Linear feedback control with prespecified performance measure

The stabilization problem of linear time-varying uncertain delay systems by means of linear constant memoryless state feedback control is investigated here. In the case when uncertain parameters may vary independently in arbitrarily large bounding sets, the locations of uncertain elements in the system parameters play an important role. So far obtained conditions of this problem have been found to have a particular geometric configuration with respect to the permissible locations of uncertain elements. In this paper, such a previously obtained configuration is developed to a basic form of antisymmetric stepwise configuration which is a necessary and sufficient condition for time-varying uncertain systems without delays to be quadratically stabilizable by means of linear constant state feedback control. It is shown that if a given system satisfies such developed conditions then the system is stabilizable via linear constant state feedback control with regardless to the upper bounds of time-varying uncertain parameters and time-varying delays

This paper concerns the problems of robust stability analysis and stabilization for uncertain linear system with time-varying delay. In order to obtain a robust stability criterion with less conservative for uncertain linear delay system, a quadratic integral inequality is improved by matrix decomposition. Further, two different kinds of controller, i.e., linear memoryless state feedback controller and linear state feedback controller with state delay, are derived in terms of the robust stability criteria. Two numeral examples are provided to demonstrate the validity of the proposed methods.

Objective: This paper implies a comparison between sliding mode control and linear state feedback controller. When the linear systems are given bounded disturbance their robustness properties are studied. Method: Pole placement, classical sliding mode control using constant rate reaching law and constant plus proportional rate reaching law, super-twisting controller. Findings: Finite time asymptotic convergence is not achieved in linear feedback controller, Sliding Mode Control when used produced finite time asymptotic convergence. The measure of the control variable is obtained by taking norm of the control input. Applications: Process Control, Aerodynamics.

This article describes the design of a linear observer–linear controller-based robust output feedback scheme for output reference trajectory tracking tasks in the case of nonlinear, multivariable, nonholonomic underactuated mobile manipulators. The proposed linear feedback scheme is based on the use of a classical linear feedback controller and suitably extended, high-gain, linear Generalized Proportional Integral (GPI) observers, thus aiding the linear feedback controllers to provide an accurate simultaneous estimation of each flat output associated phase variables and of the exogenous and perturbation inputs. This information is used in the proposed feedback controller in (a) approximate, yet close, cancelations, as lumped unstructured time-varying terms, of the influence of the highly coupled nonlinearities, and (b) the devising of proper linear output feedback control laws based on the approximate estimates of the string of phase variables associated with the flat outputs simultaneously provided by the disturbance observers. Simulations reveal the effectiveness of the proposed approach.

ABSTRACTThe regional robust stabilisation by means of linear time-invariant state feedback control for a class of uncertain MIMO nonlinear systems with parametric uncertainties and control input saturation is investigated. The nonlinear systems are described in a differential algebraic representation and the regional stability is handled considering the largest ellipsoidal domain-of-attraction (DOA) inside a given polytopic region in the state space. A novel set of sufficient Linear Matrix Inequality (LMI) conditions with new auxiliary decision variables are developed aiming to design less conservative linear state feedback controllers with corresponding larger DOAs, by considering the polytopic description of the saturated inputs. A few examples are presented showing favourable comparisons with recently published similar control design methodologies.

The (multi-player) linear quadratic state feedback control problem for index one descriptor systems

Gain-scheduled Composite Non linear Feedback (CNF) control has been implemented to Continuous Stirred Tank Reactor (CSTR) in this work. Chemical reaction takes place inside the CSTR, which is adjured from high residual concentration to low residual concentration. Control of CSTR is a bit complex, as it requires complete dynamic study and its implementation. During the entire process, the reaction kinetics changes from stable-unstable-stable range with the decrease in residual concentration. To stabilize the reaction, appropriate cooling is necessary, to ensure that overheating of the CSTR doesn't occur. Gain-scheduled composite non linear feedback controller has been implemented successfully for better tracking performance and error has been computed in terms of Integral of Absolute Error (IAE). The novelty of the work lies in lesser error obtained for this particular model of CSTR. Comparison of the IAE has been done with Model Reference Adaptive Control (MRAC) MIT control in CSTR.

The designs of two linear control systems approach to stabilize the balance of an unmanned bicycle system are presented. Both approaches are based on the use of a reaction wheel or flywheel to balance the bicycle. The two linear control approaches, based on the linearization of a nonlinear model obtained using Lagrange formalism, are the classic linear controllers, PID and State Feedback control. The performance of both controllers is verified by digital simulation and real-time experimental results.

This paper addresses the problem of designing low-order and linear robust feedback controllers that providea prioriguarantees with respect to stability and performance when applied to a fluid flow. This is challenging, since whilst many flows are governed by a set of nonlinear, partial differential–algebraic equations (the Navier–Stokes equations), the majority of established control system design assumes models of much greater simplicity, in that they are: firstly, linear; secondly, described by ordinary differential equations (ODEs); and thirdly, finite-dimensional. With this in mind, we present a set of techniques that enables the disparity between such models and the underlying flow system to be quantified in a fashion that informs the subsequent design of feedback flow controllers, specifically those based on the$\mathscr{H}_{\infty }$loop-shaping approach. Highlights include the application of a model refinement technique as a means of obtaining low-order models with an associated bound that quantifies the closed-loop degradation incurred by using such finite-dimensional approximations of the underlying flow. In addition, we demonstrate how the influence of the nonlinearity of the flow can be attenuated by a linear feedback controller that employs high loop gain over a select frequency range, and offer an explanation for this in terms of Landahl’s theory of sheared turbulence. To illustrate the application of these techniques, an$\mathscr{H}_{\infty }$loop-shaping controller is designed and applied to the problem of reducing perturbation wall shear stress in plane channel flow. Direct numerical simulation (DNS) results demonstrate robust attenuation of the perturbation shear stresses across a wide range of Reynolds numbers with a single linear controller.

Recently, magnetic telemanipulation devices have shown a great deal of promise in such areas as semi-conductor manufacturing, wind tunnels, drug delivery, and many more. However, these devices are generally associated with problems caused by payload variation and uncertainties in the parameters of the system which in turn, have limited the development and application of magnetic telemanipulation technology to its full capacity. This paper addresses and deals with these issues by implementation of a precise position control method for a magnetic telemanipulation system with high level of uncertainties in its parameters. The levitation system used in this study is primarily designed for performing remote pick and place operations. The levitated object is a 28 gr microrobot capable of grasping and releasing payloads as heavy as 8 gr. To cope with the uncertainties in the modeling and payload variation, a model reference adaptive feedback linearization (MRAFL) controller is designed and its performance compared with an ordinary feedback linearization (FL) controller. Through experimental results it is shown that the MRAFL controller enables the microrobot to grasp and transport a payload as heavy as 30% of its own weight without a considerable effect on its positioning accuracy. In the presence of the payload, the MRAFL controller resulted in a RMS positioning error of 8 μm} compared with 27.9 μm} of the FL controller. The approach presented in this work is versatile as it leads to the modeling and control of a highly nonlinear system through a modular approach that can be applied to a variety of magnetic levitation and telemanipulation systems.

Periodic stabilizability of switched linear control systems

In this paper a new linear state feedback controller for artificial pancreas is proposed to regulate the blood glucose level in diabetic patients. Diabetes mellitus is a family of chronic metabolic diseases in which body's blood glucose regulatory system doesn't function properly. In this study, Bergman's minimal model has been used as a base model, to reformulate dynamics of insulin and glucose concentrations in blood's plasma as a constrained polynomial dynamical system. Since it is hard to derive exact value of parameters in most biological systems, all parameters of the model has been considered uncertain and therefore parametric uncertainty has been exploited in control design. Based on sum of squares technique, a linear state feedback controller has been obtained to regulate the blood's insulin and glucose concentration levels around the basal levels. Main achievements of this paper are simplicity of controller structure which makes it easy to implement, parametric uncertainty to cover more patients and patient-nonspecific design, and employment of nonlinear techniques without any simplifications.

This paper presents a novel observer-based controller design method for discrete-time piecewise affine (PWA) systems. The basic idea is as follows: at first, a piecewise linear (without affine terms) state feedback controller and a PWA observer are designed separately, and then it is proved that the output feedback controller constructed by the resulting observer and state feedback controller gains can guarantee the stability of the closed-loop system. During the controller design, the piecewise-quadratic Lyapunov function technique is used. Moreover, the region information is taken into account to treat the affine terms, so the controller gains can be obtained by solving a set of linear matrix inequalities, which are numerically feasible with commercially available software. Three simulation examples are given finally to verify the proposed theoretical results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

This paper focuses on the problem of quadratic dissipative control for linear systems with or without uncertainty. We consider the design of feedback controllers to achieve (robust) asymptotic stability and strict quadratic dissipativeness. Both linear static state feedback and dynamic output feedback controllers are considered. First, the equivalence between strict quadratic dissipativeness of linear systems and a H performance is established. Necessary and sufficient conditions for the solution of the quadratic dissipative control problem are then obtained using a linear matrix inequality (LMI) approach. As for uncertain systems, we consider structured uncertainty characterized by a dissipative system. This uncertainty description is quite general and contains commonly used types of uncertainty, such as norm-bounded and positive real uncertainties, as special cases. It is shown that the robust dissipative control problem can be solved in terms of a scaled quadratic dissipative control problem without uncertainty. LMIbased methods for designing robust dissipative controllers are also derived. The results of this paper unify existing results on H and positive real control and provide a more flexible and less conservative robust control design as it allows for a better trade-off between phase and gain performances.

In this paper, the control of chaos with a single controller, which provides simplicity in implementation, is investigated in continuous time nonlinear Rucklidge system. For this purpose, a linear feedback controller and a passive controller are constructed and added to the Rucklidge chaotic system. Lyapunov function is used to realize that the controller ensures the global asymptotic stability of the system. Owing to the controller, Rucklidge chaotic system can be regulated to its equilibrium points. Numerical simulations of the proposed methods and local relay control method have been demonstrated, compared and discussed.