Class Of Feedback Controllers Research Articles

Experimental validation off-line a nonlinear controller for removal of chromium using non-living cells of Yarrowia lipolytica

The removal of hexavalent chromium [Cr (VI)] using non-living cells of Yarrowia lipolytica was investigated. Batch and continuous studies on removal of Cr (VI) achieved 97% and 99% removal from aqueous phase, respectively. The specific uptake values at pH of 2 in batch process were 40.73 ± 1.3 mg/g and 30.09 ± 0.23 mg/g on non-living cells, when 100 and 200 mg/L of metal Cr (VI) concentrations were used. In order to investigate the regulation of Cr (VI) under continuous operation based on reaction volume numerically a new class of feedback controller from structure polynomial was designed. The proposed methodology was used to an experimentally kinetic model for a removal Cr (VI) from Yarrowia lipolytica biomass was showed satisfactory closed-loop performance the proposed controller. Starting from an off-line optimization performed in simulation, we present the controller implementation, focussing on the methodology required to could be suitable for implementation in real time. In our experimental results, we highlight some discrepancies between simulation and reality despite these differences, the controller managed to perform convergence to removal Cr (VI). Finally, the results validated with off-line samples suggest that the proposed control could be suitable for in application in potential scenarios for wastewater treatment.

Online optimization of LTI systems under persistent attacks: Stability, tracking, and robustness

We study the stability properties of a closed-loop system composed of a dynamical plant and a feedback controller, the latter generating control signals that can be compromised by a malicious attacker. We consider two classes of feedback controllers: a static output-feedback controller, and a dynamical gradient-flow controller that seeks to steer the output of the plant towards the solution of a convex optimization problem. In both cases, we analyze the stability properties of the closed-loop system under a class of switching attacks that persistently modify the control inputs generated by the controllers. Our stability analysis leverages the framework of hybrid dynamical systems, Lyapunov-based arguments for switching systems with unstable modes, and singular perturbation theory. Our results reveal that, under a suitable time-scale separation between plant and controllers, the stability of the interconnected system can be preserved when the attack occurs with “sufficiently low frequency” in any bounded time interval. We present simulation results in a power-grid example that corroborate the technical findings.

Optimization of data transmission over a stochastic channel with partially observed state

The optimization problem for data transmission over a stochastic channel is considered. The data transmission model is described by the triple “queue–channel–observations”. The queueing system is fed by a non-stationary Poisson stream of data packets for further transmission over a communication channel governed by a non-homogeneous Markov chain. The system is considered with a single server, finite bu er, and service rate proportional to the transmission rate with channel-dependent factor. The observations are formed by round-trip times of sent packets and described by the Markov counting process with channel-dependent intensity. The transmission rate is to be optimized within the class of feedback controls given two performance characteristics: the average number of lost packets and the mean level of energy consumption. The approach proposed for control optimization is based on the optimal filter equations, the complete-information control algorithm, and Monte Carlo techniques. The paper presents both theoretical and simulation results.

Solving a Local Boundary Value Problem for a Nonlinear Nonstationary System in the Class of Feedback Controls

An algorithm convenient for numerical implementation is proposed for constructing differentiable control functions that transfer a wide class of nonlinear nonstationary systems of ordinary differential equations from an initial state to a given point of the phase space. Constructive sufficient conditions imposed on the right-hand side of the controlled system are obtained under which this transfer is possible. The control of a robotic manipulator is considered, and its numerical simulation is performed.

Robustness analysis of locomotion controllers for mechanical rectifier systems in natural oscillation

A class of feedback controllers has been proposed to achieve a desired locomotion behaviour for mechanical rectifier systems in recent work. It is inspired by a biological neuron circuit called central pattern generator and is expected to exhibit robust and adaptive abilities against system parameter uncertainties and external disturbances. The controller was originally designed in an ideal situation that system parameters such as friction coefficients were precisely known, and measurement channels and actuation circuits were noiseless. In this study, the authors conduct specific robustness analysis for the locomotion controller with respect to system parameter variations and measurement and actuation noises. The numerical study shows that the locomotion controller is able to maintain a reasonable performance under these circumstances.

Adaptive Finite-Time Control for Attitude Tracking of Rigid Spacecraft

AbstractThis paper investigates the attitude tracking control problem for rigid spacecraft with inertia uncertainties and external perturbations. Spacecraft attitude dynamics and kinematics are initially converted into Lagrange-like model and formulated as a state-space form described by the modified Rodrigues parameters (MRPs). Robust controllers contain two parts and use geometric homogeneity, integral sliding mode (ISM) technique, and adaptive laws. One part proposes a class of feedback controllers to accomplish finite-time stabilization of the second order dynamics without the lumped uncertainties. The other part rejects bounded uncertainties based on ISM associated with adaptive laws. Moreover, a rigorous proof of finite-time convergence is developed. The proposed control laws provide finite-time convergence, robustness, and faster and higher control precision, and these algorithms require no information about inertia uncertainties and external disturbances, which cannot be obtained in practical syst...

Control of neutral delay linear systems using feedback with dynamic structure

To solve the problem of modal controllability of linear autonomous systems of neutral type, a new class of linear difference-differential controllers with feedback of dynamic structure is proposed. The construction principle of these controllers is based on the use of aftereffect in the control action. The domain of application of such controllers includes systems that do not possess the modal controllability property in the class of conventional classes of feedback controllers of constant structure.

On Bounded Strictly Positive Operators of Closed Range and Some Applications to Asymptotic Hyperstability of Dynamic Systems

The problem discussed is the stability of two input-output feedforward and feedback relations, under an integral-type constraint defining an admissible class of feedback controllers. Sufficiency-type conditions are given for the positive, bounded and of closed range feed-forward operator to be strictly positive and then boundedly invertible, with its existing inverse being also a strictly positive operator. The general formalism is first established and the linked to properties of some typical contractive and pseudocontractive mappings while some real-world applications and links of the above formalism to asymptotic hyperstability of dynamic systems are discussed later on.

Mean–variance portfolio selection based on a generalized BNS stochastic volatility model

We study a mean–variance portfolio selection problem via optimal feedback control based on a generalized Barndorff-Nielsen and Shephard stochastic volatility model, where an investor trades in a generalized Black–Scholes market. The random coefficients of the market are driven by non-Gaussian Ornstein–Uhlenbeck processes that are independent of the underlying multi-dimensional Brownian motion. Our contribution is to explicitly compute and justify optimal portfolios over an admissible set that is large enough to cover some important classes of strategies such as the class of feedback controls of Markov type. Concretely, the mean–variance efficient portfolios and efficient frontiers are explicitly calculated through the method of generalized linear-quadratic control and explicitly constructed solutions to three integro-partial differential equations under a quite mild condition that only requires one stock whose appreciation-rate process is different from the interest-rate process. Related minimum variance issue is also addressed via our main results.

Control of a Class of Sulfate Reducing Chemostat Via Feedback Polynomial Injection

The main goal of this work is to present a new class of feedback controller which contains on its structure a polynomial form of the named control error, the proposed controller is applied to a class of sulfate-reducing chemostat in order to control the sulfate concentration, which would be useful for several biotechnological issues, as heavy metal removal in wastewater. The closed-loop behavior of the chemostat is theoretically analyzed and a practical convergence to the selected optimum trajectory is proved. The proposed methodology is applied to an experimentally corroborated kinetic model of a sulfate-reducing bacterium and further numerical experiments show the satisfactory closed-loop performance of the process in comparison with other controllers.

Robot motion planning in the presence of program constraints

The paper presents a method of a motion planning and tracking for constrained robots. Specifically, we are interested in program constraints, by which robot tasks can be defined. The program constraint is an input to a kind of a motion planning system, which has been based on a generalized motion equation method suitable for systems with bilateral constraints of arbitrary orders. For the program motion planned by the motion planner a closed-loop program motion tracking using a class of feedback controllers has been designed. Global tracking conditions were developed for the case of nonlinear dynamics using a modification of the computed torque method.

An equivalence result in linear-quadratic theory

We consider the zero-endpoint infinite-horizon LQ problem. We show that the existence of an optimal policy in the class of feedback controls is a sufficient condition for the existence of a stabilizing solution to the algebraic Riccati equation. This result is shown without assuming positive definiteness of the state weighting matrix. The feedback formulation of the optimization problem is natural in the context of differential games and we provide a characterization of feedback Nash equilibria both in a deterministic and stochastic context.

Exponential stability of a class of nonlinear dynamical systems with uncertainties

Exponential stability for a class of nonlinear dynamical systems with uncertainties is investigated. Based on the stability of the nominal systems, a new approach to synthesizing a class of continuous state feedback controllers for uncertain nonlinear dynamical systems is proposed. By such a class of feedback controllers, we can guarantee exponential stability of uncertain nonlinear dynamical systems. Our approach can give a clear insight into system analysis. Finally, an illustrative example is given to demonstrate the utilization of the approach developed in this paper.

Performance enhancement of a solid particle heat exchanger using adaptive control

Two classes of feedback controllers, proportional-integral control and adaptive control, were applied to a counterflow solid particle heat exchange prototype. The primary objective was to optimize process start-up performance of the heat exchanger. The two most significant factors affecting the controllers were: (a) limited input control effort in terms of energy; and (b) deadtime of the process which was a function of the heat exchanger design. The adaptive controller, based on parameter estimation and a digital control law derived using controller synthesis, outperformed the conventional controller during start-up by as much as 11% with respect to a performance measure comprised of both error and energy components. Proper design and implementation of the adaptive controller was crucial for successful regulation.

Feedback stabilization of a marginally stable heat conduction problem

Semigroup methods are used to study a class of feedback controls for exponential stabilization of the (marginally stable) standard heat equation in a region with insulated boundary. An example shows that seemingly reasonable feedbacks may lead to instabilities if the gain factor is too large. We compute an upper bound for the gain factors in the stable range, and also state and support a conjecture corresponding to a case when the feedback elements have a restricted sign. Generalizations in various directions are discussed.

Tracking control of high-performance robots via stabilizing controllers for uncertain systems

The development of flexible manufacturing systems calls for industrial robots characterized by robustness of performance with regard to the variations of the loads and real time specification of the trajectory in the work space. In this paper, the design of a feedback controller guaranteeing such performance is considered. At first, the manipulator dynamics are embedded into a larger class of uncertain dynamical systems and a class of feedback controls is proposed that guarantees uniform ultimate boundedness of the tracking error. Successively, the methodology is specialized for the case of robotic manipulators to track trajectories described in task-oriented coordinates; the proposed control algorithm operates without requiring any explicit coordinate transformation.

Model-Following Controls for a Class of Uncertain Dynamical Systems

Abstract Robust nonlinear model-following controls are developed for a class of imperfectly known dynamical systems via an approach which does not require full identification of the uncertain elements. Based only on knowledge of functional properties and bounds relating to the uncertainty, a class of feedback controls is developed which, under an assumption of feasibility of the model, guarantees model following with error ultimately contained within any prescribed neighbourhood of zero error.

On the Use of Low-Order Riccati-Equations in the Design of a Class of Feedback Controllers and State Estimators

On the Use of Low-Order Riccati-Equations in the Design of a Class of Feedback Controllers and State Estimators