Minimum-phase Case Research Articles

On Dead-Time Compensation in Repetitive Control

The note studies the stabilization problem for a SISO continuous-time plant, where the feedback loop contains a fixed infinite-dimensional repetitive element and a “primary controller” to be designed. A novel architecture of the primary controller is proposed, which reduces the stabilization problem to that for a finite-dimensional system. The architecture has a flavor of dead-time compensation, also in the structure of resulting closed-loop systems. In the minimum-phase case, an implementation scheme insensitive to the value of the delay in the repetitive block is proposed.

Harmonic Suppression and Stability Enhancement for Parallel Multiple Grid-Connected Inverters Based on Passive Inverter Output Impedance

In this paper, the inverter output impedance is passivized for solving the harmonic and the stability problems in the multiparallel inverters. The harmonics are easily aroused because of the disturbances, and the system stability is challenged by the grid impedance. Based on the simplified equivalent impedance model, the two problems are analyzed in the low-frequency (LF) band and the high-frequency (HF) band, respectively. Aiming at improving the LF performance, the weighted-proportional grid voltage feedforward and the harmonic quasi-resonant controller with phase compensation are proposed. The dynamic performance is enhanced with an additional current reference generation scheme. In order to improve the HF performance, a novel digital phase lead filter which brings the system back to a minimum-phase case is proposed. By the proposed control method, the high modulus of each inverter output impedance Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> is guaranteed, while the phase angles of Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> over the entire frequency band are avoided to be lower than -90°. The experiments based on four-parallel inverters have been conducted to validate the effectiveness of the proposed control method.

OPTIMAL ENERGY REGULATION PERFORMANCE OF DELAY-TIME SYSTEMS

This paper studies the regulation performance limi- tation of delay-time systems. The performance is measured by the energy of the control input with respect to an impulse dis- turbance function. We first provide the analytical closed-form expression of the optimal performance for minimum phase case by reviewing the existing result. We then extend the problem to non-minimum phase case by exploiting the results of linear time- invariant discrete-time and delta domain cases.

The effect of system zeros on the achievable H/sub ∞/ estimation level

Lower bounds on the achievable estimation accuracy of stationary linear processes in the presence of energy-bounded exogenous signals are derived. These bounds are determined by the zeros of the process transfer function matrix. A significant difference is observed between the minimum-phase and the nonminimum-phase cases. In the latter case a lower bound is derived also for the norm of the matrix that solves the corresponding Riccati equation. The difference between the cases of minimum and nonminimum phase is accentuated when the measurement noise intensity tends to zero. It is shown that in the minimum-phase case the corresponding filter gain is almost in the range of the process input matrix. In the nonminimum-phase case the columns of the corresponding gain tend to stay in the space spanned by the rows of the system output matrix.

A different look at output tracking: control of a vtol aircraft

In this paper we propose a scheme for output tracking of nonminimum phase flat systems. The technique, which is applicable even in the minimum phase case, uses an inverse trajectory for feedforward which is stabilized by a state tracker built using the flat output. In contrast to approximate-linearization based control [Hauser, J., S. Sastry and G. Meyer (1992). Nonlinear control design for slightly nonminimum phase systems: application to v/stol aircraft. Automatica, 28, 665–679], which yields good performance in slightly nonminimum phase systems, our approach applies equally well to slightly and strongly nonminimum phase systems. The proposed control scheme and the approximate-linearization based controller are applied to a Vertical Take Off and Landing (VTOL) aircraft example and the performances are compared.

Characteristics of Unknown Linear Systems Deduced from Measured CW Magnitude.

A method is presented for predicting the total response, in both frequency and time, of an unknown linear system when only the measured continuous wave (cw) magnitude is available. The approach is based on approximating the square of the measured magnitude by a rational function, from which various system transfer functions in terms of complex frequency are deduced. These transfer functions may or may not be at minimum phase. The corresponding impulse response is then obtained by taking the inverse Laplace transform of the transfer function. The impulse response of the minimum-phase case rises faster initially to its first maximum than the nonminimum-phase counterparts. This result confirms that, for the same cw magnitude response, the accumulative energy contained in the impulse response is the greatest when the transfer function is at minimum phase. Physical meaning of the energy content is also discussed.

State‐space solutions to the ℋ︁∞/LTR design problem

AbstractThe LTR design problem using an ℋ︁∞ optimality criterion is presented for two types of recovery errors, the sensitivity recovery error and the input‐output recovery error. For both errors two different approaches are presented. First, following the classical LTR design philosophy, a Luenberger observer based approach is proposed, where the ℋ︁∞ part of the controller is appended to a standard full‐order observer. Second, allowing for general controllers, an ℋ︁∞ state‐space problem is formulated directly from the recovery errors. Both approaches lead to controller orders of at most 2n. In the minimum phase case, though, the order of the controllers can be reduced to n in all cases. The control problems corresponding to the various controller types are given as four different singular ℋ︁∞ state‐space problems, and the solutions are given in terms of the relevant equations and inequalities.

Adaptive control for systems with bounded disturbances

The authors present an identification algorithm that can be used to design globally stable indirect adaptive controllers for minimum- and nonminimum-phase systems subject to bounded disturbances. The parameter estimation scheme is a least-squares algorithm with dead zone. The dead zone is such that the estimates converge and make it possible to define projected estimates having the same convergence properties as the original estimates. In the minimum-phase case, the projection facility can be used to ensure that the leading coefficient projected estimate is greater than or equal to the true leading coefficient in absolute value. The projection procedure can also be used to avoid pole-zero cancellations in an adaptive pole-placement algorithm.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Optimal robustness via constrained controller in SISO discrete-time feedback systems

A new sufficient condition for robust stabilization of SISO discrete-time feedback systems with both non-linear (or linear) time-varying uncertainties and constrained actuators is derived. In this paper, neither the plant nor the controller has to be restricted to the stable or minimum-phase case. The necessary and sufficient condition for solvability of a stabilizer satisfying such a robust constraint is also introduced. The optimal H∞-norm theory is employed to achieve the maximum robustness to tolerate the uncertainties via constrained control. Finally, a design algorithm is proposed to specify adequate parameters in the compensator to satisfy the criterion of optimal robustness and an example with computer simulation is given to illustrate the results.

The LQG/LTR procedure for multivariable feedback control design

This paper provides a tutorial overview of the LQG/LTR design procedure for linear multivariable feedback systems. LQG/LTR is interpreted as the solution of a specific weighted H2-tradeoff between transfer functions in the frequency domain. Properties of this solution are examined for both minimum-phase and nonminimum-phase systems. This leads to a formal weight augmentation procedure for the minimum-phase case which permits essentially arbitrary specification of system sensitivity functions in terms of the weights. While such arbitrary specifications are not possible for nonminimum-phase problems, a direct relationship between weights and sensitivities is developed for nonminimum-phase SISO and certain nonminimum-phase MIMO cases which guides the weight selection process.

Comments on "Apsects of PCM Regenerator Design for Crosstalk Limited Enviroments"

In the paper above-named work [ibid., vol. 30, no. 8 (this issue, Aug. 1982), pp. 2000- 2002] Millott and Nicholson use a regenerator noise figure to select an equalization function, and then check the suitability of this choice by examining the resulting eye diagram. This leads them to the conclusion that a raised cosine response with a roll-off factor α = 0.3 is the optimum choice. There are some aspects of the use of an eye diagram in this way that deserve further comment. The commentor makes it clear that he does not think that these observations invalidate the main conclusions presented in Millott and Nicholson's paper. He believes that their selection of a response with a relatively sharp roll-off, and the preferences for partial response modes, are correct. However, the commentor thinks that the minimum phase case should be considered, and that it is desirable to take account of the tolerances in the equalization functions when estimating system margins. When this is done the optimum point will be a little different, and the margins rather smaller, than those suggested by Millott and Nicholson. Comments by Millott are provided.