Fixed-structure Controller Design Research Articles

Swarm-based robust fixed-structure controller design for buck converter using Kharitonov approach: design and experiment

Swarm-based robust fixed-structure controller design for buck converter using Kharitonov approach: design and experiment

Robust fractional-order fixed-structure controller design for uncertain non-commensurate fractional plants using fractional Kharitonov theorem

This article deals with the problem of robust fractional-order fixed-structure controller design for commensurate and non-commensurate fractional-order interval systems using fractional Kharitonov theorem. The contribution of this study is to develop a simple control methodology to stabilize the fractional-order Kharitonov-defined vortex polynomials. Using the idea of robust stability testing function and extending it to the systems under study, the straightforward graphical and systematic procedures are proposed to investigate the robust stability of the system by searching for a non-conservative fractional-order Kharitonov region in the controller parameters plane. This region can establish all the fractional-order controllers that make the uncertain fractional-order systems stable. The relation between the fractional-order Kharitonov region and the parameters of the stabilizing controller is also found. Finally, comparison results with three relevant works are given to illustrate the feasibility of the proposed method.

Decentralized and Distributed Transient Control for Microgrids

This paper presents a comprehensive approach toward the design of primary and secondary controllers in low-inertia power grids with mixed lines and a large amount of inverter-interfaced generation. First, a complete dynamic phasor model is developed that represents the electromagnetic and electromechanic dynamics of lines, inverters, synchronous machines, and constant power loads. The model offers a straightforward way to combine white-, gray- and black-box models, and its structure lends itself well to control design. In a second step, it is shown how a recently developed robust fixed-structure control design method can be applied to the challenging and relevant problem of primary and secondary control in medium-and low-voltage grids. A comprehensive three-part simulation example demonstrates how frequency and voltage transient stability and performance can be achieved through a methodical design process. It is also shown how nonstandard performance specifications such as proportional power sharing can be directly incorporated in the design. Finally, a distributed secondary controller from the literature is reformulated and designed using the presented framework, and all results are validated in nonlinear simulation.

A Control Design Approach for TITO Systems Using Measured Data

This paper deals with the design of fixed-structure controllers for two-input two-output (TITO) systems using frequency-domain data. In standard control approaches, a plant model is first derived, then a suitable controller is designed to meet some user-specified performance specifications. Basically, there are two common ways for obtaining mathematical models: white-box modeling and black-box modeling. In both approaches, it is difficult to obtain a simple and accurate model that completely describes the system dynamics. As a result, errors associated with the plant modeling may result in degradation of the desired closed-loop performance. Moreover, the intermediate step of plant modeling introduced for the controller design is a time-consuming task. Hence, the concept of data-based control design is introduced as a possible alternative to model-based approaches. This promising methodology allows us to avoid the under-modeling problem and to significantly reduce the time and workload for the user. Most existing data-based control approaches are developed for single-input single-output (SISO) systems. Nevertheless, a large class of real systems involve several manipulated and output variables. To this end, we attempt here to develop an approach to design controllers for TITO systems using frequency-domain data. In such a method, a set of frequency-domain data is utilized to find an adequate decoupler and to tune a diagonal controller that meets some desired closed-loop performance measures. Two simulation examples are presented to illustrate and demonstrate the efficacy of the proposed method.

A data-driven approach to robust control of multivariable systems by convex optimization

The frequency-domain data of a multivariable system in different operating points is used to design a robust controller with respect to the measurement noise and multimodel uncertainty. The controller is fully parameterized in terms of matrix polynomial functions and can be formulated as a centralized, decentralized or distributed controller. All standard performance specifications like H2, H∞ and loop shaping are considered in a unified framework for continuous- and discrete-time systems. The control problem is formulated as a convex–concave optimization problem and then convexified by linearization of the concave part around an initial controller. The performance criterion converges monotonically to a local optimum or a saddle point in an iterative algorithm. The effectiveness of the method is compared with fixed-structure controller design methods based on non-smooth optimization via multiple simulation examples.

Solving and visualizing nonlinear parametric constraints in control based on quantifier elimination

We present a new method with a software tool for parametric robust control synthesis by symbolic-numeric computation. The method is a parameter space approach and it is especially effective for analysis and design of fixed-structure controllers of rational type, which encompass PI and PID controllers. The real quantifier elimination (QE), which is one of the recent progresses in the symbolic computation, plays a key role in our development. The QE-based approach can uniformly deal with a lot of important design specifications for robust control such as frequency restricted H ∞ norm constraints, stability (gain/phase) margin and stability radius specifications, and pole location requirement by reducing such specifications to a particular type of formulae called a “sign definite condition (SDC)”. This is also useful for improving the efficiency of QE computations since we can utilize an efficient QE algorithm specialized to the SDC using the Sturm-Habicht sequence. We have developed a MATLAB toolbox for robust parametric control based on a parameter space approach accomplished by QE. The QE-based parameter space approach and numerical simulation of performances for specific controller parameter values taken from a controller parameter space are integrated conveniently in our toolbox with the assistance of a graphical user interface (GUI). With our toolbox the feasible regions of controller parameters are visualized in a parameter space for the controllers with three or two parameters. This enables control engineers to achieve multi-objective robust controller synthesis smoothly. We also discuss how to merge the numerical computation and the symbolic operation to make our new design methods more efficient in practical control design.

Design of fixed-structure controllers with frequency-domain criteria: a multiobjective optimisation approach

An optimisation-based iterative design of fixed-structure controllers with frequency-domain criteria is presented. An interactive multiobjective optimisation procedure is presented, which is based on a direct shaping of the frequency responses, without the need to construct explicit weighting filters. At each iteration, a constrained optimisation problem is formulated in such a way that successive improvements of the design to meet the designer's specifications are achieved. For computational efficiency, time-domain expressions consisting of linear matrix equations are used to characterise the frequency responses.

Multiobjective L1/H∞ Controller Design for Systems with Frequency and Time Domain Constraints

In this paper we develop an optimal mixed-norm L1 bound/H∞ and l1 bound/H∞ controller synthesis framework for continuous-time and discrete-time systems. This multiobjective problem is treated by forming a convex combination ofboth L1 (time domain worst-case peak amplitude response) and entropy (frequency domain worst-case H∞ disturbance attenuation) performance measures. For flexibility in controller synthesis, we adopt the approach of fixedstructure controller design which allows consideration of arbitrary controller structures, including order, internal structure, and decentralization. Finally, using a quasi-Newton continuation algorithm, we demonstrate the effectiveness of the proposed mixed-norm L1/ H∞ approach via two numerical design examples.

Fixed-structure controller design for systems with actuator amplitude and rate non-linearities

In this paper we develop output feedback controllers and fixed-order (i.e., full- and reduced-order) dynamic compensators for systems with actuator amplitude and rate saturation constraints. The proposed design methodology employs a rate limiter as part of the controller architecture. The problem of simultaneous control amplitude and rate saturation is embedded within an optimization problem by constructing a Riccati equation whose solution guarantees closed-loop global/local asymptotic stability in the face of sector bounded actuator amplitude and rate non-linearities. Application of the proposed framework is demonstrated via a flight control example involving actuator amplitude and rate saturation constraints.

Robust fixed-structure controller synthesis using the implicit small-gain bound

In this paper we explore the applicability of the implicit small-gain guaranteed cost bound for controller synthesis. For flexibility in controller synthesis, we adopt the approach of fixed-structure controller design which allows consideration of arbitrary controller structures, including order, internal structure, and decentralization. A numerical example that has been addressed in the literature by means of alternative guaranteed cost bounds is presented to demonstrate the fixed-structure/implicit small-gain approach to robust controller synthesis.

Mixed H 2/L 1 fixed-architecture controller design for multi-input/single-output systems

In this paper we develop a mixed-norm H 2/L 1 controller synthesis framework via fixed-order dynamic compensation for multi-input/single-output systems. For flexibility in controller synthesis, we adopt the approach of fixed-structure controller design which allows consideration of arbitrary controller structures, including order, internal structure, and decentralization. Several numerical examples are presented to demonstrate the fixed-structure mixed-norm H 2/L 1 controller synthesis approach.

Mixed-norm H2/L1 controller synthesis via fixed-order dynamic compensation: A Riccati equation approach

One of the fundamental problems in feedback control design is the ability of the control system to reject uncertain exogenous disturbances. Since a single performance objective is seldom adequate to capture multiple and often conflicting system disturbances, in this paper we develop a Riccati equation approach for mixed H2/L1 controller synthesis via fixed-order dynamic compensation. This multiobjec2 tive problem is treated by forming a convex combination of both the H2 (quadratic) and L1 bound (worst-case peak amplitude response) performance measures. For flexibility in controller synthesis, we adopt the approach of fixed-structure controller design which allows consideration of arbitrary controller structures, including order, internal structure, and decentralization. Finally, using a quasi-Newton continuation algorithm, we demonstrate the effectiveness of the proposed mixed-norm H2/L1 Riccati equation approach via several design examples.