Showing papers in "Asian Journal of Control in 2013"

Nonlinear Robust Tracking Control of a Quadrotor UAV on SE(3)

Abstract: This paper provides nonlinear tracking control systems for a quadrotor unmanned aerial vehicle (UAV) that are robust to bounded uncertainties. A mathematical model of a quadrotor UAV is defined on the special Euclidean group, and nonlinear output-tracking controllers are developed to follow (i) an attitude command, and (ii) a position command for the vehicle center of mass. The controlled system has the desirable properties that the tracking errors are uniformly ultimately bounded, and the size of the ultimate bound can be reduced arbitrarily by control system parameters. Numerical examples illustrating complex maneuvers are provided.

An Active Disturbance Rejection Based Approach to Vibration Suppression in Two-Inertia Systems

Abstract: This study concerns the resonance problems found in motion control, typically described in a two-inertia system model as compliance between the motor and the load. We reformulate the problem in the framework of active disturbance rejection control (ADRC), where the resonance is assumed to be unknown and treated as disturbance, estimated and mitigated. This allows the closed-loop bandwidth to go well beyond the resonant frequency, which is quite difficult using existing methods. In addition, such level of performance is achieved with minimum complexity in the controller design and tuning: no parameter estimation or adaptive algorithm is needed, and the controller is tuned by adjusting one parameter, namely, the bandwidth of the control loop. It is also shown that the proposed solution applies to both the velocity and position control problems, and the fact that ADRC offers an effective and practical motion control solution, in the presence of unknown resonant frequency within the bandwidth of the control system. Finally, frequency response analysis is performed where stability margin is obtained before the simulation results are verified in the hardware experiments.

Adaptive Harmonic Steady‐State Disturbance Rejection with Frequency Tracking

Abstract: This paper is concerned with the rejection of sinusoidal disturbances of unknown frequency acting at the output of unknown plants. Disturbance rejection is based on an adaptive harmonic steady-state (ADHSS) algorithm combined with a magnitude/phase locked-loop (MPLL) frequency estimator. The harmonic steady-state method assumes that the plant can be approximated by its steady-state frequency response. For high-order plants such as those encountered in active noise and vibration control (ANVC), this assumption greatly reduces the number of parameters and enables online estimation of the plant response using simple algorithms. The paper shows that when the MPLL is integrated with the ADHSS algorithm, the two components work together in such a way that the control input does not prevent frequency tracking by the MPLL, and so that the order of the ADHSS can be reduced. Thus, the addition of the MPLL allows disturbances of unknown frequency to be considered without significantly increasing the complexity of the original ADHSS. After analyzing the reduced-order ADHSS in the ideal case, the equations describing the complete system are considered. The theory of averaging is used to gain insight into the steady-state behavior of the algorithm. It is found that the system has a two-dimensional equilibrium surface such that the disturbance is cancelled exactly. A subset of the surface is proved to be locally stable. Extensive active noise control experiments demonstrate the performance of the algorithm, even when disturbance and plant parameters are changing.

Finite-Time Stability and Stabilization of Linear Itô Stochastic Systems with State and Control-Dependent Noise

Abstract: In this paper, finite-time stability and stabilization problems for a class of linear stochastic systems are studied. First, a new concept of finite-time stochastic stability is defined for linear stochastic systems. Then, based on matrix inequalities, some sufficient conditions under which the stochastic systems are finite-time stochastically stable are given. Subsequently, the finite-time stochastic stabilization is studied and some sufficient conditions for the existence of a state feedback controller and a dynamic output feedback controller are presented by using a matrix inequality approach. An algorithm is given for solving the matrix inequalities arising from finite-time stochastic stability (stabilization). Finally, two examples are employed to illustrate the results.

Linear Observer‐Based Active Disturbance Rejection Control of the Omnidirectional Mobile Robot

Abstract: This article describes the design of a linear observer-linear controller-based robust output feedback scheme for output reference trajectory tracking tasks in an omnidirectional mobile robot. The unknown, possibly state-dependent, additive nonlinearities influencing the input-output tracking error dynamics are modeled as an absolutely bounded, additive, unknown “time-varying disturbance” input signal. This procedure simplifies the system tracking error description to that of three independent chains of second order integrators with, known, position-dependent control gains. These simplified systems are additively perturbed by the unknown, smooth, time-varying signal which is proven to be trivially observable. Generalized proportional integral (GPI) observers, are shown to naturally estimate, in an arbitrarily close manner, the unknown perturbation input of the simplified system and a certain number of its time derivatives. This information is used to advantage on the linear, observer-based, feedback controller design via a simple cancellation effort. The results are implemented on a laboratory prototype of an omnidirectional mobile robot.

Fractional Order Controller Design for A Flexible Link Manipulator Robot

Abstract: In this paper a novel controller for a flexible link manipulator based on fractional calculus is proposed. A hybrid system that combines the advantages in terms of robustness of the fractional control and the sliding mode control is proposed. Due to adding the extra degree of freedom, the fractional order sliding mode controller can achieve better control performance than the integer order sliding mode controller. For the problem of determining the design parameters, the particle swarm optimization (PSO) algorithm is used. The proposed controller is applied for a single-link flexible manipulator robot. Finally, the performance and the significance of the closed loop system are investigated. The simulation results signify the performance of the proposed controller.

Numerical approximations of fractional derivatives with applications

Abstract: Two approximations, derived from continuous expansions of Riemann–Liouville fractional derivatives into series involving integer order derivatives, are studied. Using those series, one can formally transform any problem that contains fractional derivatives into a classical problem in which only derivatives of integer order are present. Corresponding approximations provide useful numerical tools to compute fractional derivatives of functions. Application of such approximations to fractional differential equations and fractional problems of the calculus of variations are discussed. Illustrative examples show the advantages and disadvantages of each approximation. MSC 2010: 26A33, 33F05, 34A08, 49M99, 65D20.

Multiple fuzzy relation and its application to coupled fuzzy control

Abstract: Using semi-tensor product (STP) of matrix, this paper investigates the fuzzy relation of multiple fuzzy and uses this to design coupled fuzzy control is designed. First of all, under the assumption that the universe of discourse is finite, a fuzzy logical variable can be expressed as a vector, which unifies the expression of elements, subsets, and fuzzy subsets of a universe of discourse. Then, the matrix expression of set mappings is naturally extended to fuzzy sets. Second, based on STP, logic-based matrix addition and product are proposed. These are particulary useful for the calculation of compounded fuzzy relations. Third, a dual fuzzy structure is introduced, which assures the finiteness of the universe of discourse, and is used for fuzzification and defuzzification. Finally, using the results obtained, a new technique is developed to design a coupled fuzzy controller for multi-input multi-output (MIMO) systems with coupled multiple fuzzy relations.

Dα‐Type Iterative Learning Control for Fractional‐Order Linear Time‐Delay Systems

Abstract: This paper presents a second order -type iterative learning control (ILC) scheme for a class of fractional-order linear time-delay systems with fractional order α (0 ≤ α < 1). First, by analyzing the control and learning processes, a discrete system for -type ILC is established. Then, ILC design problem is converted to a stabilization problem for such a discrete system. Next, by introducing the (λ, ξ)-norm and using a generalized Gronwall-Bellman lemma, the sufficient condition for the robust convergence with respect to the bounded external disturbance of the control input and the tracking errors is obtained. Finally, the validity of the method is verified by two numerical examples.

Output Feedback Terminal Sliding Mode Control for a Class of Second Order Nonlinear Systems

Abstract: In this study, a novel output feedback terminal sliding mode control (TSMC) approach is proposed for a class of second order nonlinear systems in light of the equivalent output injection sliding mode observer (SMO) method and TSMC principle. The SMO method is applied to reconstruct full states in finite time and the non-singular TSMC algorithm is designed to stabilize system states to equilibrium points in finite time. The corresponding stability analysis is presented. An indispensable illustrative example is bench tested to validate the effectiveness of the proposed approach.

Bounded Consensus Algorithms for Multi‐Agent Systems in Directed Networks

Abstract: In this paper, the consensus problem is investigated via bounded controls for the multi-agent systems with or without communication. Based on the nested saturation method, the saturated control laws are designed to solve the consensus problem. Under the designed saturated control laws, the transient performance of the closed-loop system can be improved by tuning the saturation level. First of all, asymptotical consensus algorithms with bounded control inputs are proposed for the multi-agent systems with or without communication delays. Under these consensus algorithms, the states’ consensus can be achieved asymptotically. Then, based on a kind of novel nonlinear saturation functions, bounded finite-time consensus algorithms are further developed. It is shown that the states’ consensus can be achieved in finite time. Finally, two examples are given to verify the efficiency of the proposed methods.

Robust H ∞ Control in Fast Atomic Force Microscopy

Abstract: This paper develops a robust H ∞ method for fast tracking position control problems arising in an atomic force microscope (AFM). A commercial type NT-MDT AFM is used to generate 3D images of scanned material surfaces at high speeds and accuracies. A major component of this AFM is a piezoelectric tube actuator used for position control in three directions. Due to the nature of the piezoelectric actuator, there is nonlinear hysteresis present which affects the AFM scanning qualities. The original commercial AFM uses traditional proportional-integral-derivative position control and can only obtain good quality images for scanning rates under about 20 Hz in both the x and y directions. In this paper, a robust H ∞ controller is designed based on a physical model of the AFM piezoelectric tube positioner in the x and y directions. On the electrical side of the positioning system, external capacitors are connected in series with the x and y contacts of the piezoelectric tube to provide measured voltages which are proportional to the charge on the actuator. The parameters for a nonlinear model are obtained from measurements of the system frequency response and time domain response. This model also takes into account the time delay resulting from the sensor electronics. This nonlinear model is represented as a linear uncertain system model with norm bounded uncertainty. The uncertain system model is used to design a robust H ∞ tracking controller for the AFM scanning system. Experimental results show that the robust H ∞ controller can improve the AFM scanning quality and increase the scanning speed significantly. The controller performs well in tracking a given reference scanning signal with frequencies up to 125 Hz.

Robust PID‐PSD Controller Design: BMI Approach

Abstract: A new robust proportional-integral-derivative (PID)–proportional-sum-derivative (PSD) controller design method based on linear (bilinear) matrix inequalities (LMI, BMI) is proposed for uncertain affine linear system. The design procedure guarantees the parameter dependent quadratic stability, and guaranteed cost control with a new quadratic cost function (LQRS) including the derivative term for the state vector as a tool to influence the overshoot and response rate. The second approach to the PSD controller design procedure is based on a Lyapunov function with a special term corresponding to the time-delay part of the control algorithm. The results obtained are illustrated on three examples to show the robust PID, PSD control design procedure and the influence of the choice of matrix S in the extended cost function.

Adaptive Control of the Electro‐Hydraulic Servo‐System with External Disturbances

Abstract: The paper deals with the structure of the adaptive control electro-hydraulic servo-system (EHSS) with external load disturbances, practical verification of the identification, and control algorithms. The electro-hydraulic servo system composed of a servo-cylinder controlled with a servo-valve is discussed. It is a strongly nonlinear object with parameters changing over time. Adaptive adjuster parameters were determined by means of current identification resulting in the parametric model. Identification was conducted on the basis of measurement of the controlling size and regulated size objects. The identified model of the object was applied to carry out the on-line synthesis of the proportional–integral–derivative (PID) controller. The selected problems connected with obtaining the algorithm of adaptive control are presented. The computer program for implementing the algorithm with numerical simulation and identification of the control physical model object were calculated. The aim of the research was to examine the effectiveness of the adaptive control method in an electro-hydraulic servo system, both theoretically and experimentally.

Adaptive dynamic surface control of a hypersonic flight vehicle with improved tracking

Abstract: This work presents a nonlinear adaptive dynamic surface air speed and a flight path angle control design procedure for the longitudinal dynamics of a generic hypersonic flight vehicle. The proposed design scheme takes into account the magnitude, rate, and bandwidth constraints on the actuator signals. A new approach is used to enhance tracking performance and avoid a large initial control signal. The uncertain nonlinear functions in the flight vehiclemodelareapproximatedbyusingradialbasisfunctionneuralnetworks. A detailed stability analysis of the designed controllers shows that all the signalsoftheclosed-loopsystem areuniformlyultimatelybounded.Therobust performance of the design scheme is verified through numerical simulations of the flight vehicle model for various parameter variation test cases.

Active Unbalance Control of Rotor Systems Using On‐Line Algebraic Identification Methods

Abstract: An active control scheme based on compensation of perturbation force signals is proposed to balance rotating machinery with unknown system parameters and variable operation speed. The algebraic parameter identification methodology is applied to estimate the mass, stiffness, damping, rotor eccentricity, and on-line reconstruction of the unknown centrifugal forces induced by rotor unbalance. In addition, an asymptotic estimation scheme of perturbation signals, which requires position measurements only, is proposed as another alternative to estimate such unbalance forces. Our design methodology considers that a disturbance signal can be locally approximated by a family of Taylor polynomials. Some simulation results are included to show the dynamic and robust performance of the active balancing scheme and perturbation force estimation methods proposed for a rotor-magnetic bearing system.

Quantized H∞ Control for Networked Systems with Communication Constraints

Abstract: The problem of quantized H∞ control for networked control systems (NCSs) subject to time-varying delay and multiple packet dropouts is investigated in this paper. Both the control input and the measurement output signals are quantized before being transmitted and the quantized errors are described as sector bound uncertainties. The measurement channel and the control channel packet dropouts are considered simultaneously, and the stochastic variables satisfying Bernoulli random binary distribution are utilized to model the random multiple packet dropouts. Sufficient conditions for the existence of an observer-based controller are established to ensure the exponential mean-square stablility of the closed-loop system and achieve the optimal H∞ disturbance attenuation level. By using a globally convergent algorithm involving convex optimization, the nonconvex feasibility can be solved successfully. Finally, a numerical example is given to illustrate the effectiveness and applicability of the proposed method.

Chattering Free Sliding Mode Control for Uncertain Discrete Time-Delay Singular Systems

Abstract: The problem of chattering free sliding mode control for a class of uncertain discrete singular systems with state delay is investigated in this paper. As a component of the solution, a new least squares support vector machine (LS-SVM) reaching law is proposed. In terms of linear matrix inequalities, a delay-dependent condition for sliding mode dynamics to be regular, causal, and asymptotically stable is established, and the chattering problem that appears in traditional variable structure systems is eliminated. Numerical examples are provided to demonstrate the applicability of the proposed methods.

Adaptive-Like Vibration Control in Mechanical Systems with Unknown Paramenters and Signals

Abstract: This paper describes the application of an on-line algebraic identification methodology for parameter and signal estimation in vibrating mechanical systems. An important property of the algebraic identification is that the parameter identification is not asymptotic but algebraic, that is, the parameters are computed as fast as the system dynamics are being excited by some external input or by changes in the initial conditions. The algebraic identification is then employed to estimate mass, stiffness, and viscous damping in simple mechanical systems using only position measurements. This approach is also used in the identification of frequency, phase, and amplitude of exogenous vibrations affecting a mechanical system. The algebraic identification is then combined with a certainty equivalence controller to asymptotically stabilize the system response and, simultaneously, cancel harmonic vibrations. The proposed adaptive-like control scheme is fast and robust against unknown parameters and frequency variations. Some numerical and experimental results illustrate the dynamic and robust performance of the algebraic identification and the active vibration controller.

Variable Order Fractional Controllers

Abstract: This paper addresses variable order fractional controllers. Four situations where variable order fractional controllers may be used to cope with time-varying plants are used as examples. In all cases a constant phase margin is sought, thus resulting in a constant overshoot in step responses, which is otherwise unattainable. The first two examples concern first generation Crone controllers for plants with time-varying gains. The other two examples concern a logarithmic phase Crone controller for a plant with time-varying poles and gain. Numerical simulation results are given for all examples.

Design and Implementation of a Flight Control System for an Unmanned Rotorcraft using RPT Control Approach

Abstract: In this paper, we apply a so-called robust and perfect tracking (RPT) control technique to the design and implementation of the flight control system of a miniature unmanned rotorcraft, named HeLion. To make the presented work self-contained, we will first outline some background knowledge, including mainly the nonlinear flight dynamics model and the inner-loop flight control system design. Next, the highlight of this paper, that is, the outer-loop flight control system design procedure using RPT control technique, will be detailed. Generally speaking, RPT control technique aims to design a controller such that (i) the resulting closed-loop system is asymptotically stable, and (ii) the controlled output almost perfectly tracks a given reference signal in the presence of any initial conditions and external disturbances. Since it makes use of all possible information including the system measurement output and the command reference signal together with all its derivatives (if available) for control, RPT control technique is particularly useful for the outer-loop layer of an unmanned aircraft. Both simulation and flight-test results will be presented and analyzed at the end of this paper, and the efficiency of the RPT control approach will be evaluated comprehensively.

Set‐point weight tuning rules for fractional‐order PID controllers

Abstract: The problem of tuning the set-point weight for fractional-order proportional-integral-derivative (FOPID) controllers is addressed in this paper. Tuning rules are given in order to use the set-point weight effectively for the recovering of the set-point following performance when the FOPID controller is tuned in order to optimize the load disturbance rejection performance. Self-regulating, integral and unstable processes are considered. Simulation results show the effectiveness of the proposed tuning rules and the comparison with integer-order PID controllers.

Reliable Dissipative Control for Singular Markovian Systems

Abstract: In this paper, the problem of reliable dissipative control is investigated for a continuous-time singular Markovian system with actuator failure. First, a sufficient condition is established in terms of linear matrix inequalities (LMIs), which guarantees a singular Markovian system to be stochastically admissible and strictly (Q,S,R)-dissipative. Based on this criterion, a state feedback controller design method is given in terms of strict LMIs. Moreover, the dissipative control results include the results of H ∞ control and passive control as special cases. The effectiveness of the controller designed method in this paper is illustrated by a numerical example.

Robust Saturated PI Joint Velocity Control for Robot Manipulators

Abstract: It is well known that many industrial manipulators use an embedded linear proportional-integral (PI) joint velocity controller to guarantee motion control through proper velocity commands. However, although this control scheme has been very successful in practice, not much attention has been paid to designing new PI velocity control structures. The problem of analyzing a saturated PI velocity joint velocity controller is addressed in this paper. By using the theory of singularly perturbed systems, the closed-loop system is studied. The robot dynamics assumed in this paper take into account bounded time–varying disturbances which may include the friction at the joints. An experimental study in a planar two degrees-of-freedom direct-drive robot is also presented, confirming the advantage of the new saturated PI joint velocity controller.

A New Observer‐Type Consensus Protocol for Linear Multi‐Agent Dynamical Systems

Abstract: The consensus problem is investigated in this paper for a class of multi-agent systems with general linear node dynamics and directed communication topologies. A new distributed observer-type consensus protocol is designed based only on the relative output measurements of neighboring agents. Compared with existing observer-type protocols, the one presented here does not require information about the relative states of the observers. Tools from small gain theory and matrix analysis, some sufficient conditions are obtained for achieving consensus in such multi-agent systems where the underlying network topology contains a directed spanning tree. Finally, some numerical examples including an application in low-Earth-orbit satellite formation flying are provided to illustrate the theoretical results.

Switched State Model Predictive Control of Fractional-Order Nonlinear Discrete-Time Systems

Abstract: Model predictive control is one of the more effective and frequently employed-in-industry control methods, especially for multiple input multiple output (MIMO) processes, in which a dynamic model of the process is used to predict its behavior over some time horizon and to determine the optimal future control policy. In this paper, a novel predictive algorithm for advanced process control for nonlinear and/or uncertain fractional-order discrete-time processes is proposed. First, a state model predictive controller for MIMO linear fractional-order discrete-time systems is introduced, and then the concept is extended to MIMO nonlinear and uncertain fractional-order processes which can be modeled by means of linear multimodels of fractional order. The algorithm is based on fast model selection to cope with process uncertainty and represents a class of so-called switched systems. Finally, a simulation example is provided.

Descriptor Fractional Linear Systems with Regular Pencils

Abstract: New classes of descriptor fractional continuous-time and discrete-time linear systems with regular pencils are introduced. Electrical circuits are an example of descriptor fractional continuous-time systems. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and Laplace transformation the solution to the state equation of descriptor fractional linear systems is derived. It is shown that every electrical circuit is a descriptor fractional systems if it contains at least one mesh consisting of branches with only ideal supercondensators and voltage sources, or at least one node with branches containing supercoils. Using the Weierstrass regular pencil decomposition the solution to the state equation of descriptor fractional discrete-time linear systems is derived. A method for decomposition of the descriptor fractional linear systems with regular pencils into dynamic and static parts is proposed. The considerations are illustrated by numerical examples.

Optimal Vibration Control for Vehicle Active Suspension Discrete‐Time Systems with Actuator Time Delay

Abstract: This study researches the vibration control approach for vehicle active suspension discrete-time systems with actuator time delay under road disturbances. First, the discrete-time models for the quarter vehicle active suspension system with actuator time delay are presented, and road disturbances are considered as the output of an exosystem. By introducing a discrete variable transformation, the discrete-time system with actuator time delay and the quadratic performance index are transformed into equivalent ones without the explicit appearance of time delays. Then, the problem of original vibration control with actuator time delay is transformed into the optimal vibration control for a non-delayed system with respect to the transformed performance index. Based on the maximum principle, the feedforward and feedback optimal vibration control law is obtained from Riccati and Stein equations. The existence and uniqueness of the optimal control law is proved. A reduced-order observer is constructed to solve the physically realizable problem of the feedforward compensator. Finally, the feasibility and effectiveness of the proposed approaches are validated by a numerical example.

A Quasi-Sliding Mode Observer-based Controller for PMSM Drives

Abstract: In this paper a quasi-sliding mode control for a permanent magnet synchronous motor (PMSM) is proposed where a cascade control scheme based on a properly designed state observer provides accurate speed tracking performance. The ultimate boundedness of both the observation error and the speed tracking error is proven. The controller performance has been validated using hardware in the loop (HIL) tests on a simulator based on the model of a commercial PMSM drive. Tests show that the proposed observer-based controller produces good speed trajectory tracking performance and it is robust in the presence of disturbances affecting the system.

Hybrid Model Predictive Power Management of A Fuel Cell‐Battery Vehicle

Abstract: This paper considers optimal power management of a fuel cell-battery hybrid vehicle (FCHV) powertrain having three distinct modal configurations (modes): electric motor propelling/battery discharging, propelling/charging, and generating/charging. Each mode has a distinct set of dynamics and constraints. Using component dynamical/algebraic models appropriate to power flow management, the paper develops a supervisory-level switched system model as an interconnection of subsystems. Given the model, the paper sets forth a hybrid model predictive control strategy based on a minimization of a performance index (PI) that trades off tracking and fuel economy in each operational mode. Specifically, the PI trades off velocity tracking error, battery state of charge variance, and electric drive and hydrogen fuel usages while penalizing frictional braking to encourage regenerative braking. The optimization is performed using an embedded system model and collocation with matlab's fmincon to compute mode switches and continuous time controls. The methodology avoids the computational complexity of alternate approaches based on, e.g., mixed integer programming. Projection methods for approximating the switched system solution from the embedded solution are empirically evaluated. To demonstrate the methodology, an example of a FCHV is simulated using three standard velocity driving profiles: a sawtooth profile with a hill climb, the EPA urban dynamic driving schedule, and the New European Driving Cycle. Also, drive cycle fuel usage is compared to that from the Equivalent Consumption Minimization Strategy.