Robust Control Synthesis Research Articles

Sliding Mode Control of Crowd Dynamics

In this paper, the design of nonlinear sliding mode controllers for models representing crowd dynamics in one dimension is presented. The main contribution of this paper is the stability analysis and robust control synthesis of hyperbolic partial differential equation (PDE) system models using the sliding mode method. The application of this research is in crowd control and in dynamically controlling the evacuation of pedestrians in the presence of disturbances. Crowd densities can change due to blocked exits or due to a varying influx of people. Recent advances in sensor technology have made the measurement of pedestrian densities and velocities possible. As such, the development and implementation of efficient control algorithms to control crowd movements that can avoid jams is realizable. The crowd model presented here is a system of nonlinear hyperbolic PDEs based on the laws of conservation of mass and momentum. The sliding mode control is designed in the presence of both matched and unmatched uncertainties due to external disturbance and parametric variations. The controllers designed are shown to be robust to disturbances.

Admissibility analysis and control synthesis for descriptor systems with random abrupt changes

This article addresses the admissibility analysis and state-feedback robust control synthesis problem for a class of uncertain descriptor systems with time delays and Markovian jumping parameters. In particular, the delay factor is assumed to be time varying which belongs to a given interval and parameter uncertainties are assumed to be time-varying but norm bounded. By implementing linear matrix inequality optimization approach together with delay fractioning technique, a new set of delay dependent sufficient condition is derived which guarantees that the uncertain singular system to be regular, impulse-free and stochastically stable. Further, a static robust control design with an appropriate gain control matrix has been derived to achieve the robust stabilization for uncertain singular systems in the presence admissible parameter uncertainties and random abrupt changes. By considering the relationship among the time varying delay and its lower and upper bounds, a new set of sufficient conditions are established for the existence of state feedback control in terms of LMIs, which can be efficiently solved via MATLAB LMI toolbox. More precisely, when these LMIs are feasible, an expression of a desired static robust control will be determined. Further, numerical examples with simulation result are given to show that the obtained result significantly improve the allowable upper bounds of delays over some existing results.

Data-Driven Model Development for the SuperSonic SemiSpan Transport

We investigate two common approaches to model development for robust control synthesis in the aerospace community; namely, reduced-order aeroservoelastic modeling based on structural finite-element and computational-fluid-dynamics-based aerodynamic models and a data-driven system-identification procedure. It is shown via analysis of experimental SuperSonic SemiSpan Transport wind-tunnel data that, using a system-identification approach, it is possible to estimate a model at a fixed Mach number that is parsimonious and robust across varying dynamic pressures while the numerical reduced-order model offers significantly less predicative capability.

Robust static output feedback control synthesis for linear continuous systems with polytopic uncertainties

This paper studies the static output feedback (SOF) control problem of continuous-time linear systems with polytopic uncertainties. Novel LMI conditions with a line search over a scalar variable for designing robust SOF controllers are proposed, where the uncertain output matrix of the considered system is allowed to be not of full row rank. In particular, it is shown that the new method can give less or at least the same conservative results than those methods by inserting a matrix equality constraint between system output matrix and Lyapunov matrix. Furthermore, the result is extended to the case of H∞ control. Numerical examples are given to illustrate the effectiveness of the proposed method.

Synthesis of dynamic output feedback RMPC with saturated inputs

For polytopic uncertain systems with unmeasurable system states, a synthesis of output feedback robust model predictive control (OFRMPC) is proposed, which adopts a category of dynamic output feedback controller. In order to improve the utilization of the actuator capability, the saturation function is applied to the output of the dynamic output feedback controller. Based on it, the OFRMPC is proposed with an online update algorithm of the estimated error set. All the designs are verified to considerably improve the control performance. Meanwhile, a simplified design of OFRMPC is also developed to make the proposed design more practical.

A New Approach to Robust and Non-Fragile Control of Uncertain T-S Fuzzy Systems with Interval Time-Delay

This paper describes the synthesis of robust and non-fragile state feedback controllers for T-S fuzzy system with time-varying delay in a range and parameter uncertainties. A new method is proposed by de¯ning new Lyapunov functionals and introducing some free-weighting matrices. Impr oved delay-dependent results are presented.

Synthesis of fixed-structure robust controllers using a constrained particle swarm optimizer with cyclic neighborhood topology

The purpose of this paper is to develop design scheme based on an easy-to-use meta-heuristic approach with superior reliability and validity for fixed-structure robust controllers, satisfying both multiple control specifications and system stability conditions. For this purpose, a particle swarm optimizer is first developed, which reduces the probability of premature convergence to local optima in the PSO (particle swarm optimization) by exploiting the particle's local social learning based on the idea of cyclic-network topology. Next, it is shown how to obtain a fixed-structure robust controller with constraints on multiple H~ specifications and system stability based on the developed PSO technique incorporated with a simple constraint handling method. Finally, typical numerical examples are studied to show the applicability of the proposed methodology to the synthesis of fixed-structure robust controllers. These examples clearly verify that the developed design scheme gives a novel and powerful impetus with remarkable reliability to fixed-structure robust controller syntheses.

Switching Robust Control for Transparent and Stable Teleoperation

The inherent transparency-stability trade-off in bilateral teleoperation poses a challenge to design controllers that find a proper balance between both requirements. Furthermore, when the environment of the teleoperation system varies within a wide range, a single controller might no be sufficient to achieve both stability and transparency. Therefore, we propose the synthesis of a switching robust controller that guarantees both stability and transparency for a predefined range of environment stiffness. Moreover, we take into account during the design process the fact that environment estimators will have limited accuracy due to noise and uncertainty. Subsequently, we show the potential of the approach by numerical simulation of a 1-DOF teleoperated system.

Robust resilient controllers synthesis for uncertain fractional order large-scale interconnected system in the case of 1

The paper solves the problem of stabilization of large-scale fractional order interconnected system with a commensurate order 1 <α < 2 under controller gain perturbations. On the basis of the stability criterion of fractional order system, sufficient conditions on the decentralized stabilization of fractional order large-scale interconnected system with norm-bounded uncertainties are presented by applying a complex Lyapunov inequality. Furthermore, decentralized stabilization resilient controllers are designed. Numerical examples are used to illustrate the effectiveness of the proposed method.

Enhanced Linear Fractional Transformation: a Matlab Toolbox for Space System Modeling and Controller Analysis and Synthesis

Through an example of orbital rendezvous between a flexible spacecraft and a rigid target, this paper presents the Enhanced Linear Fractional Transformation Toolbox (ELFTT) developed under ESA contract in order to support advanced design, validation and verification processes of space system control loop. ELFTT will be distributed within the ESA Member States under an Open Source-like license. It is built on (and fully compatible with) Matlab Robust Control Toolbox RCT. It is dedicated to build, verify, manage Linear Fractional Transformations LFT specialized for space applications. On the one hand, it contains a library of generic LFT models relevant for space applications including typical uncertain actuators models (reaction wheels, thrusters.) uncertain dynamics models (flexible spacecraft, rendezvous dynamics.), uncertain sensors models (star trackers, gyrometer. ), etc. On the other hand, it implements new Matlab functions dedicated to manage the LFT models and to support robust controller synthesis and analysis.

Modern Attitude Control and Co-design for the Biomass Satellite (Earth Explorer Core Mission 7)

The purpose of this paper is to describe the current results and future activities of the European Space Agency (ESA) Robust AOCS technology program in support to the Biomass, Earth Explorer Core Mission 7. Due to the specificity of the chosen Biomass configuration this activity is driven by the expected interaction between the large flexible reflector antenna structure and its attitude control system. Currently ESA has developed a technology program to enable the capabilities of integrating the structural sizing and control system design in order to avoid interactions problems. The objective is the development of an Integrated Modeling, Control and Analysis framework IMCA: it incorporates uncertainty modeling via LFT's, robustness analysis via the Structured Singular Value μ and various robust control synthesis techniques such as H∞ and μ methods. This framework results as natural multivariable extensions of the classical Bode frequency domain techniques. It shall be integrated with a structural design loop into an unified computational framework to exploit control structures interactions in order to increase the spacecraft capabilities, such as better pointing stability, and to improve the overall design when compared to the traditional approach. Following the conclusion of the Phase A, the outcome of two parallel activities will be presented.

Demonstrating the Effectiveness of Noncausal LPTV Scaling through Control Experiments with Cart Inverted Pendulum

This paper aims at demonstrating the effectiveness of robust controller synthesis with discrete-time noncausal linear periodically time-varying scaling, through control experiments with a cart inverted pendulum whose pendulum length can be set from three different values. We regard the difference in the pendulum length as the uncertainty, construct a generalized plant suitable for our synthesis problem, and design a single LPTV robust performance controller independent of the pendulum length. The control experiments confirm a theoretical advantage of increasing the period of the controller and demonstrate the effectiveness of the noncausal LPTV scaling technique.

Robust control with finite frequency specification for uncertain discrete linear repetitive processes

This paper is dedicated to the study of robust stability and controller synthesis for discrete linear repetitive processes with polytopic uncertainty. In the robust control domain, conditions based on parameter dependent Lyapunov functions are proposed in order to reduce the conservatism related to uncertainty problems. The solution is a class of Lyapunov functions that depends in a polytopic way on the uncertain parameters and that can be derived from linear matrix inequality conditions. Nevertheless, in many cases in practice, the frequency range of reference signals, noises and disturbances are known beforehand. Therefore, performing controller synthesis in the full frequency range is not practically suited and may introduce conservatism to some extent. Based on generalized Kalman–Yakubovich–Popov Lemma, a finite frequency controller is derived for uncertain discrete linear repetitive processes which are the most investigated class of 2D systems. Hence, the designer can specify a frequency range where the prescribed control performance is required, where, for example, this range could be determined by inspection of frequency spectrums of the available signals.

Synthesis of robust PID controllers with complete information on pre-specifications for the FOPTD systems

Given a first order plus time delay (FOPTD) model, all stabilizing PID controllers can be found in terms of a 3D plot of three gains. Given specifications such as gain crossover frequency and phase margin, the three PID gains are not unique. To make three gains unique, this paper adds an additional specification called “flat phase” condition, that is, the phase slope at the gain crossover frequency is zero, guaranteeing robustness to loop gain variations. This paper offers an analytical synthesis method for obtaining unique PID gains. Furthermore, a procedure is suggested to find out all feasible specifications. With a scaling idea, the FOPTD model can be reduced to having only one plant parameter (delay to time constant ratio), therefore, a lookup table can be constructed for practical design scenario: given the delay to time constant ratio, the feasible ranges of specifications can be determined; given (feasible) specifications, unique PID parameters can be retrieved from the table, with “flat phase” property embedded. This paper serves as an example to completely solve the robust PID synthesis problem for FOPTD models widely used in process industry.

Toroidal current profile control during low confinement mode plasma discharges in DIII-D via first-principles-driven model-based robust control synthesis

In order for ITER to be capable of operating in advanced tokamak operating regimes, characterized by a high fusion gain, good plasma confinement, magnetohydrodynamic stability and a non-inductively driven plasma current, for extended periods of time, several challenging plasma control problems still need to be solved. Setting up a suitable toroidal current density profile in the tokamak is key for one possible advanced operating scenario characterized by non-inductive sustainment of the plasma current. At the DIII-D tokamak, the goal is to create the desired current profile during the ramp-up and early flat-top phases of the plasma discharge and then actively maintain this target profile for the remainder of the discharge. The evolution in time of the toroidal current profile in tokamaks is related to the evolution of the poloidal magnetic flux profile, which is modelled in normalized cylindrical coordinates using a first-principles, nonlinear, dynamic partial differential equation (PDE) referred to as the magnetic diffusion equation. The magnetic diffusion equation is combined with empirical correlations developed from physical observations and experimental data from DIII-D for the electron temperature, the plasma resistivity and the non-inductive current drive to develop a simplified, control-oriented, nonlinear, dynamic PDE model of the poloidal flux profile evolution valid for low confinement mode discharges. In this work, we synthesize a robust feedback controller to reject disturbances and track a desired reference trajectory of the poloidal magnetic flux gradient profile by employing the control-oriented model of the system. A singular value decomposition of the static gain matrix of the plant model is utilized to identify the most relevant control channels and is combined with the dynamic response of system around a given operating trajectory to design the feedback controller. A general framework for real-time feedforward + feedback control of magnetic and kinetic plasma profiles was implemented in the DIII-D Plasma Control System and was used to demonstrate the ability of the feedback controller to control the toroidal current profile evolution in the DIII-D tokamak. These experiments constitute the first time ever a first-principles-driven, model-based, closed-loop magnetic profile controller was successfully implemented and tested in a tokamak device.

Optimal State-Feedback Control of Bilinear DC–DC Converters With Guaranteed Regions of Stability

This paper deals with the modeling and the robust controller synthesis for nonlinear dc-dc converters. In the first part of this paper, a model for the bilinear dynamics is presented. Such nonlinear dynamics can be included in a convex polytope such that the trajectories of the converter out of the equilibrium are assured to remain inside a guaranteed region of stability despite of the bilinear term. Such a description of the dynamic response of the converter is employed, in the second part of this paper, to propose synthesis algorithms that can guarantee, a priori, the stability and performance requirements of the design. The resulting region of stability can take into account not only the bilinear terms but also the saturation of the control input, which is a topic of major importance in high-performance dc-dc converters. The aim of this paper is to contribute with a robust control framework which allows the designers to deal with the common requirements of regulated dc-dc converters. The correctness of the results has been verified both with numerical simulations and experimental measurements from dc-dc converter prototypes.

Dynamics and robust control of underwater vehicles for depth trajectory following

This paper addresses the robust control synthesis of diving/climbing manoeuvres for underwater vehicle in the vertical plane. First, a new state–space representation for the vehicle dynamics is presented, and the corresponding problem formulation is clearly stated. Next, the two-controller set-up using a H∞-loop shaping design is employed to deal with the bottom following capability and robustness issues. Then the reduced order control system with a Hankel norm is evaluated in the frequency domain. In addition, the preview control approach is used to improve the overall tracking performance for undersea manoeuvres. The specific control tasks include the tracking of a set of depth profiles or ocean floors. Simulation results show that control objectives are effectively accomplished in spite of model uncertainties. Finally, it is found that the proposed control methodology is suitable for the depth trajectory following applications over a wide range of operating conditions.

Stabilizing and robust fractional order PI controller synthesis for first order plus time delay systems

For all the stable first order plus time delay (FOPTD) systems, a fractional order proportional integral (FOPI) or a traditional integer order proportional integral derivative (IOPID) controller can be designed to fulfill a flat phase constraint and two design specifications simultaneously: gain crossover frequency and phase margin. In this paper, a guideline for choosing two feasible or achievable specifications, and a new FOPI/IOPID controller synthesis are proposed for all the stable FOPTD systems. Using this synthesis scheme, the complete feasible region of two specifications can be obtained and visualized in the plane. With this region as the prior knowledge, all combinations of two specifications can be verified before the controller design. Especially, it is interesting to compare the areas of these two feasible regions for the IOPID and FOPI controllers. This area comparison reveals, for the first time, the potential advantages of one controller over the other in terms of achievable performances. A simulation illustration is presented to show the effectiveness and the performance of the designed FOPI controller compared with the optimized integer order PI controller and the IOPID controller designed following the same synthesis for the FOPI in this paper.

System identification for achieving robust performance

The performance of robust controllers hinges on the underlying model set. The aim of the present paper is to develop a system identification procedure that enables the design of a controller that achieves optimal robust performance. Hereto, the complex interrelation between system identification and robust control is thoroughly analyzed and novel connections are established between (i) control-relevant and coprime factor identification and (ii) model uncertainty size and the control criterion. The key technical results include new robust-control-relevant and (Wu,Wy)-normalized coprime factorizations. The results enable the identification of multivariable model sets that achieve high robust performance in a subsequent robust control synthesis. Superiority of the proposed results compared to existing approaches is shown by means of an example.

Selecting Uncertainty Structures in Identification for Robust Control with an Automotive Application

The selection of uncertainty structures is an important aspect in system identification for robust control. The aim of this paper is to investigate the consequences for multivariable systems. Hereto, first a theoretical analysis is performed that establishes the connection between the associated model set and the robust control criterion. Second, an experimental case study for an automotive application confirms these connections. In addition, the experimental results provide new insights in the shape of associated model sets by using a novel validation procedure. Finally, the improved connections are confirmed through a robust controller synthesis. Both the theoretical and experimental results confirm that a recently developed robust-control-relevant uncertainty structure outperforms general dual-Youla-Kučera uncertainty, which in turn outperforms traditional uncertainty structures, including additive uncertainty.