Feedback Controller and Observer Design to Maximize Stability Radius

International audience

Circle Condition-Based Robust Feedback Control Against Plant Perturbation

The dynamics of a web transport system are coupled and interactive among spans of web and rolls/rollers. As the process speed or variation of the speed is high, system friction and inertia of rotation of rolls could cause problems in implementation of observer techniques for tension estimation and control. In the author's previous study (see IEEE International Conference on Industrial Electronics, Control and Instrumentation, Denver, Colorado, USA (2001)), an observer-based tension feedback controller with friction and inertia compensation was proposed. However, the gains of observer and controller were determined based on the trial-and-error approach. This paper continues the author's previous study and presents an analytical approach for the gain design of observers in the time domain but design of controllers in the frequency domain. The linearization and decentralization techniques are implemented. Design of tension observers and feedback controllers with friction and inertia compensation is studied. Approaches for the gain design are discussed, and summarized procedures are given. The proposed analytical approach for design of tension observers and feedback controllers has been proven to be adequate by experiment.

Results on the design of robust memoryless state feedback controllers for uncertain time-delay systems with norm bounded uncertainty are presented. It is proved that the feasibility of a linear matrix inequality (LMI) problem is necessary and sufficient for the quadratic stabilisation of an uncertain time-delay system. A robust state feedback controller can be constructed using the corresponding feasible solution of the LMI problem. A procedure is given to select a suitable state feedback controller that is also suboptimal in the sense of minimising a bound on a quadratic performance index.

A vector decomposition approach to F–M model realization and its application to robust observed-state feedback control

This paper presents the design and implementation of optimal and robust state feedback controller for rotary inverted pendulum system. The Particle Swarm Optimization (PSO) method is used to find the optimal values of the state feedback gains subject to time response specifications and H_∞ constraints. To improve the tracking of the system, a robust state feedback plus integral controller is designed. The simulation results show that the proposed controller can effectively stabilize the pendulum at the upright position. Further, the proposed controller can compensate the variations in system parameters. The effectiveness of the proposed controller is verified experimentally using real rotary inverted pendulum.

This paper reviews robust feedback control applications in power system. Robust control concept in power system control area evolves by the way of uncertainty modeling. Uncertainties can be caused by variation of loading, load parameters, network topology and machine parameters. One direct way to take into consideration of uncertainties is to enumerate various system operating conditions and use a set of linear time invariant systems to model the power systems. Enumeration method is used in robust control signal selection and robust controller design. Another way is to model uncertainties as structured or unstructured uncertainties. Controllers are designed based on nominal system condition to tolerate uncertainty as much as possible. The controller synthesis problem is solved by either Algebraic Ricatti Equation (ARE) or Linear Matrix Inequality (LMI). LMI is shown to be more flexible in controller design since it provides a way to specify system dynamic performance. Most recently, linear parameter varying (LPV) concept expands the use of enumeration method to express a set of linear time invariant (LTI) systems with state space dependent on linear parameters. LPV based control methods extend gain scheduling to design linear control for each operating conditions and overall a nonlinear controller for the varying parameter system.

This paper proposes guaranteed cost design of robust output feedback controller for continuous linear parametric uncertain systems. New necessary and sufficient conditions for static output feedback stabilizability of linear continuous time systems underly the design procedure. Proposed algorithms are computationally simple and tightly connected with the Lyapunov stability theory and the LQR optimal state feedback design. The proposed approach allows for prescribing the structure of the output feedback gain matrix (including the decentralized one) by the designer. New design method proposed in this paper, exploit genetic algorithm to design robust controller with guaranteed cost for polytopic linear continuous time systems. Numerical example is given to illustrate the performance of the proposed robust controller.

6 - Design and Performance of Feedback Controllers

This paper investigates the design of a robust fault detection observer for Wireless Networked Control Systems (WNCS) subject to random packet delays introduced by the wireless communication networks. The concept of input-delay analysis is adopted for analyzing the impacts of the packet delay on the residual generation, and a robust observer design and optimization method is proposed to improve the robustness of fault detection against the network induced delay. For the purpose of realistic simulation, a mixed simulation is carried out, where the control system is simulated in MATLAB and the network-induced delays are achieved by simulating an IEEE 802.11b wireless network at the recently developed OMNeT++ platform. The simulation results validate the proposed robust fault detection observer design approach.

This paper presents a novel Sliding Mode Control (SMC) approach for a three phase AC/DC/AC Voltage source UPS used in Industrial applications. The proposed controller is robust for sudden change in loads and more efficient. Most of the industries run with critical loads, so there is always a need to supply better quality of inverter output voltage waveform. A mathematical model of the system is derived using state space modeling. Using the model, a design procedure of controller implementation using the state variables necessary to obtain a stable system is developed. It can be operated for both linear and non-linear load conditions very effectively. It reduces steady state error and is easy to implement. Load voltage regulation is also found to be within the standards. The dynamic nature of the controller is verified. A phase trajectory is plotted to show the nature of the SMC characteristic in reaching the origin. Frequency response characteristics are plotted to realize the state variables to obtain stability. The simulation work is performed in PSCAD/EMTDC version 4.6. and the system stability condition is analyzed from frequency response plots obtained in MATLAB R2012b platform. The proposed controller can be effectively used in all high power industrial applications.

Detailed in this paper is a SISO non-linear modelling and robust controller design methodology experimentally verified on an internal combustion engine. The methodology begins with the identification of a NARMAX model that captures the non-linear dynamics relating the input to the output of a system. This model is converted to a describing function representation for the purpose of robust feedback controller design. The ideology for the describing function recovery is developed in the form of an algorithm which can be extended to other NARMAX model structures not considered here. The controller design is executed in the frequency domain where the output performance specification is |y(t)|≤β∀t>0 and the actuator saturation constraint is |u(t)|≤K∀t>0. For the engine idle speed control application of this study, a SISO NARMAX model of the engine is developed between the by-pass idle air valve (BPAV) and engine speed. The performance objective for the controller design is the time domain tolerance of |Δ rpm| ≤ 100 rpm on idle speed perturbations despite a non-measurable 20 N m external torque disturbance. The controller is validated through numerical simulations as well as experimental verification.

This paper studies the robust discrete-time pole-placement state feedback controller design in the LMI framework. The inner ellipse is used to approximate originally non-convex discrete-time closed loop pole region respective to the prescribed damping factor. The resulting LMI conditions use parameter dependent Lyapunov function to reduce conservatism in robust controller design. Contribution of this paper is in the application of this procedure on the case study - unstable Magnetic Levitation System, analysis of the results and comparison with standard robust stabilizing controller design.

This paper deals with the design of robust state feedback controller based on fuzzy logic and its evaluation in adjusting the speed of an induction machine. The basic idea of the proposed controller is similar to the gain scheduling approach. The design is based on a reduced order state space model of the motor drive from which a family of local state space models covering the operating range of the drive system are defined. We then use the state feedback design concept to get a linear state feedback controller for each local model using pole placement topology. The performance of the fuzzy state feedback controller is evaluated under different operating regimes of the drive system.

A robust delay-dependent guaranteed cost PID multivariable output feedback controller design for time-varying delayed systems: An LMI optimization approach