Design Of Linear Control Systems Research Articles

Less Conservative Control Design for Linear Systems with Polytopic Uncertainties via State‐Derivative Feedback

The motivation for the use of state‐derivative feedback instead of conventional state feedback is due to its easy implementation in some mechanical applications, for example, in vibration control of mechanical systems, where accelerometers have been used to measure the system state. Using linear matrix inequalities (LMIs) and a parameter‐dependent Lyapunov functions (PDLF) allowed by Finsler’s lemma, a less conservative approach to the controller design via state‐derivative feedback, is proposed in this work, with and without decay rate restriction, for continuous‐time linear systems subject to polytopic uncertainties. Finally, numerical examples illustrate the efficiency of the proposed method.

Observer-based controller design for linear systems with limited communication capacity via a descriptor augmentation method

This study investigates the problem of observer-based control for linear time-invariant system with limited communication capacity. The system states are unavailable and the system outputs are subject to logarithmic quantisation, which can be regarded as outputs with disturbances. Traditional Luenberger observers and proportional and derivative observers are not effective to deal with such kind of estimation problems. A new estimation technique to cope with discontinuous quantised outputs is proposed such that the estimation of system states and quantisation error can be obtained simultaneously. In this design, the state variables of the derived error system are discontinuous at quantisation switching times, and traditional Lyapunov function cannot be used to perform the stability analysis. Hence, a new time-dependent Lyapunov functional and a generalised Newton–Leibniz formula are proposed to deal with this difficulty. A sufficient condition for the stability analysis of the error dynamics is established and an observer-based control scheme is proposed to stabilise the plant. Finally, a numerical example is presented to illustrate the effectiveness and applicability of the proposed technique.

Control Óptimo- L2 Basado en Red Mediante Funcionales de Lyapunov-Krasovskii

This paper deals with the problem of optimal control design for linear network control systems (NCS) with L2-gain disturbance rejection. Networked control systems close the control loop using a communication network, that usually accounts for network-induced delays and packet dropouts. Resorting to Lyapunov Krasovskii functionals (LKF), the problem of stabilization of NCS with joint performance index optimization and L2- gain disturbance rejection is addressed. The paper initially develops a general solution for the problem, then an specific LKF is particularized to provide a solution in terms of linear matrix inequalities. Performance of the proposed control structure is shown by simulations comparing with LQR control on an intervehicle distance regulation problem.

Linear quadratic optimal control system design using particle swarm optimization algorithm

Selecting appropriate weighting matrices for desired linear quadratic regulator (LQR) controller design using evolutionary algorithms is presented in this paper. Obviously, it is not easy to determine the appropriate weighting matrices for an optimal control system and a suitable systematic method is not presented for this goal. In other words, there is no direct relationship between weighting matrices and control system characteristics, and selecting these matrices is done by using trial and error based on designer’s experience. In this paper, we use the particle swarm optimization (PSO) method which is inspired by the social behavior of fish and birds in finding food sources to determine these matrices. Stable convergence characteristics and high calculation speed are the advantages of the proposed method. Simulation results demonstrate that in comparison with genetic algorithms (GAs), the PSO method is very efficient and robust in designing of optimal LQR controller. Key words: Linear quadratic regulator (LQR), weighting matrices, particle swarm optimization, genetic algorithm.

A robust adaptive feedforward control in repetitive control design for linear systems

This paper proposes a new adaptive feedforward cancellation (AFC) control that achieves periodic tracking and/or periodic disturbance rejection. The new control design is a direct scheme in the sense that it adaptively updates the desired control without estimating the unknown disturbance. The proposed new control has several advantages. First, its adaptation gain can be arbitrarily chosen without upsetting the system stability if given the exact system model. Second, it can be applied to not only minimum-phase systems, but also non-minimum phase systems. Third, the new control law is independent of where the disturbance enters the system. Finally, a robustness analysis is made to show that the proposed control is robust with respect to un-modelled dynamics.

Direct design of a U-model-based generalized predictive controller for a class of non-linear (polynomial) dynamic plants

Facing the big challenge of directly designing a generalized predictive controller (GPC) for a class of smooth non-linear dynamic plants described with polynomial models, this study reformulates the classical GPC into a U-model-based implementation. Mathematically, the final solution of the controller output is converted into resolving a polynomial equation in terms of current controller output u( k), which dramatically reduces the difficulties and complexity encountered in non-linear control system synthesis, algorithm development, and online implementation. It is believed that the integrated procedure provides a straightforward methodology to apply linear control system design techniques to design non-linear control systems without any enforced linearization of plant models. For a demonstration of the feasibility and effectiveness of the designed procedure, a continuously stirred tank reactor, and the other simulated example to represent chemical kinetics, are selected for the initial bench tests. The key contribution of the study is to derive and demonstrate feasibility and effectiveness of the U-model approach to GPC of non-linear systems. This is further evidence to support the author’s insight on the U-model approach that was previously used to design pole placement controller (PPC).

Sliding mode controller design for linear systems with unmeasured states

This paper addresses the optimal controller problem for a linear system over linear observations with respect to different Bolza–Meyer criteria, where (1) the integral control and state energy terms are quadratic and the non-integral term is of the first degree or (2) the control energy term is quadratic and the state energy terms are of the first degree. The optimal solutions are obtained as sliding mode controllers, each consisting of a sliding mode filter and a sliding mode regulator, whereas the conventional feedback LQG controller fails to provide a causal solution. Performance of the obtained optimal controllers is verified in the illustrative example against the conventional LQG controller that is optimal for the quadratic Bolza–Meyer criterion. The simulation results confirm an advantage in favor of the designed sliding mode controllers.

L2-Gain-based controller design for linear systems with distributed input delay

L2-Gain-based controller design for linear systems with distributed input delay

Development of a Customized Autopilot for Unmanned Helicopter Model Using Genetic Algorithm via the Application of Different Guidance Strategies

The objective of this paper is to develop a customized autopilot system that enables a helicopter model to carry out an autonomous flight using on-board microcontroller. The main goal of this project is to provide a comprehensive controller design methodology, Modeling, simulation, guidance and verification for an unmanned helicopter model. The autopilotsystem was designed to demonstrate autonomous maneuvers such as flying over the planned waypoints with constant forward speed and considerable steep maneuvers. For the controller design, the nonlinear dynamic model of the Remote Control helicopter was built by employing Lumped Parameter approach comprising of four different subsystems such as actuator dynamics, rotary wing dynamics, force and moment generation process and rigid body dynamics. The nonlinear helicopter mathematical model was then linearized using small perturbation theory for stability analysis and linear feedback control system design. The linear state feedback for the stabilization and control of the helicopter was derived using Pole Placement Method. The overall dynamic system control with output feedback was computed using Genetic Algorithm. Series of Matlab-Simulink models and guidance algorithms were presented in this work to simulate and verify the autopilot system performance. The proposed autopilot has shown acceptable capability of stabilizing and controlling the helicopter during tracking the desired waypoints. This paper is presenting a detailed comparison study for two different guidance strategies. The first strategy is concerning the difference between the desired heading or elevation referred to the next waypoint and the actual heading or elevation of the unmanned helicopter model. The second strategy is concerning the relative distance between the actual and the desired trajectories. In other words the first method is tracking the waypoints while the second one is tracking the trajectory. In this work a comparison study was conducted through the mentioned strategies simulation to show the significant differences in the output performance. Some performance indexes were presented to evaluate the system performance errors and the control effort needed for both strategies using the same desired trajectory and the same waypoints.

Variable structure controller design for linear systems with bounded inputs

This paper studies the design of variable structure systems with saturation inputs. Sliding mode domain, reaching domain, and unescapable reaching domain of linear systems with variable structure are defined and investigated. When the state matrix of the linear system is Hurwitz, the stability of the variable structure systems is proven by using passivity theory. Moreover, variable structure systems with novel nonlinear switching surfaces are proposed for second order systems. Two strategies for designing variable structure control for high order linear systems are also proposed, such as stepby-step variable structure control and moving-surface variable structure control, which were found to guarantee that the reaching condition of the variable structure control is always satisfied. Finally, an illustrative example pertaining to the attitude control of a flexible spacecraft demonstrates the effectiveness of the proposed methods.

H ∞ controller design for linear systems with time-invariant uncertainties

This paper considers the problem of designing robust H ∞ state feedback controller for linear continuous-time systems with time-invariant uncertainties. The main result given here concerns H ∞ controller design using the parameter dependent Lyapunov function approach and a new control law. A new condition ensuring the linear systems to be is asymptotically stable with a prescribed H ∞ performance is proposed in terms of a set of linear matrix inequalities (LMIs). Theoretic proof is given to show that the proposed condition is less conservative than existing results in the literature. An example is provided to demonstrate the efficiency of the proposed method.

RBF Neural Network Based Adaptive Tracking Control for a Class of Nonlinear Plant Using Stochastic U-Model

In this paper an adaptive tracking control algorithm and its step by step implementation procedure are developed for a class of nonlinear plants within a U-model framework with unknown parameters. With the author’s previous justification, not only the control oriented model represents a wide range of smooth (polynomial) nonlinear dynamic plants (without using linearisation approximation at all), but also make almost all linear control system design techniques directly applicable (with a root solver bridging the linear design and calculation of controller output). A new technique is proposed to design an online control algorithm using the Radial Basis Functions Neural Network (RBFNN). The plant parameters are estimated online and are used to update the weights of the RBFNN. The weights update equations are derived based on the well known LMS (least mean square). A number of simulated case studies are conducted to illustrate the efficiency of the claimed insight and design procedure.

U-model-based adaptive control for a class of stochastic non-linear dynamic plants with unknown parameters

In this paper, an adaptive control algorithm within a U-model framework is developed for controlling a class of stochastic non-linear discrete-time models with unknown parameters. With the authors' previous justification, the control-oriented model not only represents a wide range of smooth (polynomial) non-linear dynamic plants (without using linearisation approximation at all), but also makes almost all linear control system design techniques directly applicable to non-linear dynamic plants (with a root solver bridging the linear design and calculation of controller output). A new recursive least squares algorithm is derived and its convergence is proved for the online estimation of time-varying parameters. For initial bench test, a pole placement controller for non-linear stochastic polynomial models is designed using the corresponding linear design technique. Accordingly a step by step procedure is listed to implement the adaptive control operation. A number of simulated case studies are conducted to illustrate the efficiency of the claimed insight and design procedure.

Bode optimal loop shaping with CRONE compensators

Ideal Bode characteristics give a classical answer to optimal loop design for linear time invariant feedback control systems in the frequency domain. This work recovers eight-parameter Bode optimal loop gains, providing a useful and simple theoretical reference for the best possible loop shaping from a practical point of view. The main result of the paper is to use CRONE compensators to make a good approximation and in addition a way for the synthesis of the Bode optimal loop. For that purpose, a special loop structure based on second and third generation CRONE compensators is used. As a result, simple design relationships will be obtained for tuning the proposed CRONE compensator.

Linear matrix inequality-based repetitive controller design for linear systems with time-varying input delay

This style deals with the problem of delay-dependent stability criterion and repetitive controller design for linear systems with time-varying input delay. First, based on the existing literature, a rate-dependent state feedback controller is designed so that the closed-loop system is stabilised and the effect of disturbances is reduced to an ideal level. Second, by combining the state vectors of the stabilised system and repetitive controller, a delay-dependent stability criterion is derived in the form of linear matrix inequality (LMI) for the augmented system. Third, by reformulating the LMIs given in the stability criterion, the design problem of the repetitive controller is transformed to an optimisation problem subject to LMI constraints. Two simulation examples are provided to illustrate the validity of the proposed method.

Linear discrete-time global and regional anti-windup: an LMI approach

In this article we address linear anti-windup design for linear discrete-time control systems guaranteeing regional and global stability and performance. The techniques that we develop are the discrete-time counterpart of existing techniques for anti-windup augmentation which lead to convex constructions by way of linear matrix inequalities (LMIs) when adopting static and plant order anti-windup augmentation. Interesting system theoretic interpretations of the performance bounds for the non-linear closed loop can also be given. We show here that parallel results apply to the discrete-time case. We derive the corresponding conditions and prove their effectiveness by adapting the continuous-time approaches to the discrete-time case.

Design of Step Motor Fuzzy Control System and its Application

The classical PID controller is based on the concrete model of the object and is only suitable for the design of linear control system. Step servo system is a typical nonlinear system, so the intelligent control strategies should be adopted. In this paper an approximate model of the step motor is presented, a compound fuzzy PI controller is designed to fulfill the control of the step motor, and is successfully applied to the automatic control the scanning device of eddy current nondestructive testing (ECNDT). The proposed controller is robust to load torques, cogging forces, and other disturbances. The fuzzy PI controller also guarantees asymptotic stabilization and possesses better dynamic performance compared with the traditional PID control algorithm. The simulation study and an experimental validation carried out on the automatic control system of the scanning device confirmed the suitability of the proposed approach.

On the Optimal Design of Linear Networked Systems

This paper addresses the problem of optimal design for linear networked control systems (NCSs). We deal with the delayed NCSs in the continuous time-domain and propose a computational approach to optimization problems based on the hybrid LQ-type techniques. In particular, we develop an explicit connection between the networked control processes and the corresponding hybrid systems. For the constructive feedback control design procedure we derive the necessary Riccati-formalism and propose an implementable solution algorithm.

Robust Reduced-order Output-feedback H∞ Control

The problem of robust H∞ reduced-order control design for linear systems in presence of polytopic type uncertainties is addressed. The controller is obtained by transforming the problem into a robust static output-feedback control design problem. Applying a recent method for solving the latter by means of linear matrix inequalities, a sufficient condition is obtained for the existence of a solution to the problem. A simple method for deriving the reduced-order controller is given in the case where the latter condition is satisfied.

Review of "Linear control systems analysis and design - conventional and modern", d'Azzo, J.D. and Houpis, C.; 1981 (Reprint) [25 years ago

This month, 25 Years Ago revisits the second edition of a classic text with a book review written by Richard S. Marleau (from IEEE Control Systems Magazine, vol. 3, no. 4, Nov. 1983, pp. 8?9). Contributed by Kent Lundberg.