation permits a continuous-time model parameterization. The method is useful in cases where it is important to estimate the coefficients of a continuous-time transfer function and to maintain a physical interpretation of the transfer function results.

Abstract: The paper describes synthesis of the transfer function of a multistage wideband amplifier having the monotonic step response. The procedure is based on approximation of a specially chosen impulse response in the time domain. This target impulse response is constructed using a delayed and exponentially attenuated sin/sup 2/ t function. The Laplace transform of this pulse is a transcendental function, yet the real and imaginary parts of this transform may be approximated by the polynomials with alternating zeros. The approximation allows one to obtain a realizable transfer function. The design example shows that the step response of this transfer function is practically monotonic, and, in addition, has a superior delay-to-rise-time ratio.

Abstract: An approach for obtaining simple, approximate, and analytical expressions for the roots of a quadratic expression is detailed. The approach facilitates evaluation of accurate analytical expressions for the poles and zeros of transfer functions associated with linear electronic circuits. The approach complements order-reduction techniques.

Abstract: Realization possibilities of the all-pole third-order transfer functions are discussed. For this purpose, the ladder network with a controlled voltage source in any shunt branch is used. The voltage source is controlled by the shunt branch voltage. The transfer functions are expressed with cumulants. Because of the high degree of symmetry, there are the rules for cumulant development. In this paper, the controlled voltage source with the controlling voltage placed in the shunt branch behind the source is considered. In this case, the transfer function contains only poles. The realization of the all-pole third-order transfer function is given in an example. The transfer function stability is analyzed using the Routh-Hurwitz criterion for the third degree polynomials.

Abstract: This paper is concerned with the flexibility in the closed loop pole location when solving the H 2 optimal control problem (also called the H 2 optimal disturbance attenuation problem) by proper measurement feedback. It is shown that there exists a precise and unique set of poles which is present in the closed loop system obtained by any measurement feedback solution of the H 2 optimal control problem. These "H 2 optimal fixed poles" are characterized in geometric as well as structural terms. A procedure to design H 2 optimal controllers which simultaneously freely assign all the remaining poles, is also provided.

Abstract: This chapter provides an overview of analog active filter design. Active filters can be designed from a set of numbers known as the pole and zero locations. Poles and zeroes are located on a two-dimensional plane, known as the S-plane. In the S-plane, one axis is real and is related to signal decay. The other axis is imaginary and is related to frequency. Their locations are obtained from a filter's transfer function. Typical pole and zero location patterns are illustrated, giving an idea of how a filter will behave if it has a certain pole-zero pattern or a certain transfer function. Tables of pole and zero locations are given and can be used in formulae to find resistor and capacitor values. These normalized lowpass pole and zero values can be used to design lowpass, highpass, bandpass, or bandstop filters. Scaling either the poles and zeroes, or the component values obtained from them, allows the frequency response to be changed from the normalized 1 rad/s cutoff frequency. Pole and zero placing include natural and 3dB attenuation limited passbands. Tables of pole and zero values are produced by these formulae.

Abstract: The linear algebra method for designing rational control systems consists of two steps: Selecting an overall transfer function and then designing the controller. Once an overall transfer function is chosen, the rest of the design is straightforward. This paper will discuss how to select a suitable overall transfer function for linear plant with time delay. The problem can be formulated as: Given a linear proper plant with time delay, search an overall transfer function such that the overall system is internally stable and has some other desired properties. Sufficient and necessary conditions are given and constructing procedure is developed. Numerical examples are provided to illustrated the proposed method.

Abstract: This paper describes wide-band amplifiers that were designed using the first semi-period of the sin/sup k/ t function as an approximation of their impulse response. For this class of amplifier, with monotonic step response, one can establish a simple relationship between the delay-to-rise-time ratio and the order of transfer function. Choosing the order, one can find the transfer function roots and, hence, finish the design. To simplify the design, the delay-to-rise-time ratio and the transfer function roots are given for the transfer functions from the fourth to tenth order. The delay-to-rise-time ratio of the proposed transfer functions is better than that of Bessel or Gaussian filter functions by fifteen to twenty percent.

Abstract: Properties of a plant input generated by a properly designed feedback control system are studied based on the transfer function from the reference input to the plant input The effects of poles of the plant and the closed-loop system on the plant input are studied for the first order case of this transfer function subjected to a step reference input Introducing the concept of virtual plant poles, the results are then extended to the second-order case for an over-damped closed-loop system

Abstract: A measure for evaluating the L/sub 2/-sensitivity of a closed-loop transfer function with respect to the coefficients of a state-estimate feedback continuous-time controller is presented by using a pure L/sub 2/ norm and taking into account 0, /spl plusmn/1 coefficients. A technique is then developed for synthesizing the structure of a state-estimate feedback continuous-time controller with very low L/sub 2/- sensitivity. This is achieved by applying an orthonormal ladder filter with several 0 coefficients. Finally, a numerical example is given to illustrate the utility of the proposed technique.

Abstract: In this paper, a new approach for solving the problem of pole assignment, using static output feedback, has been proposed. The proposed approach is based on genetic algorithm where it can place all the closed-loop poles at desired locations with a high accuracy, provided that there exists a solution to the problem. It is also shown that how some known difficulties of static output feedback like order of system, multiplicity of the desired poles and the need for having closed-loop poles to be distinct or different from the open loop poles have been solved. Numerical examples at the end of the paper illustrate the applicability and the performance of the proposed method.

Abstract: Analytical methods of polynomial algebra, heuristic techniques, and digital modeling are used to study the robustness domain of linear dynamic systems with model “input–output” controllers as a function of the mutual locations of zeros and poles of the transfer function of the controlled object and poles of the characteristic polynomial. Conditions for parametric robustness are determined. A method of choosing the measured output coordinate of the automatic control system during structure formation from optimal-speed requirements is described.