Practical Controller Design Research Articles

Infinite-dimensional nonlinear predictive control design for open-channel hydraulic systems

A nonlinear predictive control design based on Saint Venant equations is presented in this paper in order to regulate both water depth and water flow rate in a single pool of an open-channel hydraulic system. Thanks to variational calculus, some necessary optimality conditions are given. The adjoint partial differential equations of Saint Venant partial differential equations are also derived. The resulting two-point boundary value problem is solved numerically by using both time and space discretization and operator approximations based on nonlinear time-implicit finite differences. The practical effectiveness of the control design is demonstrated by a simulation example. A extension of the predictive control scheme to a multi-pool system is proposed by using a decomposition-coordination approach based on two-level algorithm and the use of an augmented Lagrangian, which can take advantage of communication networks used for distributed control. This approach may be easily applied to other problems governed by hyperbolic PDEs, such as road traffic systems.

Design of practical sliding-mode controllers with constant switching frequency for power converters

A novel experimentally motivated method in order to design a family of easy-to-implement sliding-mode controllers for power converters is proposed. Two main results are presented. First, the relation between sliding-mode control and average control is reinterpreted so that the limitation of the switching frequency for the closed-loop system is achieved in a more direct way than other methods so far reported in the literature. For this purpose, a class of sliding surfaces which makes the associated equivalent control be the system average control is proposed. Second, the achievement of a constant switching frequency in the controlled system is assured without requiring the sliding-mode-based controller to be modified, unlike most previous works. As a result, the proposed sliding surfaces-type can be directly implemented via a pulse-width modulator. The control methodology is implemented for the voltage control in a boost converter prototype in which the load is considered unknown. Experimental results confirm high performance and robustness under parameters variation. Furthermore, the solution proposed is easy to implement and well-suited for other power converters.

Robust tracking control design for uncertain robotic systems with persistent bounded disturbances

AbstractIn this study, a robust nonlinear L∞‐gain tracking control design for uncertain robotic systems is proposed under persistent bounded disturbances. The design objective is that the peak of the tracking error in time domain must be as small as possible under persistent bounded disturbances. Since the nonlinear L∞ ‐gain optimal tracking control cannot be solved directly, the nonlinear L∞ ‐gain optimal tracking problem is transformed into a nonlinear L∞ ‐gain tracking problem by given a prescribed disturbance attenuation level for the L∞ ‐gain tracking performance. To guarantee that the L∞ ‐gain tracking performance can be achieved for the uncertain robotic systems, a sliding‐mode scheme is introduced to eliminate the effect of the parameter uncertainties. By virtue of the skew‐symmetric property of the robotic systems, sufficient conditions are developed for solving the robust L∞ ‐gain tracking control problems in terms of an algebraic equation instead of a differential equation. The proposed method is simple and the algebraic equation can be solved analytically. Therefore, the proposed robust L∞ ‐gain tracking control scheme is suitable for practical control design of uncertain robotic systems. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Robust PID control design for permanent magnet synchronous motor: A genetic approach

In this paper, a robust PID control scheme is proposed for the permanent magnet synchronous motor (PMSM) using a genetic searching approach. Genetic algorithms (GAs) are powerful searching algorithms based on the mechanics of natural selection and natural genetics. Based on a simple genetic algorithm, a set of PID parameters can be obtained such that the robust stability for the closed-loop system is guaranteed, the tracking performance is minimized subject to certain related cost function, and the disturbance rejection ability ( H ∞ performance) subject to a prescribed attenuation level can also be achieved. Numerical solutions of the PID parameters constrained by three different objectives and simulation results are provided to illustrate the design procedure and the expected performances. Finally, the proposed PID control scheme for the PMSM is implemented by a DSP-based fully digital controller. From the experimental results, the performances can be achieved using the proposed PID control scheme. In opposition to trial and error, the PID parameters can be obtained systematically in this study. The proposed method is simple and is suitable for practical control design in the motor drive.

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.

A hybrid optimization method of evolutionary and gradient search

This article proposes a hybrid optimization algorithm, which combines evolutionary algorithms (EA) and the gradient search technique, for optimization with continuous parameters. Inheriting the advantages of the two approaches, the new method is fast and capable of global search. The main structure of the new method is similar to that of EA except that a special individual called the gradient individual is introduced and EA individuals are located symmetrically. The gradient individual is propagated through generations by means of the quasi-Newton method. Gradient information required for the quasi-Newton method is calculated from the costs of EA individuals produced by the evolution strategies (ES). The symmetric placement of the individuals with respect to the best individual is for calculating the gradient vector by the central difference method. For the estimation of the inverse Hessian matrix, symmetric Rank-1 update shows better performance than BFGS and DFP. Numerical tests on various benchmark problems and a practical control design example demonstrate that the new hybrid algorithm gives a faster convergence rate than EA, without sacrificing the capability of global search.

Study on the stability of switched dissipative Hamiltonian systems

The hybrid Hamiltonian system is a kind of important nonlinear hybrid systems. Such a system not only plays an important role in the development of hybrid control theory, but also finds many applications in practical control designs for obtaining better control performances. This paper investigates the stability of switched dissipative Hamiltonian systems under arbitrary switching paths. Under a realistic assumption, it is shown that the Hamiltonian functions of all the subsystems can be used as the multiple-Lyapunov functions for the switched dissipative Hamiltonian system. Based on this and using the dissipative Hamiltonian structural properties, this paper then proves that the P-norm of the state of switched dissipative Hamiltonian system converges to zero with the time increasing, and presents two sufficient conditions for the asymptotical stability under arbitrary switching paths. Utilizing these new results, this paper also obtains two useful corollaries for the asymptotical stability of switched nonlinear time-invariant systems. Finally, two examples are studied by using the new results proposed in this paper, and some numerical simulations are carried out to support our new results.

A robust LQG-controller design for DPS

We review the popular Linear Gaussian Quadratic (LQG) controller design for DPS and its shortcomings. In particular, its applicability is essentially restricted to exponentially stabilizable and detectable DPS with finite-rank bounded input and output operators. As an alternative, we propose a new practical control design that is applicable to DPS with unbounded, finite-rank input and output operators, provided that the generator has finitely many unstable eigenvalues and satisfies the spectrum determined growth assumption.

Design and Test Results of Active Magnetic Bearing Control System for High-speed Turbo Compressor

In designing turbo compressors driven by high-speed motor directly, there is a rotordynamic problem due to lowered bending mode frequencies. In order to support such flexible and high-speed rotating shaft, active magnetic bearing (AMB) will be one of the solutions. In this paper, the design and test results of the AMB system for such a compressor that has two compression stages are discussed. In a digital processing of AMB control, a large phase lag in high frequency domain cannot be avoided. In order to solve this problem, the following control methods are presented. For levitation control, a practical controller design that uses a combination of phase shifting filters and second order low-pass filters is presented. For unbalance control, a synchronous filter that has an arbitrary phase shift at the reference frequency is applied to cross over the first bending critical speed. By adopting these control methods, very stable operation from zero speed to the rated speed of 55 000 min-1 was realized.

539 分数階微積分による制御器の一設計法 : ギアバックラッシュを持つ倒立振子系への応用

This paper presents an efficient numerical method to realize discrete models of fractional order controllers for systems containing backlash nonlinearity. The presented method is to calculate fractional derivatives and integrals on inhomogeneous time intervals which are getting longer as the operation points go back toward the initial time. It leads to the effective quality which has low computational costs and enough accuracy. A practical controller design is applied for an inverted pendulum system containing gear-backlash. The simulation and experimental results show that the fractional control system has superior performance against backlash nonlinearity and thus the backlash vibration can be suppressed.

Interactive evolutionary computation in process engineering

In practical system identification, process optimization and controller design, it is often desirable to simultaneously handle several objectives and constraints. In some cases, these objectives and constraints are non-commensurable and they are not explicitly/mathematically available. This paper proposes a new subjective optimization method based on interactive evolutionary computation (IEC) to handle these problems. IEC is an evolutionary algorithm whose fitness function is provided by human users. The whole approach has been implemented in MATLAB (EAsy-IEC Toolbox) and applied to two case-studies: tuning a Model Predictive Controller and temperature profile design of a batch beer fermenter. The results show that IEC is an efficient and comfortable method to incorporate the prior knowledge of the user into optimization problems. The developed EASy-IEC Toolbox (for MATLAB) can be downloaded from the website of the authors: http://www.fmt.vein.hu/softcomp/EAsy.

A student control competition through a remote robotics lab

The Automatic Control Telelab (ACT) laboratory at the University of Siena, Italy, has developed a new module called the student competition system. In the ACT module, students or groups of students compete to develop the best controller for a given remote process. The competition not only stimulates students' interest in control systems but also enhances learning by facilitating the understanding of practical control design issues.

Problems on time-varying port-controlled Hamiltonian systems: geometric structure and dissipative realization

To apply time-varying port-controlled Hamiltonian (PCH) systems to practical control designs, two basic problems should be dealt with: one is how to provide such time-varying systems a geometric structure to guarantee the completeness of representations in mathematics; and the other is how to express the practical system under consideration as a time-varying PCH system, which is called the dissipative Hamiltonian realization problem. The paper investigates the two basic problems. A suitable geometric structure for time-varying PCH systems is proposed first. Then the dissipative realization problem of time-varying nonlinear systems is investigated, and serval new methods and sufficient conditions are presented for the realization.

Project-based learning - design of a prototype semiautonomous vehicle

This article described how project-based learning helps engage students in the design of a complicated system. Throughout the course of the project, a student demonstrated a holistic learning process and managed to accomplish all the stated objectives of the project. The project emphasized techniques for solving control problems. To give the student a manageable learning experience, the project was divided into eight subtasks. Through the completion of subtasks, the student learned problem-solving techniques for practical controller design such as planning, literature survey, reading technical datasheets, trouble-shooting, and experimental testing and evaluation. These techniques can be used for other engineering design projects. The project involved vertical and horizontal integration of different subjects for a meaningful application. The prototype vehicle is currently used for undergraduate demonstrations and research in autonomous vehicles.

Robust gain-scheduled control for vibration suppression

Limited control authority is a key issue in the field of structural control and is a major research area since most of the practical control problems are dominated by constraints on the control signal. The paper presents a simple and practical gain-scheduled controller design procedure for active vibration suppression of a three-storey flexible structure. First, system identification experiments are performed and the plant’s uncertainty is derived. Next, robust controller design with constraint on the control signal is presented. For a better trade-off between control performance and control constraint a gain-scheduling approach is investigated. Stability analysis of the gain-scheduled controller is analysed using a parameter-independent Lyapunov function (quadratic stability) as well as a parameter-dependent Lyapunov function (biquadratic stability). Finally, the gain-scheduled controller is tested experimentally when the flexible structure is excited with a scaled historical earthquake record (1940 El Centro record). Successful experimental results show that the proposed robust gain-scheduled control approach offers good performance in the case of control authority limitation.

Nonlinear modeling and identification of a DC motor for bidirectional operation with real time experiments

Modeling and identification of mechanical systems constitute an essential stage in practical control design and applications. Controllers commanding systems that operate at varying conditions or require high precision operation raise the need for a nonlinear approach in modeling and identification. Most mechanical systems used in industry are composed of masses moving under the action of position and velocity dependent forces. These forces exhibit nonlinear behavior in certain regions of operation. For a multi-mass rotational system, the nonlinearities, like Coulomb friction and dead zone, significantly influence the system operation when the rotation changes direction. The paper presents nonlinear modeling and identification of a DC motor rotating in two directions together with real time experiments. Linear and nonlinear models for the system are obtained for identification purposes, and the major nonlinearities in the system, such as Coulomb friction and dead zone, are investigated and integrated in the nonlinear model. The Hammerstein nonlinear system approach is used for identification of the nonlinear system model. Online identification of the linear and nonlinear system models is performed using the recursive least squares method. Results of the real time experiments are graphically and numerically presented, and the advantages of the nonlinear identification approach are revealed.

Fire Model Analysis and Experimental Validation on Smoke Compartments

Referring to fire accidental data, more than half the deaths from accidental fires are due to smoke rather than fire. In addition to using smoke curtain to accumulate smoke, it is necessary to consider appropriate smoke compartmentation effects for practical smoke control design. Otherwise evacuation and extinguishing systems would not be operated adequately. However, under the existing fire code of Taiwan, there are many constraints applied to construct smoke compartments inside buildings. Sometimes, it cannot work out for practical design purposes, such as the area of smoke compartments were limited without exception of performance consideration. Therefore, the purpose of this paper is to investigate the phenomena related to fire, heat, and smoke during some postulated fire scenarios occurring in a multicompartment enclosure and the distribution of smoke flow field. Two different fundamental fire models, CFAST and SMARTFIRE, are used for analyzing and predicting the experimental results from a full-scale test. The comparison results show quite reasonable variations between numerical simulation and experimental data. Although the temperature data are higher than experimental data, the predicted smoke layer heights are lower than experimental data. However, the fire models present correct trend of accumulated smoke layer height and temperature distributions in a multi-compartment structure.

Two-dimensional loop shaping

This article considers the design of practical feedback controllers for a class of spatially distributed processes where the state of a uniform physical substrate is influenced by an array of evenly distributed, identically constructed actuators and measured by an array of evenly distributed, identical sensors. A constructive procedure is introduced for designing spatially distributed feedback controllers with the objective of practical implementation. The full controller design cycle is addressed; including specification, synthesis, and implementation. The proposed design procedure has been field-tested and forms the basis of a software tool that has recently been implemented in a commercial product for the design of industrial paper machine controllers.

Minimax LQG optimal control of a flexible beam

The paper presents a practical robust controller design methodology based on recent theoretical results on minimax LQG control. This controller design methodology is illustrated with the design of a robust feedback controller for the control of vibrations in a flexible cantilever beam. The minimax LQG control approach is used to design a controller which minimizes the total vibration energy in the beam which is subject to white noise disturbances. The controller is designed to be robust against uncertainties introduced by neglecting the higher order modes of the beam.

Construction of optimal quality control for oligo arrays.

Oligo arrays are important experimental tools for the high throughput measurement of gene expression levels. During production of oligo arrays, it is important to identify any faulty manufacturing step. We describe a practical algorithm for the construction of optimal quality control designs that identify any faulty manufacturing step. The algorithm uses hillclimbing, a search technique from combinatorial optimization. We also present the results of using this algorithm on all practical quality control design sizes. On request from the authors.