Infinity Control Research Articles

Comparative analysis of traditional and modern controller for piezoelectric actuated nanopositioner

Nanopositioning, Precise control and manipulation of devices and materials at nanoscale is the most important constraint of nanotechnology. Nanopositioning stage consisting of piezoelectric actuator has widespread use in applications requiring positioning with precision at nanoscale. In this paper, open loop characteristics of the non minimum phase nanopositioning system are investigated. To guarantee high precision positioning and improvement in the system characteristics demands different types of feedback controllers. The main aim of the controller is to design a closed loop system with good dynamic characteristics and to maintain the desired stability margins. PID controller is a generic closed loop controller widely used for industrial control applications. This paper presents design of PID controller using Ziegler Nichols tuning method. This paper analyzes time and frequency response of traditional PID controller. Non minimum phase system can be stabilized more effectively by modern controller such as pole placement controller, Linear Quadratic Regulator (LQR) and H infinity controllers. This paper develops a methodology for the design of full state feedback controller using pole placement and LQR control techniques. Step response and frequency responses under variety of conditions are plotted and analyzed to verify the effectiveness of the proposed controllers. Closed loop system is analyzed in both time and frequency domain for different dynamic characteristics such as rise time, settling time, maximum overshot and stability margins. A comparative assessment based upon the system’s response characteristics of traditional PID controller, pole placement controller and LQR controller is presented. Simulation results for the performance analysis are carried out on MATLAB and demonstrate effectiveness and adaptability of controller for precise control of piezoelectric actuated nanopositioning system.

Geometric approach and structure at infinity controls for the disturbance rejection

This study presents two methods to solve the disturbance rejection problem: the structure at infinity control and geometric approach control. The main result of this study is although the two methods are different, in both cases if the problem has a solution, the transfer function of the outputs and the disturbances is null. Both methods are applied in a mechanical system and a thermal system showing a good performance.

Research of Electrified Railway Harmonic Suppression Based on H-infinity Control

Because of using the nonlinear high-power, single-phase, multi-step full wave or bridge rectifier electric locomotive in electrified railway, the electrified railway traction power supply system has serious power quality problems, which affect safe operation of the electrified railway and impact the local power grid adversely. Aiming at the electrified railway power quality problems, a homogenization model of the inverter is established, and the robustness of active power filter is analyzed based on the H- infinity control theory. Simulation results show that the harmonic control effect of electrified railway is good based on H-infinity control. Under various parameters perturbation, THD is changed relatively small, the system can well follow load changed and has strong robustness. So based on H-infinity control of active power filter in electrified railway harmonic suppression has wide application prospects.

A Partially Augmented Lagrangian Method for Low Order ${\rm H}$-Infinity Controller Synthesis Using Rational Constraints

This technical note proposes a method for low order H-infinity synthesis where the constraint on the order of the controller is formulated as a rational equation. The resulting nonconvex optimization problem is then solved by applying a partially augmented Lagrangian method. The proposed method is evaluated together with two well-known methods from the literature. The results indicate that the proposed method has comparable performance and speed.

Coprime‐inner/outer factorization of SISO time‐delay systems and FIR structure of their optimal H‐infinity controllers

SUMMARYThe approach in Foias et al. (Robust control of Infinite Dimensional: Frequency Domain Methods. Springer: Berlin, 1996) is one of the well‐developed methods to design H‐infinity controllers for general infinite dimensional systems. This approach is applicable if the plant admits a special coprime‐inner/outer factorization. We give the largest class of single‐input–single‐output (SISO) time‐delay systems for which this factorization is possible and factorize the admissible plants. Based on this factorization, we compute the optimal H‐infinity performance and eliminate unstable pole‐zero cancellations in the optimal H‐infinity controller. We extend the results on the finite impulse response structure of optimal H‐infinity controllers by showing that this structure appears not only for plants with input/output delays, but also for general SISO time‐delay plants. Copyright © 2011 John Wiley & Sons, Ltd.

Central suboptimal H ∞ controller design for linear time-varying systems with unknown parameters

This article presents the central finite-dimensional H ∞ controller for linear time-varying systems with unknown parameters, that is suboptimal for a given threshold γ with respect to a modified Bolza–Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, this article reduces the original H ∞ controller problem to the corresponding H 2 controller problem, using the technique proposed in Doyle et al. [Doyle, J.C., Glover, K., Khargonekar, P.P., and Francis, B.A. (1989), ‘State-space Solutions to Standard H 2 and H Infinity Control Problems’, IEEE Transactions Automatic Control, 34, 831–847]. This article yields the central suboptimal H ∞ controller for linear systems with unknown parameters in a closed finite-dimensional form, based on the corresponding H 2 controller obtained in Basin and Calderon-Alvarez [Basin, M.V., and Calderon-Alvarez, D. (2008), ‘Optimal LQG Controller for Linear Systems with Unknown Parameters’, Journal of The Franklin Institute, 345, 293–302]. Numerical simulations are conducted to verify performance of the designed central suboptimal controller for uncertain linear systems with unknown parameters against the conventional central suboptimal H ∞ controller for linear systems with exactly known parameter values.

The H-infinity Control of a kind of Lurie Switched Time-delay System

The designation idea of infinity controller is introduced to a class of Lurie switched systems with time-delay and sector restricted nonlinearities. We Construct Lyapunov function and apply the stablity theory to analyze Lurie switched system. The theoretical proof showed that this system is gradually stable. The result is expressed by using linear matrix inequality (LMI), so it is easy to realize.

H_infinity Controller Design to Control the Single Axis Magnetic Levitation System with Parametric Uncertainty

In this study the force control design of single axis magnetic levitation system using H_infinity controller is presented. First, the system dynamics are linearized and described in transfer function form. Second, the magnetic force is regulated using H_infinity controller to achieve robust stability, disturbance/noise rejection and asymptotic tracking. A multiplicative unstructured model extracted from the parametric uncertainty is used for H_infinity control design. The obtained results showed that robust stability and performance have been achieved. On the other hand, an improved and more reliable time response compared with previous work also has been achieved in this study.

Piecewise Lyapunov Functionに基づくSwitchingファジィ制御器によるH∞制御系の設計

Piecewise Lyapunov Functionに基づくSwitchingファジィ制御器によるH∞制御系の設計

A Robust Reinforcement Learning Control Design Method for Nonlinear System with Partially Unknown Structure

We propose a robust control system which has robustness for disturbance and can deal with a nonlinear system with partially unknown structure by fusing reinforcement learning and robust control theory. First, we solved an optimal control problem without using unknown part of functions of the system, using neural network and the repetition learning of reinforcement learning algorithm. Second, we built the robust reinforcement learning control system which permits uncertainty and has robustness for disturbance by fusing the idea of H infinity control theory with above system.

Dynamic Output Integral Sliding-Mode Control With Disturbance Attenuation

This technical note proposes a dynamic output feedback sliding-mode control algorithm for linear MIMO systems with mismatched norm-bounded uncertainties along with disturbances and matched nonlinear perturbations. A control law is first designed to ensure that the system behavior can satisfy the reaching and sliding condition. A scheme designed to combine the output-dependent integral sliding surface with a full-order compensator is then proposed. Through utilizing H infin control analytical technique, once the system is in the sliding mode, the proposed algorithm can guarantee robust stabilization and sustain the nature of performing disturbance attenuation when the solutions to two algebraic Riccati inequalities can be found. Finally, the feasibility of our proposed algorithm is illustrated using a numerical example.

Average dwell time approach to ℒ 2 –ℒ ∞ control of switched delay systems via dynamic output feedback

This study is concerned with the L 2 -L infin control problem for continuous-time switched systems with time-varying delay. A dynamic output feedback (DOF) controller is designed, which is assumed to be switching with the same switching signal as in the original system. By using an average dwell time approach and the piecewise Lyapunov function technique, a delay-dependent sufficient condition is proposed to guarantee the exponential stability and a weighted L 2 -L infin performance for the closed-loop system with the decay estimate explicitly given. The corresponding solvability condition for a desired DOF controller is established, and an explicit parametrisation of all desired DOF controllers is also given. Finally, a numerical example is given to illustrate the effectiveness of the proposed theories.

Delay-Dependent Robust $\hbox{\it H}_\infty$ Control for Uncertain Discrete-Time Fuzzy Systems With Time-Varying Delays

This paper deals with the robust H infin control problem for discrete-time Takagi-Sugeno (T-S) fuzzy systems with norm-bounded parametric uncertainties and interval time-varying delays. First, based on a new Lyapunov functional, we present a sufficient condition guaranteeing that the resulting closed-loop system is robustly stable and satisfies a prescribed H infin performance level. The Lyapunov functional used here depends on not only the fuzzy basis function but on the lower and upper bounds of the time-varying delay as well. Second, two classes of delay-dependent conditions for the existence of the concerned H infin fuzzy controllers are given in terms of relaxed linear matrix inequalities (LMIs), and a desired controller can be designed by using the solutions to these LMIs. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed design method.

H ∞ control of non-linear dynamic systems: a new fuzzy delay partitioning approach

The problem of robust H infin control for Takagi-Sugeno (T-S) fuzzy systems with norm-bounded parameter uncertainties and a time delay in the state is investigated. Attention is focused on the design of robust H infin controllers via the parallel distributed compensation scheme such that the closed-loop fuzzy time-delay system is asymptotically stable and the H infin disturbance attenuation is below a prescribed level. By utilising the instrumental idea of delay partitioning, a new Lyapunov-Krasovskii functional is introduced, and some novel ideas for achieving delay dependence and basis dependence have been employed, which guarantee the obtained conditions to be much less conservative than most existing results in the literature. These conditions are formulated in the form of linear matrix inequalities (LMIs), based on which, the controller design is cast into a convex optimisation problem subject to LMI constraints. Finally, two examples are illustrated to show the feasibility and effectiveness of the obtained results.

Robust Output Feedback Guaranteed Cost Control of Nonlinear Stochastic Uncertain Systems Via an IQC Approach

This technical note presents a new approach to constructive output feedback robust nonlinear controller design based on the use of IQCs and minimax LQG control. The approach involves a class of controllers which include copies of the nonlinearities in the controller. The linear part of the controller is synthesized using minimax LQG control theory which is closely related to H infin control theory.

Control of Constrained Discrete-Time Systems With Bounded $\ell_{2}$ Gain

We consider the problem of designing a control law for a constrained linear system with bounded disturbances that ensures constraint satisfaction over an infinite horizon, while also guaranteeing that the closed-loop system has bounded lscr2 gain. To this end, we propose a receding horizon control strategy based on the repeated calculation of optimal finite horizon feedback policies. We parameterize these policies such that the input at each time is an affine function of current and prior states, and minimize a worst-case quadratic cost where the disturbance energy is negatively weighted as in H infin control. We show that the resulting receding horizon controller has two advantages over previous results for this problem. First, the policy optimization problem to be solved at each time step can be rendered convex-concave, with a number of decision variables and constraints that grows polynomially with the problem size, thereby making its solution amenable to standard techniques in convex optimization. Second, the achievable lscr2 gain of the resulting closed-loop system is bounded and non-increasing with increasing control horizon. A numerical example is included to demonstrate the improvement in achievable lscr2 gain relative to existing methods.

Quadrilateral Modelling and Robust Control of a Nonlinear Piezoelectric Cantilever

Piezocantilevers are commonly used for the actuation of micromechatronic systems. These systems are generally used to perform micromanipulation tasks which require high positioning accuracy. However, the nonlinearities, i.e., the hysteresis and the creep, of piezoelectric materials and the influence of the environment (vibrations, temperature change, etc.) create difficulties for such a performance to be achieved. Various models have been used to take into account the nonlinearities but they are often complex. In this paper, we study a one degree of freedom piezoelectric cantilever. For that, we propose a simple new model where the hysteresis curve is approximated by a quadrilateral and the creep is considered to be a disturbance. To facilitate the modelling, we first demonstrate that the dynamic hysteresis of the piezocantilever is equivalent to a static hysteresis, i.e., a varying gain, in series with a linear dynamic part. The obtained model is used to synthesize a linear robust controller, making it possible to achieve the performances required in micromanipulation tasks. The experimental results show the relevance of the combination of the developed model and the synthesized robust H infin controller.

Nonlinear H_infinity Control Designs with Axisymmetric Spacecraft Control

In this paper, we study nonlinear control of a spacecraft symmetric about its principal axis with two control torques. Using a computationally efficient H ∞ control design procedure, attitude stabilization and command tracking problems of the axisymmetric spacecraft are solved locally. The proposed nonlinear H ∞ control approach uses higher order Lyapunov functions and reformulates the difficult Hamilton―Jacobian―Isaacs inequalities as semidefinite optimization conditions. Sum-of-squares programming techniques are then applied to obtain computationally tractable solutions, from which nonlinear control laws will be constructed. The nonlinear H ∞ control designs for spacecraft are capable of exploiting the most suitable forms of Lyapunov functions for performance improvement.

$H_{\infty }$ Fuzzy Control of Nonlinear Systems Under Unreliable Communication Links

This paper investigates the problem of H infin fuzzy control of nonlinear systems under unreliable communication links. The nonlinear plant is represented by a Takagi--Sugeno (T-S) fuzzy model, and the control strategy takes the form of parallel distributed compensation. The communication links existing between the plant and controller are assumed to be imperfect (that is, data packet dropouts occur intermittently, which appear typically in a network environment), and stochastic variables satisfying the Bernoulli random binary distribution are utilized to model the unreliable communication links. Attention is focused on the design of H infin controllers such that the closed-loop system is stochastically stable and preserves a guaranteed H infin performance. Two approaches are developed to solve this problem, based on the quadratic Lyapunov function and the basis-dependent Lyapunov function, respectively. Several examples are provided to illustrate the usefulness and applicability of the developed theoretical results.

Self-Triggered Feedback Control Systems With Finite-Gain ${\cal L}_{2}$ Stability

This paper examines a class of real-time control systems in which each control task triggers its next release based on the value of the last sampled state. Prior work used simulations to demonstrate that self-triggered control systems can be remarkably robust to task delay. This paper derives bounds on a task's sampling period and deadline to quantify how robust the control system's performance will be to variations in these parameters. In particular we establish inequality constraints on a control task's period and deadline whose satisfaction ensures that the closed-loop system's induced L 2 gain lies below a specified performance threshold. The results apply to linear time-invariant systems driven by external disturbances whose magnitude is bounded by a linear function of the system state's norm. The plant is regulated by a full-information H infin controller. These results can serve as the basis for the design of soft real-time systems that guarantee closed-loop control system performance at levels traditionally seen in hard real-time systems.