A design procedure is developed that combines linear-quadratic optimal control with regional pole placement. Specifically, a static and dynamic output-feedback control problem is addressed in which the poles of the closed-loop system are constrained to lie in specified regions of the complex plane. These regional pole constraints are embedded within the optimization process by replacing the covariance Lyapunov equation by a modified Lyapunov equation whose solution, in certain cases, leads to an upper bound on the quadratic cost functional. The results include necessary and sufficient conditions for characterizing static output-feedback controllers with bounded performance and regional pole constraints. Sufficient conditions are also presented for the fixed-order (i.e. full- and reduced-order) dynamic output-feedback problem with regional pole constraints. Circular, elliptical, vertical strip, parabolic, and section regions are considered. >

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Controller design with regional pole constraints

The three-phase pulsewidth modulation (PWM) AC/DC voltage-source converter with the control laws proposed so far is not only unstable against large-signal disturbances, but also has the problem that its stability depends on the circuit parameters such as the DC-output capacitance. This paper describes a new control law based on Lyapunov's stability theory. It is shown that the converter can be stabilized globally for handling large-signal disturbances. The resulting closed-loop system not only guarantees a sufficient stability region (independent of the circuit parameters) in the state space, but also exhibits good transient response both in the rectifying and regenerating modes. Also, a new simulation technique is introduced which increases the speed of the simulation process considerably. Computer simulations are presented to confirm the effectiveness of the proposed control strategy and the validity of the simulation technique. Experimental results are also presented to verify the theoretical and simulation studies.

Lyapunov-based control for three-phase PWM AC/DC voltage-source converters

In this study, an adaptive fuzzy-neural-network control (AFNNC) scheme is designed for the voltage tracking control of a conventional dc-dc boost converter. First, the description of the circuit framework of a conventional boost converter and system modeling is introduced. Then, a total sliding-mode control (TSMC) strategy without the reaching phase in the conventional SMC is developed for enhancing system robustness during the transient response of the voltage control. In order to alleviate the control chattering phenomena caused by the sign function in the TSMC design and relax the requirement of detailed system dynamics, an AFNNC scheme is further investigated to imitate the TSMC law for the boost converter. In the AFNNC scheme, online learning algorithms are derived in the sense of Lyapunov stability theorem and projection algorithm to ensure the stability of the controlled system without the requirement of auxiliary compensated controllers despite the existence of uncertainties. The output of the AFNNC scheme can be easily supplied to the duty cycle of the power switch in the boost converter without strict constraints on control parameters selection in conventional control strategies. In addition, the effectiveness of the proposed AFNNC scheme is verified by realistic experimentations, and its advantages are indicated in comparison with the TSMC strategy.

Adaptive Fuzzy-Neural-Network Design for Voltage Tracking Control of a DC–DC Boost Converter

This work presents an analytical study and an experimental verification of a robust control design based on a linear matrix inequalities (LMI) framework for boost regulators. With the proposed LMI method, non-linearities and uncertainties are modelled as a convex polytope. Thus, the LMI constraints permit to robustly guarantee a certain perturbation rejection level and a region of pole location. With this approach, the multiobjective robust controller is computed automatically by a standard optimisation algorithm. The proposed method results in a state-feedback law efficiently implementable by operational amplifiers. PSIM simulations and experimental results obtained from a prototype are used to validate this approach. The results obtained are compared with a conventional PID controller.

LMI robust control design for boost PWM converters

The idea of pole-region assignment is extended to interval gain and phase margin assignment. The internal model control proportional-integral-derivative (IMC-PID) design is examined from the frequency domain point of view. Equations for typical frequency domain specifications such as gain margin, phase margin and bandwidth are derived for the IMC-PID design. The gain and phase margins are monitored in real time and a self-tuning controller with interval gain and phase margin assignment is proposed. An implementation example in the laboratory is also given.

Self-tuning IMC-PID control with interval gain and phase margins assignment

Brief paper: Determining quadratic weighting matrices to locate poles in a specified region

A linear optimal quadratic regulator problem (an LQ-problem) is applied to assign all poles of the multivariable continuous-time system in a suitable region of the left-half complex plane. In particular, two design methods based on an LQ-problem for pole assignments in a truncated sector region of the left-half complex plane, which is given as a common area of a half plane Re λ≧-l > 0 and an open sector tan−1|Im λA/Re λ≦½ are proposed. Each design method is given for the cases where 0 ≧ ½π and 0 ≦ ½π respectively. As these two design methods are derived from two basically different ideas, they will prove more useful if each method can be applied according to the demands of the system's dynamical characteristics.

Pole placement in a specified region based on a linear quadratic regulator

Abstmct-,The state space averaging models of Boost, BuckBoost and Cuk converters are shown to be bilinear systems. Because of the difficulties in analyzing such bilinear systems, most of the previous works dealing with such converters in the state space are confined to the discussions of their linear approximated systems (small signal model). A new control law based on the bilinear large signal models, not linearly approximated, is proposed for achieving the output regulation of these converters. The control law is derived from directly applying the Lyapunov stability theory to the bilinear large sihal models, so that the closed bp systems possess excellent output properties, some of which are illustrated by numerical simulations.

https://ieeexplore.ieee.org/iel3/63/8799/00387997.pdf

A New Control Law of Bilinear DC-DC Converters Developed by Direct Application

https://www.jstage.jst.go.jp/article/ieejeiss1987/108/1/108_1_55/_pdf

Naoya Kawasaki

Papers

Brief paper: Determining quadratic weighting matrices to locate poles in a specified region

Pole placement in a specified region based on a linear quadratic regulator

A New Control Law of Bilinear DC-DC Converters Developed by Direct Application

Selectable Turn Over Design Method with Assigning Dominant Poles for Linear Systems

A Method for Deciding Weighting Matrices in a Linear Quadratic Regulator Problem to Locate all Poles in the Specified Region