Properties Of Closed-loop System Research Articles

Robustness and averaging properties of a large-amplitude, high-frequency extremum seeking control scheme

We investigate robustness and averaging properties of an extremum seeking scheme which employs oscillatory dither signals with sufficiently large amplitudes and frequencies. Our study takes both input and output disturbances into account. We consider general L∞-disturbances, which may correlate with the oscillatory dither signals. A suitable change of variables followed by an averaging procedure reveals that the closed-loop system approximates the behavior of an averaged system. The disturbances in the averaged system are directly linked to the disturbances in the closed-loop system. This allows us to conclude stability and robustness properties of closed-loop system from respective properties of the averaged system. In particular, we show that, if the averaged system tolerates L∞-disturbances of a certain magnitude, then the same is true for the approximating closed-loop system. Another feature of the proposed method is that it steers the closed-loop system approximately into descent directions of an averaged objective function. This property can be beneficial for the purpose of global optimization because an averaged objective function is expected to have fewer undesired critical points than the original objective function.

How Training Data Impacts Performance in Learning-Based Control

When first principle models cannot be derived due to the complexity of the real system, data-driven methods allow us to build models from system observations. As these models are employed in learning-based control, the quality of the data plays a crucial role for the performance of the resulting control law. Nevertheless, there hardly exist measures for assessing training data sets, and the impact of the spatial distribution of the data on the closed-loop system properties is largely unknown. This letter derives - based on Gaussian process models - an analytical relationship between the density of the training data and the control performance. We formulate a quality measure for the data set, which we refer to as ρ-gap, and derive the ultimate bound for the tracking error under consideration of the model uncertainty. We show how the ρ-gap can be applied to a feedback linearizing control law and provide numerical illustrations for our approach.

Optimal tuning of fractional-order controllers based on Fibonacci-search method

This paper presents a new optimization-based tuning method for fractional- and integer-order controllers. The method is based on minimizing an arbitrary cost function which is taken here as the integrated absolute tracking error, and it can be used for tuning purposes as well as the assessment of controller performance. The presented results are obtained from experiments with a servo drive system with a 2- and 3-parameter fractional-order controller. They depict performance improvement and ability of the proposed method to find the global minimum of a selected performance index in experimental conditions. The method does not need any model of the plant, and it has great potential for applications in general controllers or for an extension to different parameter tuning problems. The method offers a new way of changing dynamic properties of closed-loop systems, by rapid tuning of controllers. This makes possible new applications of this method, as opposed to other tuning methods, which basically require knowledge of the plant.

Robust PID controller design with H2 performance: Descriptor systems approach

Abstract The paper deals with the problem to obtain robust PID controller design procedure to linear time invariant descriptor uncertain polytopic systems using descriptor system stability theory and H 2 criterion approach in the form of quadratic cost function. In the frame of Lyapunov function, H 2 quadratic cost function and Bellman-Lyapunov equation the obtained designed novel procedure guarantees the robust properties of closed-loop system with parameter dependent quadratic stability/quadratic stability. In the obtained design procedure, the designer could use controller with different structure like as P, PI, PID, PI-D. For PI-D controllers D-part feedback the designer could choose any available output/state derivative variables of real systems. The effectiveness of the obtained results is demonstrated on the randomly generated examples.

Verifying fragility in digital systems with uncertainties using DSVerifier v2.0

Control-system robustness verification with respect to implementation aspects lacks automated verification approaches for checking stability and performance of uncertain control systems, when considering finite word-length (FWL) effects. Here we describe and evaluate novel verification procedures for digital systems with uncertainties, based on software model checking and satisfiability modulo theories, named as DSVerifier v2.0, which is able to check robust stability of closed-loop control systems with respect to FWL effects. In particular, we describe our verification algorithms to check for limit-cycle oscillations (LCOs), output quantization error, and robust non-fragile stability on common closed-loop associations of digital control systems (i.e., series and feedback). DSVerifier v2.0 model checks new properties of closed-loop systems (e.g., LCO), including stability and output quantization error for uncertain plant models, and considers unknown parameters and FWL effects. Experimental results over a large set of benchmarks show that 35%, 34%, and 41% of success can be reached for stability, LCO, and output quantization error verification procedures, respectively, for a set of 396 closed-loop control system implementations and realizations.

Fractional PID controller design for nonlinear systems based on singular perturbation technique

This paper deals with the output regulation of nonlinear control systems in order to guarantee desired performances in the presence of plant parameters variations and external disturbances. The proposed control law structures are based on the fractional order PI (FOPI) and PID (FOPID) control schemes. By introducing the two-time-scale notions in the closed-loop system, the presented design methodology of fractional PID control guarantees desired transients. Then, the singular perturbations technique is used to analyse the closed-loop system properties and to get explicit expressions for evaluation of the controller parameters. The tuning of the controller parameters is based on a constrained optimisation algorithm. Simulation examples are presented to show the effectiveness of the proposed method.

Missile autopilot design based on robust LPV control

This paper proposes an effective algorithm to work out the linear parameter-varying (LPV) framework autopilot for the air defense missile so as to simultaneously guarantee the closed-loop system properties globally and locally, which evidently reduces the number of unknown variables and hence increases the computational efficiency. The notion of quadratic is inducted to meet the global properties, including the robust stability and robust performance, while the regional pole placement scheme together with the adoption of a model matching structure is involved to satisfy the dynamic performance, including limiting the fast poles. In order to reduce the conservatism, the full block multiplier is employed to depict the properties, with all specifications generalized in integral quadratic constraint frame and finally transformed into linear matrix inequalities for tractable solutions through convex optimization. Simulation results validate the performance of the designed robust LPV autopilot and the proposed framework control method integrating with the full block multiplier approach and the regional pole placement scheme, and demonstrate the efficiency of the algorithm. An efficient algorithm for the air defense missile is proposed to satisfy the required global stability and local dynamical properties by a varying controller according to the flight conditions, and shows sufficient promise in the computational efficiency and the real-time performance of the missile-borne computer system.

Robust economic model predictive control of a community micro-grid

In this paper we propose a novel economic robust predictive controller for periodic operation. The proposed controller joins dynamic and economic trajectory planning and robust predictive controller for tracking in a single layer taking into account bounded disturbances, algebraic constraints and periodic operation. We study the closed-loop system properties of the proposed controller and provide a design procedure that guarantees that the perturbed closed-loop system converges asymptotically to the optimal economic reachable periodic trajectory, constraint satisfaction and recursive feasibility. The proposed controller has been applied to control a cluster of interconnected micro-grids. Each nano-grid is connected to an electric utility and has a renewable energy source, a cluster of batteries and a metal hydride based hydrogen storage system. The cluster must satisfy a periodic energy demand while maximizing the profit of the energy sold to the electric utility taking into account time varying prices.

Output Regulation of Pulse-Width-Modulated Nonlinear Nonaffine-in-Control Systems via Singular Perturbation

AbstractThis paper addresses the problem of output regulation for nonlinear nonaffine-in-control systems in the presence of a high-frequency pulse-width modulation (PWM) in feedback loop. The problem of controller design is reduced to the continuous-time controller design based on Filippov's average model which is affine-in-control system. The proposed controller is an extension of PI/PID control scheme. The presented design methodology guarantees desired output transient performance indices by inducing of two-time-scale motions in the closed-loop system. The analysis of the closed-loop system properties is provided via the singular perturbation method. Stability conditions imposed on the fast and slow modes and sufficiently large mode separation rate between fast and slow modes can ensure that the full-order closed-loop nonlinear system achieves the desired properties in such a way that the output transient performances are desired and insensitive to external disturbances and plant's parameter variations. Numerical example and simulation results are presented.

Output Regulation of Uncertain Nonaffine in Control Systems via Singular Perturbation Technique

The problem of output regulation for nonlinear control systems with guaranteed transient performances in the presence of uncertainties is discussed, where the nonlinear systems are nonaffine in the control. The fast dynamical controller with the highest output derivative in feedback loop is used, where the controller is proper and can be implemented without ideal differentiation. Two-time-scale motions are induced in the closed-loop system and the method of singular perturbations is used to analyze the closed-loop system properties. Stability conditions imposed on the fast and slow modes and sufficiently large mode separation rate can ensure that the full-order closed-loop system achieves the desired properties in such a way that the output transient performances are desired and insensitive to external disturbances and variations of nonlinear system parameters. The problem of absolute stability analysis of the fast-motion subsystem for nonaffine systems with two-time-scale motions is considered in the presence of a sector-like condition in the control.

Direct Torque Tracking PI-Controller Design for Switched Reluctance Motor Drive using Singular Perturbation Method

The problem of torque tracking PI-controller design for switched reluctance motor (SRM) drive is discussed, where SRM magnetization characteristics are highly nonlinear, and torque is a complex and coupled function of phase current and rotor position. A distinctive feature of the control system designed is that two-time-scale motions are artificially forced in the closed-loop system by the selection of control law parameters. Hence, singular perturbation method is used to analyze the closed-loop system properties. Stability conditions imposed on the fast and slow modes, and a sufficiently large mode separation rate, can ensure that after fast ending of the fast-motion transients, the torque tracking error dynamics are as desired by the control system design specifications and they are insensitive to SRM nonlinearities. An accurate polynomial model of a prototype SRM magnetization characteristics is used for simulation studies of the proposed controller. However, only a simple trapezoidal profile for SRM inductance is used for calculation of the control voltage. Simulation results for constant motor torque at different speeds show that motor peak-to-peak torque ripples are minimized to about 5% of the average torque, especially for low speed operation.

Robust nonlinear output feedback control for brake by wire control systems

This work proposes a nonlinear output feedback control law for active braking control systems. The control law guarantees bounded control action and can cope also with input constraints. Moreover, the closed-loop system properties are such that the control algorithm allows to detect—without the need of a friction estimator—if the closed-loop system is operating in the unstable region of the friction curve, thereby allowing to enhance both braking performance and safety. The design is performed via Lyapunov-based methods and its effectiveness is assessed via simulations on a multibody vehicle simulator.

Anti-windup synthesis via sampled-data piecewise affine optimal control

Discrete-time receding horizon optimal control is employed in model-based anti-windup augmentation. The optimal control formulation enables designs that minimize the mismatch between the unconstrained closed-loop response with a given controller and the constrained closed-loop response with anti-windup augmentation. Recently developed techniques for off-line computation of the constrained linear regulator's solution, which is piecewise affine, facilitate implementation. The resulting sampled-data, anti-windup closed-loop system's properties are established and its performance is demonstrated on a simulation example.

An LQR/LQG theory for systems with saturating actuators

An extension of the LQR/LQG methodology to systems with saturating actuators, referred to as SLQR/SLQG, where S stands for saturating, is obtained. The development is based on the method of stochastic linearization, whereby the saturation is replaced by a gain, calculated as a function of the variance of the signal at its input. Using the stochastically linearized system and the Lagrange multiplier technique, solutions of the SLQR/SLQG problems are derived. These solutions are given by standard Riccati and Lyapunov equations coupled with two transcendental equations, which characterize both the variance of the signal at the saturation input and the Lagrange multiplier associated with the constrained minimization problem. It is shown that, under standard stabilizability and detectability conditions, these equations have a unique solution, which can be found by a simple bisection algorithm. When the level of saturation tends to infinity, these equations reduce to their standard LQR/LQG counterparts. In addition, the paper investigates the properties of closed-loop systems with SLQR/SLQG controllers and saturating actuators. In this regard, it is shown that SLQR/SLQG controllers ensure semi-global stability by appropriate choice of a parameter in the performance criterion. Finally, the paper illustrates the techniques developed by a ship roll damping problem.

Digital controller design — Alternative emulation approaches

The emulation approach to digital controller design involves two steps: (1) the design of a continuous controller to satisfy performance and robustness objectives, and (2) the conversion of the continuous controller into a digital controller with the objective of obtaining comparable closed-loop system properties. This paper addresses the second step of the emulation approach. Previously developed methods are discussed, and several new methods are shown to be effective in accounting for computational delay and for sample-and-hold delay in closed-loop control applications. When the step response of the digitally controlled system is required to be closed to that of the corresponding continuous system, the selection of the sampling period T and the emulation performance are related in a fundamental way. This is illustrated in a closed-loop example.

Robust control for servo-mechanisms under inexact friction compensation

Uncertainties in the parameters but also in the structure of the friction model may lead to inexact friction compensation in servo-mechanisms. This will lead to differences between the predicted friction and the real friction forces, provoking, in certain cases (overcompensation) an oscillatory behaviour. This paper proposes a new control scheme seeking to strengthen the closed-loop system properties in the eventuality of friction overcompensation. This control design has the advantage that, in the case of friction overcompensation, the oscillations can be reduced in amplitude and modified in frequency independently of the closed-loop system specifications.

The relation between open-loop and closed-loop properties of multivariable feedback systems

Certain rules of thumb relating open- and closed-loop system properties played an important role in classical design. Examples are loop gain implies disturbance response and small loop gain implies noise response. These rules have previously been generalized to multivariable systems only in special cases. The purpose of this paper is to obtain rules of thumb for systems possessing both large and gain in different directions at the same frequency. The effect of coupling between high and low gain loops is discussed and generalizations of gain crossover frequency are obtained. The results are illustrated with an example.