Non-minimum Phase Part Research Articles

Non-Integer Order Approximation of a PID-Type Controller for Boost Converters

In this work, the voltage regulation of a boost converter is addressed. A non-integer order PID controller is proposed to deal with the closed-loop instability of the system. The average linear model of the converter is obtained through small-signal approximation. The resulting average linear model is considered divided into minimum and normalized non-minimum phase parts. This approach allows us to design a controller for the minimum phase part of the system, excluding temporarily the non-minimum phase one. A fractional-order PID controller approximation is suggested for the minimum phase part of the system. The proposal for the realization of the electrical controller is described and its implementation is used to corroborate its effectiveness when regulating the output voltage in the boost converter. The fractional-order PID approximation achieves regulation of the output voltage in the boost converter by exhibiting the iso-damping property and using a single control loop, which confirmed its effectiveness in terms of controlling non-minimum phase/variable parameter systems.

Model Approximate Method of Complex System

During the internal model control of multivariate multiple time delay system, process model is very important in the design of controller, but complicated mathematical model is often encountered in decoupled multivariable multiple time delay system and needs to be reduced order. So this paper proposes a low order identification structure and an optimization method for model approximation of the complex model containing the time delay and non-minimum phase parts. In this paper, with the adoption of Pade approximation, a suboptimal approximate algorithm is used for the model approximation and model identification. The integral square error index and the frequency-domain integral square error index, as well as the integral time absolute error index is used to evaluate the approximate model comprehensively. Simulation results show that using the proposed model identification structure and adopting the suboptimal approximate algorithm to deal with this kind of approximation, that can get an approximate model that well reveals the dynamic characteristics of system and has a high approximation precision.

Robust Proportional-Integral-Derivative Controller Design for Stable/Integrating Processes with Inverse Response and Time Delay

Processes that exhibit dynamic behaviors of inverse response and time delay increase the difficulty of control system design. This paper presents the design concepts that lead to robust tuning of a proportional-integral-derivative (PID) controller for stable/integrating processes with inverse response and time delay. The proposed control system design is based on a Smith-type compensator for nonminimum phase dynamics, which aims to remove these elements from the feedback loop. In this control scheme, it is necessary to factorize the process model into minimum phase and nonminimum phase parts. By investigating and comparing different factorization methods, this study shows that a system based on the direct factorization method can achieve better trade-off between control performance and system robustness. Furthermore, this study approximates the equivalent feedback controller for the proposed control configuration as a classical PID controller based on Maclaurin-series approach. Analytical tuning rules for...

Output tracking for nonlinear non-minimum phase systems and application to PVTOL aircraft

In this paper, we consider a class of multi-input multi-output (MIMO) nonlinear non-minimum phase systems. For such nonlinear system, an output tracking control approach based on decomposition is presented and applied to a planar vertical takeoff and landing (PVTOL) aircraft. The external dynamics of the system can be separated into minimum-phase and non-minimum-phase parts. The internal dynamics of the system is separated to linear part and nonlinear part, and the linear part of the internal dynamics is only related with the non-minimum phase part of the external dynamics and the states of itself. Consequently, two low-dimensional controllers are designed separately to stabilize the two subsystems, and make the overall closed-loop system stable in spite of the existence of disturbances. Through this method, the design of the controller parameters is very simple. The theoretical results are confirmed by computer simulations.

Multivariable Smith Predictors Design for Nonsquare Plants

The goal of this brief is to provide a solution to the optimal design problem of decoupled multivariable Smith Predictor for general linear stable plants with multiple time delays. The design procedure is divided into three steps. In the first step, a nonsquare plant is factored into the free part and delay part, and the free part is further factored into minimum phase part and nonminimum phase part. In the second step, the factorization is utilized to analytically derive the optimal multivariable Smith Predictor based on only output feedback. Finally, the controller is shaped by a filter for specified inputs and a simple procedure is developed to quantitatively tune the closed-loop response expressed in time domain or frequency domain

MULTI MODEL APPROACH TO MULTIVARIABLE LOW ORDER STRUCTURED-CONTROLLER DESIGN

The method presented here offers an effective and time saving tool for robust low order multivariable controller design. The relation between controller complexity and closed loop performance can easily be evaluated. The method consists of five steps: 1. A desired behavior of the closed loop system is specified. Considering the nonminimum phase part of the process model the closed loop attainable performance is determined. 2. The process model and the attainable performance are scaled by the RPN-scaling procedure. 3. This defines an “ideal” scaled controller, which is usually too complex to be realized. 4. The frequency response of the ideal scaled compensator is approximated by a simpler one with structure and order chosen by the user. 5. Since the approximation in frequency response is performed with the scaled system, it is necessary to return to the original system's units. This procedure can be implemented using a multi-model approach, what increase the robustness of synthesized controller.

Multivariable low order structured-controller design by frequency response approximation

The method presented here offers an effective and time saving tool for multivariable controller design. The relation between controller complexity and closed loop performance can easily be evaluated. The method consists of five steps: 1. A desired behavior of the closed loop system is specified. Considering the nonminimum phase part of the process model the closed loop attainable performance is determined. 2. The process model and the attainable performance are scaled by the RPN-scaling procedure. 3. This defines an scaled controller, which is usually too complex to be realized. 4. The frequency response of the ideal scaled compensator is approximated by a simpler one with structure and order chosen by the user. 5. Since the approximation in frequency response is performed with the scaled system, it is necessary to return to the original system’s units.

Approximation of the optimal minimum-phase output for control of nonlinear nonminimum-phase processes

Nonminimum-phase parts are better removed in the feedback loop like the time delay term. For this, Wright and Kravaris [1992] proposed the concept of optimal minimum-phase output to control nonlinear nonminimumphase processes. However, their optimal minimum-phase output has no analytic solutions for processes with more than three state variables. Here, methods for analytic minimum-phase outputs approximating the optimal ones are proposed, having no limitations in the number of state variables. The proposed methods provide analytic solutions for processes with three state variables and simple numerical solutions for those with more state variables.

Adaptive equalisation in oversampled subbands

The potential presence of fractional delays, nonminimum phase parts, and a colouring of the channel output can require adaptive equalisers to adapt very long filters, which can have slow convergence for LMS-type adaptive algorithms. The authors present a novel oversampled subband approach to adaptive equalisation, which can both significantly reduce computational complexity and improve convergence speed.

Control-affine neural network approach for nonminimum-phase nonlinear process control

The design of controllers for nonlinear, nonminimum-phase processes is very challenging and remains as one of the more difficult control research problems. Most currently available control algorithms rely implicitly or explicitly upon an inverse of the process. Linear control methods for nonminimum-phase processes are typically based on a decomposition of the process into a minimum-phase and a nonminimum-phase part, and subsequent inversion of the minimum-phase component. A similar scheme for nonlinear systems is still an open problem. In this work, an internal model control strategy employing a minimum-phase model is proposed. The minimum-phase model is first-order, minimum-phase and control-affine but statically equivalent to the original process. Because the model is identified directly from input-output data, a first principles model of the process is not required. The inverse of the process is obtained through analytical inversion of the process model. The proposed control scheme is applied to a van de Vusse reactor and a complex continuous stirred tank bioreactor.

Loop Transfer Recovery Techniques for Time-Delay Systems with Non-Minimum Phase Lumped Part

For a plant consisting of a lumped non-minimum phase part and an output delay, we discuss LTR (Loop Transfer Recovery) techniques for designing a predictor-based LQG controller. We focus our attention to the feedback property achieved at the plant output side. We show that a feedback property recovered by the formal application of the conventional LTR procedure can be achieved by the partial LTR technique which has a clear system-theoretic meaning. This fact provides a theoretical justification of the formal application of the conventional LTR technique to a plant including finite unstable zeros and a time delay. In addition, we point out that the partial LTR technique provides more freedom in shaping target feedback properties. We propose a simple technique exploiting this freedom. A numerical example is given to illustrate usefulness of the proposed technique.

Perfect and subperfect regulation in linear multivariable control systems

This paper is concerned with the synthesis of a high-gain feedback control, called perfect regulation (p.r.), for linear multivariable systems with external signals. The existence condition for p.r. is derived, in which the minimum phase property plays an essential role. The use of an observer is discussed for achieving p.r. under restricted state observation. Some asymptotically ideal feedback properties are demonstrated, such as the complete desensitization, the complete servo performance with decoupling and the complete disturbance rejection, which formulate the loop-tightness for multivariable systems. A design method for applying p.r. to non-minimum phase systems, called subperfect regulation (s.p.r.), is proposed based on the factorization of the plant transfer function matrix into the minimum phase part and the totally non-minimum phase part. It is a multivariable extension of a well-known design technique for scalar systems to overcome the difficulty of phase non-minimality. Computational procedures for p.r. and s.p.r. are discussed. An illustrative example is shown.

Perfect and Subperfect Regulation in Linear Multivariable Control Systems

The perfect regulation (p.r.) of linear multivariable systems with external signal is considered. The minimal phase property plays an essential role for the existence of the p.r. Some asymptotically ideal closed-loop properties of the p.r. are demonstrated, such as the complete desensitization, the complete servo performance with decoupling and the complete disturbance rejection, which characterize the multivariable loop-tightness. An extension of the p.r. to non-minimum phase systems (the subperfect regulation) is derived, based on the cascade decomposition of the plant into the minimum phase part and the totally non-minimum phase part. It is a multivariable extension of a well-known design technique for scalar systems to overcome the difficulty of phase non-minimality.