Large Plant Uncertainty Research Articles

Robust Cascade Control inside a New Model-Matching Architecture

Whenever additional states of a plant can be measured, closing nested feedback loops can be exploited in a variety of ways. The goal here is to reduce the bandwidth of feedback controllers and thus reduce the amplification of sensor noise that can otherwise spoil the expected performance when the actuator saturates. This can be particularly relevant for demanding tracking specifications and large plant uncertainties. In this context, the current work proposes a novel model-matching control architecture with a feedforward controller and two feedback controllers, which is accompanied by a new robust design method in the frequency domain of Quantitative Feedback Theory (QFT). The use of a feedforward controller reduces the amount of feedback to the minimum necessary to constrain the spread of the tracking error responses as specified. Furthermore, this amount of feedback is quantitatively distributed along the frequency between the inner and outer loops to reduce the total sensor noise at the control input as much as possible. A theoretical example illustrates the method and highlights the advantages of the new architecture over two other previously feasible QFT solutions: one with double feedback and another with single feedback plus feedforward. The importance of choosing the correct switching frequency between loops is also demonstrated. Finally, the angle of rotation of a commercial servo motor is successfully controlled using the motor speed as an internal measure.

Model Reference Input Shaping Using Quantitative Feedforward-Feedback Controller

Input shaping convolutes the reference signal with a sequence of impulses, whose amplitudes and timings are designed to produce a shaped reference that avoids exciting lightly-damped modes to reduce residual vibration from a quick movement. The input shaper can be made robust to uncertain mode parameters by adding more impulses, which delays the reference signal, resulting in longer move time. Instead of using more impulses, in this paper, a feedforward-feedback control system, based on the quantitative feedback theory, is placed in the loop to match the closed-loop system, with uncertain plant, to a known reference model. The feedforward-feedback system handles the uncertainty, so the input shaper, placed outside the loop, needs not be robust. The closed-loop system emphasizes on selected frequencies and reduces the cost of feedback. It is shown that the proposed feedforward-feedback system is less conservative than the pure-feedback system. Other sources of vibration such as external disturbances and noise can be handled by the feedforward-feedback system as well. Simulation shows that the proposed technique can withstand large plant uncertainty with fast move time when compared to traditional robust input shaper.

Output Feedback Cooperative Control for Linear Uncertain Multi-Agent Systems With Nonidentical Relative Degrees

In this technical note, we present an output feedback control for the cooperative robust output regulation problem of a class of heterogeneous minimum phase linear uncertain multi-agent systems with the arbitrary large plant uncertainty and the arbitrary nonidentical relative degrees. To estimate the system state, we propose a novel distributed observer that contains two distinct parts, where the first part is of the distributed form to estimate the regulated error, while the second part is a modified version of the standard reduced-order high-gain observer by replacing the regulated error with its estimation given in the first part. Our design significantly extends some current literatures in that it strictly removes the assumption of the identical relative degree, and hence applies to a much larger class of linear multi-agent systems.

Experimental design of a fuzzy controller for improving power factor of boost rectifier

This article presents the design and the implementation of dSPACE DS1104 controller board-based PI and fuzzy logic peak current-mode controllers in the voltage loop and two controllers in the current loop based first on a standard fixed hysteresis band control, followed by a variable hysteresis band control to achieve constant switching frequency for a single-phase active power factor corrector in the continuous conduction mode. All these controllers have been verified via simulation in Simulink and a real-time implementation is performed on an experimental test bench utilising a rapid prototyping tool. The controllers are experimentally compared for steady-state performance and transient response. It is shown that the PI and fuzzy logic controllers give a superior steady-state performance, whereas the fuzzy logic inference based controller can achieve better dynamic response than its PI counterpart under large load disturbance and plant uncertainties. Furthermore, the variable hysteresis band control in the current loop gives a low total harmonic distortion of the input current compared to a standard fixed hysteresis band control.

On Transient Improvement of Variable Structure Controlled Systems Using Multimodel Switching 1

This paper presents a multiple model/controller scheme for robust tracking of a class of nonlinear systems in the presence of large plant uncertainties and disturbance. Each model is associated with a sliding mode controller, and a switching logic is designed to pick the model that best approximates the plant at each instant. Theoretically, it is shown that the proposed control scheme achieves perfect tracking despite the existence of disturbance, whereas simulation results verify the improvement in the transient performance.

Transient Improvement of Variable Structure Controlled Systems Via Multi-Model Switching Control

A solution is presented in this note to the problem of improving the transient response of a MIMO nonlinear system driven by a VSC law, in the presence of large plant uncertainties. The proposed control scheme is given in terms of a supervisor and of a deterministic time-varying compensator, built using sliding-mode control and assuming a finite number of possible different configurations. The task of the supervisor is that of guiding the scanning among the elements of the family, according to a suitably defined experimental test. The proposed approach noticeably improves the performances of sliding-mode control in the presence of large plant uncertainties, and has the substantial advantage of a great simplicity of design and implementation. Moreover, even in case of a large number of configurations constituting the stabilizing family, it has been shown to be able to attain the stabilizing controller in an arbitrarily small time interval. Another appealing feature of the paper consists in the inclusion of an intelligent adaptation scheme in the control algorithm.

Design of sampled-data systems with large plant uncertainty using quantitative feedback theory

This paper proposes a new quantitative feedback theory (QFT) design framework for dealing with sampled-data systems with large plant uncertainty. After the QFT-based design in the continuous-time domain is completed, the analogue controller can be transformed directly into a rational discrete-time transfer function via approximate Z transform, with the sampling time as a free parameter. The sampling time can therefore be adjusted to make the uncertain sampled-data system robustly stable. In comparison with other approaches, our approach is much more systematic without the solvability problem and yet significant enough to guide the designer to realize the physical controller in which the plant transfer function has prescribed bounds on its parameters. Several examples are used to illustrate the proposed approach and excellent results are obtained.

Multi-Model Switching Control of a Class of Nonlinear Systems Using Sliding Modes

The robust tracking problem for a family of nonlinear uncertain plants is considered. The solution presented is in terms of a deterministic time-varying compensator and of a supervisor. The compensator is based on sliding-mode control, and may assume a finite number of possible different configurations, among which there is at least one stabilizing the plant. The task of the supervisor is that of guiding the scanning among the elements of the family, according to a suitably defined experimental test, and of determining the switching instants. The proposed approach noticeably improves the performances of sliding-mode control in the presence of large plant uncertainties, which cannot be easily dealt with in practice. This paper extends results previously obtained with a narrower plant family. Another appealing feature of the paper consists in the inclusion of an intelligent adaptation scheme in the control algorithm. The idea is that of defining a suitable performance index, and to switch the time-varying controller to the configuration producing the minimum index at each time instant. The convergence of the algorithm has been proved.

Parametric model development and quantitative feedback design for automotive torque converter bypass clutch control

Customer demands for large high-performance vehicles in the face of increasingly stringent fuel economy targets have led automobile makers to seek innovative ways of meeting these requirements, especially in the North American market. One of the most critical elements in automotive powertrain systems is the torque converter bypass clutch which is now in almost universal use in automatic transmission-equipped vehicles. The clutch is used to bypass the fluid coupling of the torque converter during steady state conditions (i.e. highway cruise), thus eliminating a 15–20 percent loss of efficiency. Generally, the clutch is disengaged during dynamic events (e.g. vehicle launch, braking and gear changes) when the torque converter functionality is required. Further gains in fuel economy can now be realized through modulation of the bypass clutch in some situations where it had been considered necessary that the clutch be disengaged (i.e. during gear changes). In this case, the clutch is operated in a state of continuous slip; the transmitted torque is controlled through modulation of the clutch apply pressure. The dynamics of this system, however, exhibit considerable complexity. Characterization of this behaviour has been of considerable interest among automobile makers in recent years. However, investigation of the non-linear dynamics of this system is beyond the scope of this paper; a more in-depth treatment generally requires bifurcation analysis and/or exhaustive simulation studies. The focus in this paper is upon the detailed development of a linear parametric differential equation model and the design of a linear robust feedback control system. Parametric uncertainty is included to capture the effects of variations in system damping, bulk modulus, coefficient of friction and constants of linearization. Based upon a specific operating point, a linear robust controller is developed using the quantitative feedback theory (QFT) technique. The QFT methodology is aimed at designing feedback controllers so that pointwise frequency response specifications on closed-loop tracking and disturbance rejection are met in spite of large parametric plant uncertainty. The local stability and performance of the non-linear feedback system are subsequently verified by simulation. Since the feedback design is based upon a linear parametric model, no specific guarantees can be made as to the performance of the non-linear closed-loop system, although the results are found to be satisfactory in this case.

Adaptive Control: Towards a Complexity-Based General Theory

Two recent developments are pointing the way towards an input–output theory of H ∞− l 1 adaptive feedback: The solution of problems involving: (1) feedback performance exact optimization under large plant uncertainty on the one hand (the two-disc problem of H ∞); and (2) optimally fast identification in H ∞ on the other. Taken together, these are yielding adaptive algorithms for slowly varying data in H ∞− l 1. At a conceptual level, these results motivate a general input–output theory linking identification, adaptation, and control learning. In such a theory, the definition of adaptation is based on system performance under uncertainty, and is independent of internal structure, presence or absence of variable parameters, or even feedback.

Identification and adaptive control: Towards a complexity-based general theory

Two recent developments will be surveyed here which are pointing the way towards an input–output theory of H ∞- l 1 adaptive feedback: The solution of problems involving; (1) feedback performance (exact) optimization under large plant uncertainty on the one hand (the two-disc problem of H ∞); and (2) optimally fast identification in H ∞ on the other. Taken together, these are yielding adaptive algorithms for slowly varying data in H ∞- l 1. At a conceptual level, these results motivate a general input-output theory linking identification, adaptation, and control learning. In such a theory, the definition of adaptation is based on system performance under uncertainty, and is independent of internal structure, presence or absence of variable parameters, or even feedback.

Adaptive Control: Towards a Complexity-Based General Theory

Abstract Two recent developments are pointing the way towards an input-output theory of H - l adaptive feedback: The solution of problems involving; (1) feedback performance (exact) optimization under large plant uncertainty on the one hand (the two-disc problem of H ); and (2) optimally fast identification in H on the other. Taken together, these are yielding adaptive algorithms for slowly varying data in H - l At a conceptual level, these results motivate a general input-output theory linking identification, adaptation, and control learning. In such a theory, the definition of adaptation is based on system performance under uncertainty, and is independent of internal structure, presence or absence of variable parameters, or even feedback.

Numerically robust pole assignment for second-order systems

We propose two new methods for solution of the eigenvalue assignment problem associated with the second-order control system \global\hsize=30pc Specifically, the methods construct feedback matrices F 1 and F 2 such that the closed-loop quadratic pencil has a desired set of eigenvalues and the associated eigenvectors are well conditioned. Method 1 is a modification of the singular value decomposition-based method proposed by Juang and Maghami which is a second-order adaptation of the well-known robust eigenvalue assignment method by Kautsky et al. for first-order systems. Method 2 is an extension of the recent non-modal approach of Datta and Rincon for feedback stabilization of second-order systems. Robustness to numerical round-off errors is achieved by minimizing the condition numbers of the eigenvectors of the closed-loop second-order pencil. Control robustness to large plant uncertainty will not be explicitly considered in this paper. Numerical results for both the two methods are favourable. A compara...

Quantitative Feedback Design of Decentralized Control Systems

In the spirit of practical applicability, design transparency and quantitative specifications, this paper presents a new robust decentralized control design framework—model reference quantitative feedback design (MRQFD)—for multivariable control systems with large plant uncertainty and strong cross-coupling. The MRQFD method provides a connection between Rosenbrock’s Nyquist array and Horowitz’s quantitative feedback theory. There are two main stages in the MRQFD method. First, an internal model reference loop, based on non-negative matrix theory, is used to obtain robust generalized diagonal dominance and hence the reduction of uncertainty in the resultant compensated internal loop system. Then a single-loop quantitative feedback design scheme is applied to solve the resulting series of individual loops to guarantee the satisfaction of predefined MIMO quantitative specifications. The design procedure can be carried out either in the direct or in the inverse plant domains, as in Rosenbrock’s Nyquist array. The conditions of robust diagonal stabilization are also given for the MRQFD framework. The effectiveness of the MRQFD method and its ease of application are demonstrated by a 3 × 3 uncertain multivariable example.

Duality theory of robust disturbance attenuation

The nonstandard minimization problem inf QξH ∞ ‖ |W(1−PQ)|+|VPQ| ‖∞ underlies many questions of robust control. Here its solutions are characterized using Banach space duality theory, and shown to be allpass. The results are applied to the optimization of weighted sensitivity to disturbances, in feedback systems subject to large plant-uncertainty.

Technique of optimum design of control systems with large plant uncertainty

A modified technique for optimum design with significant plant uncertainty is presented using Wiener's least-square optimization with a quadratic constraint in the frequency domain. The plant uncertainty is transformed into an external disturbance and the procedures of the optimum design problem become much simpler. Examples are used to illustrate the design process. Computer simulations are performed to show that the designed results meet the specifications.

Synthesis of feedback control systems with large plant uncertainty and time-varying gain

A practical design method for feedback systems with large plant uncertainty and time-varying gain is presented. By combining quantitative feedback theory and the circle criterion, the design method assures the stability of the system and improves the performance of the system when the time-varying gain exists.

Expert adaptive control for drug delivery systems

The goal of this investigation is the development of an adaptive drug delivery system for use in regulation of critical care patients suffering from cardiac failure. It is assumed that adaptive control algorithms combined with expert system techniques are necessary to maintain stable patient statues within narrow physiological bounds in the presence of large plant uncertainty, and a hybrid controller is presented. Its structure is adjusted by an expert system that attempts to select the best control scheme in accordance with the dynamic structure of the plant. An illustrative example is presented, demonstrating the improved performance provided by the hybrid control scheme.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Optimal design of digital control systems with large plant uncertainty

In this paper, we extend a practical optimal-design procedure that has been presented in our previous work for single-loop digital control systems. The plant transfer function is given with prescribed bounds on its parameters, and a digital controller is to be designed so that the system response to a deterministic input is optimal and lies within permissible bounds. The w-plane method for the discrete design is used so that the design procedure to be presented is still based on frequency-domain concepts.

Guaranteed cost control of tracking problems with large plant uncertainty

ABSTRACT A linear tracking problem with large plant uncertainty is studied. The guaranteed cost method is applied to design the controller so that the system responses follow the reference model. A modified Riccati matrix equation is obtained. From the numerical simulation of a second-order system, it is shown that the present method provides good performance in both tracking property and sensitivity immunity.