Dynamic Controller Synthesis Research Articles

A dynamic controller synthesis methodology for negative imaginary systems using the internal model control principle

This paper proposes a new controller design methodology for stable and minimum-phase Negative Imaginary (NI) systems relying on the classical Internal Model Control (IMC) principle. The closed-loop stability of the proposed scheme depends only on the DC loop gain, which is theoretically justified by the feedback stability results of the NI theory. The main objective is to design the Youla parameter of an IMC scheme, which has been cast as a Negative Imaginary (NI) controller synthesis problem. Two different methodologies have been proposed. A frequency-domain IMC design approach is first presented, which depends on solving a constrained, linear, least-square estimation problem. Then, an LMI-based methodology is developed, which can be solved by the commercially available SDP solver packages. An in-depth simulation case study on the vibration attenuation problem of a lightweight cantilever beam (a potential application of the NI theory) was carried out to demonstrate the usefulness of the NI-based IMC design methodology. Finally, the simulation results were experimentally validated on a custom-made vibration suppressor to confirm the feasibility of the proposed scheme.

Nonlinear dynamic analysis and control synthesis for the Swinging Omnidirectional (SWINGO) Wave Energy Converter

We introduce, in this paper, an analysis of the dynamics of the Swinging Omnidirectional (SWINGO) wave energy converter. Such a device is an inertial reacting Wave Energy Converter (WEC), that exploits the dynamics of a gyropendulum mechanism which, being excited by the wave-induced whirling motion (i.e. coupling between pitch and roll on a floater), can successively activate an electric generator connected to the grid. In particular, we apply the harmonic balance method, tuned to the system fundamental harmonic, to identify the effect of nonlinearities on the SWINGO dynamics and their impact on energy production. Furthermore, we present the so-called van der Pol plane to assess the stability properties of the system. The SWINGO model is derived via a Lagrangian approach formulated with respect to quasi-coordinates. We demonstrate that multi-stability behaviour can be found for this nonlinear system, completely absent in its associated linearisation. Finally, we synthesise so-called ‘passive’ (i.e. proportional) energy-maximising controllers by leveraging the Harmonic Balance (HB) procedure, providing control parameters which are effectively tuned by exploiting the presented nonlinear description of SWINGO.

A Contract Theory Approach to Dynamic Incentive Mechanism and Control Synthesis for Moral Hazard in Power Grids

This article proposes a synthesis of a novel dynamic incentive mechanism and optimal control for moral hazard in power grids with real-time power balancing markets. For the liberalization of the balancing markets, it is an indispensable requirement to integrate dynamic subsystems controlled by individual agents into a stabilized power grid via an incentive mechanism. Meanwhile, without the proper use of the agents’ private information, high-speed market-clearing achieving an appropriate social objective cannot be ensured. Consequently, a market mechanism is needed that contains some dynamic incentive mechanisms for eliciting their private information and proper controls under moral hazard, which is called incentivizing market in this article. Drawing on dynamic contract theory in microeconomics, a novel method for designing the incentivizing market is proposed on the basis of the integration of economic models and a dynamic grid model. Conventional contract problems have been analyzed for both static and dynamic systems whose control inputs are operated directly by an independent system operator. However, these analyses do not accord with the design for the dynamic incentive mechanism in the incentivizing market. The approach in this article requires adapting the dynamic contract problems to the market. To achieve this objective, the fundamental formulas for optimal design are established and the basic properties of the designed market based on a model-based approach are clarified. We next propose optimal pricing and control synthesis for social-objective designs. The performance of our proposed method is illustrated through simulations with an Institute of Electrical Engineers of Japan (IEEJ) East 30-machine system.

Dynamic analysis and performance assessment of the Inertial Sea Wave Energy Converter (ISWEC) device via harmonic balance

Given the particular energy-maximising performance objective, wave energy converter (WEC) systems are prone to exhibit highly nonlinear behaviour. We present, in this paper, a detailed dynamic analysis and control synthesis for the Inertial Sea Wave Energy Converter (ISWEC) system, deriving and considering a comprehensive associated nonlinear model. In particular, we adopt a harmonic balance (HB) method to achieve this objective, producing the so-called amplitude-frequency curves (AFC) for the corresponding ISWEC nonlinear model, derived via a Lagrangian approach. We demonstrate that the system can present a variety of different behaviours which are completely neglected by its linear model counterpart. Leveraging both the efficiency, and convenient representation of the HB method, we synthesise so-called ‘passive’ (i.e. proportional) energy-maximising controllers using a variety of input conditions. We provide a comparison of the obtained control parameters with those arising from standard linear modelling, showing a consistent improvement in performance by effectively considering the relevant nonlinear ISWEC dynamics.

Reduced order dynamic controller synthesis conditions for LPV periodic discrete-time systems subject to input saturation

A method for the synthesis of reduced-order dynamic output-feedback controllers for periodic discrete-time LPV systems, subject to input saturations and external noises, is proposed in this paper. The controllers are designed to guarantee the robustness of the closed-loop system to exogenous noises, achieved through the minimization of a bound for the L2 gain. The proposed method is based on a two-stage procedure, where a state-feedback gain is computed in the first stage and then applied on the second step to generate the desired controller. A third stage is then developed to synthesize an anti-windup compensation to deal with the input saturation, but since the controller is not fixed in this step, the control system dynamics can be redesigned to better aggregate the desired robustness to the external noises and input saturation, decreasing the conservativeness of the technique. The validity of the proposed method is validate through a numerical example.

Optimum Parametric Identification of a Stand-Alone Photovoltaic System with Battery Storage and Optimization Controller Using Averaging Approach

The dimensioning of photovoltaic systems is the major concern of researchers and power industry practitioners. This aims to improve energy efficiency and protect the conversion units by a consistent assessment of power conditioning circuits and interconnections for the PV application. In this context, this paper sets out to fulfill detailed modeling and control steps of a standalone photovoltaic (PV) power system with energy storage, according to practical specifications of the load, PV generation unit, and battery pack. The main goal is to estimate all unknown parameters, as the diode ideality factor and revers saturation current, the controller, and the PV link. The PV link interfacing the PV source circuit to the PV-side converter (PVSC) provides a filtering function to maintain a steady voltage at the link. The charge controller used in the PV-side converter is a DC/DC buck converter. It transfers the PV power to the battery and supplies the load. Using pulse- width modulation (PWM) technical, of which the switching duty cycle is the control-input variable; the PVSC power-conditioning circuit is permanently controlled by the maximum power point tracking (MPPT) algorithm to achieve the maximum energy. The battery pack voltage is properly maintained by the charge controller and specified to match the load voltage rating, to avoid a high ratio of voltage conversion. A method is proposed to integrate both the MPPT function and the battery cycle charge. The PV generator output and the power conditioning circuits, mainly constructed from switching- mode power converters, are nonlinear. An averaged model is then derived for dynamic analysis and controller synthesis, using the state-space averaging and linearization method. A PV array of nine PV modules configured into three strings is used in this application to demonstrate the effectiveness of modeling, design, control, and simulation. Simulation model for the controller and power interface is built and developed in short term, using the fundamental blocks of Matlab Simulink.

Dynamic Programming and Control Synthesis for Variational Problems with Polynomial Impulses

Abstract The paper suggests a framework of control synthesis (feedback) for differential systems driven by nonlinear impulses. We propose a simple but relevant notion of control synthesis and a related concept of sampling solution. For extremal problems stated for input-polynomial systems, we fix two connected issues: establish the dynamic programming principle, including the characterization of the value function and verification theorem (sufficient optimality condition), and design an optimal synthesis procedure. Finally, we discuss a different, to some extent “dual” to the verification theorem, issue — a sufficient condition for non-optimality, — which performs an application of the control synthesis to discarding non-optimal extrema of the impulsive maximum principle.

Observer-based dynamic surface control for high-performance aircraft subjected to unsteady aerodynamics and actuator saturation

In this article, a novel observer-based dynamic surface control scheme is designed for high-performance aircraft attitude tracking in the presence of model uncertainties, unsteady aerodynamics and actuator saturation. Attitude dynamics with unsteady effects is first established to improve model accuracy, of which properties are investigated via open-loop analysis. Based on the compound observer, precise estimation of model uncertainties and unsteady states are achieved simultaneously. The magnitude and rate saturation are approximated by sigmoid function and addressed separately in dynamic surface control synthesis, where two auxiliary subsystems are employed as well to describe the constrained actuator dynamics and solve the non-affine issue, respectively. By using adaptive laws and first-order filters, estimate and approximate errors are robust compensated and the “explosion of terms” problem is also eliminated. Moreover, tracking error can be adjusted to arbitrarily small by choosing proper design parameters. The robustness and effectiveness of the proposed control scheme are verified by numerical simulations.

Fingertip Radius Effect of an on-Surface-Manipulated Object

Cooperative arms are two or more arms in series which assume the structure of a parallel robot on account of gripping an intermediary object, and are commonly used in accurate assembly industries, coaxialization, movement of object, etc. Gripping an intermediary object is one of the complicated subjects in analysis of cooperative arms, whose analysis is mostly dependent upon the manner the object is gripped by the arms fingertips. In the case of griping objects in frictional manner, the elimination of unwanted slippage of fingertips on the object due to the environmental factors, and also the effect of the fingertips geometry on the movement equations are among the major topics in such arms analysis. The dynamic analysis and control synthesis of the undesired slippage between an object and robot fingertips in object manipulation and the effects of finger radius or geometry of the fingertip on the function dynamics and slippage control is studied in this article. The slip/roll contact model is applied in the dynamic formulation and analysis of the finger geometry the effects of which are studied using numerical simulation.

Anti-windup-based dynamic controller synthesis for lipschitz systems under actuator saturation

This paper presents a new method for simultaneous synthesis of dynamic controller and static anti-windup compensator for saturated Lipschitz systems. Thanks to the reformulated Lipschitz property, the Lipschitz systems can be transformed into LPV (linear parameter-varying) systems whose system matrices are affine in a parameter matrix. Based on the modified sector condition dealing with saturation nonlinearity, the design of a nonlinear anti-windup-based controller leads to the solvability of a set of bilinear matrix inequalities (BMI) on the vertices of a bounded convex set which can be solved by the so-called iterative linear matrix inequality (ILMI) algorithm. A numerical example is presented to illustrate the effectiveness of the proposed method.

Linear parameter varying feedforward control synthesis using parameter-dependent Lyapunov function

This paper presents the dynamic feedforward control synthesis for linear parameter varying (LPV) systems. It is assumed that all system matrices are dependent on varying parameters, which are measurable with sensor or observable. The parameters have bounded variation rates. Parameter-dependent Lyapunov function is used for the feedforward control synthesis such that the robust stability is assured for all varying parameters at the time of the operation. The method is formulated in terms of linear matrix inequalities for LPV feedforward controller that guarantees the stability of the transfer matrix having \(L_{2}\)-gain. This compensator is designed by adding on the feedback controller in two degrees of freedom control configuration. This controller can be used for the disturbance attenuation or decreasing the tracking error. The numerical examples and simulations are given to provide the applicability of the proposed solution.

Anti-windup-based dynamic controller synthesis for nonlinear systems under input saturation

This paper describes the design of dynamic controller and static anti-windup compensator (AWC) for Lipschitz nonlinear systems under input saturation. Global and local AWC-based control schemes for stabilization of the nonlinear systems are proposed, and necessary conditions for feasibility of the control approaches are investigated. A one-step approach for simultaneous design of H∞ controller and AWC by means of linear matrix inequalities (LMIs) is presented herein, which supports multi-objective synthesis to attain stabilization or tracking, robustness against disturbance and noise, and penalization of large and high frequency control signals. This multi-objective synthesis can be accomplished by incorporating design weights, as commonly used in the standard H∞ control theory, to design a performance-oriented anti-windup-based control scheme. LMIs for the global control of the nonlinear systems subject to input saturation are derived by application of a quadratic Lyapunov function, the Lipschitz condition, the global sector condition, L2 gain reduction, substantial matrix algebra and variable transformation. In order to cope with unstable and oscillatory nonlinear systems, LMI-based local results are established using a local sector condition. Additional conditions are derived, by incorporating properties of the saturation function, to ensure well-posedness of the controller. Two simulation examples are provided to show the effectiveness of the proposed control schemes for control of stable and chaotic nonlinear systems under input saturation.

Attitude tracking control for variable structure near space vehicles based on switched nonlinear systems

An adaptive robust attitude tracking control law based on switched nonlinear systems is presented for a variable structure near space vehicle (VSNSV) in the presence of uncertainties and disturbances. The adaptive fuzzy systems are employed for approximating unknown functions in the flight dynamic model and their parameters are updated online. To improve the flight robust performance, robust controllers with adaptive gains are designed to compensate for the approximation errors and thus they have less design conservation. Moreover, a systematic procedure is developed for the synthesis of adaptive fuzzy dynamic surface control (DSC) approach. According to the common Lyapunov function theory, it is proved that all signals of the closed-loop system are uniformly ultimately bounded by the continuous controller. The simulation results demonstrate the effectiveness and robustness of the proposed control scheme.

Dynamic Analysis and Control Synthesis of Undesired Slippage of End-Effectors in a Cooperative Grasping

This paper addresses dynamic analysis and control synthesis of object grasping in a cooperative multirobot system with n-serial manipulators from an undesired slippage point of view. Two control approaches are presented in this article; a modified version of a conventional method in grasp synthesis and a new method based on a new modeling of system dynamics. A new formulation for frictional contact is used in dynamical modeling, where equality and inequality equations of the standard Coulomb friction model are all converted to a single second-order differential equation. A multiphase controller is utilized to control the object trajectory tracking as well as object slippage in the new control approach. Performance and robustness of both approaches are studied numerically. The results show superiority of the new method and its desirable and excellent performance.

Discrete-Time LPV Controller Synthesis Using Dilated LMIs with Application to an Arm-Driven Inverted Pendulum

AbstractThis paper considers the synthesis of linear parameter-varying controllers based on dilated linear matrix inequalities (LMIs). It is an extension of robust output feedback dynamic controller synthesis based on dilated LMIs. The parameters are assumed to vary inside a convex polytope. Introducing a slack variable allows the separation between system matrices and a Lyapunov matrix and enables the use of a parameter-dependent Lyapunov function. The linear parameter-varying controller obtained by the proposed method does not require a bound on the rate of change of variation of the scheduling parameters in real time, which make the linear parameter-varying controller synthesis approach more practical. The main idea is to have a simple less conservative method based on a parameter-dependent Lyapunov function so that to apply it experimentally. The efficiency of the method is illustrated with experimental results on an Arm- Driven Inverted Pendulum.

Dynamic Simulation and Control of a Continuous Bioreactor Based on Cell Population Balance Model

Saccharomyces cerevisiae (baker's yeast) can exhibit sustained oscillations during the operation in a continuous bioreactor that adversely affects its stability and productivity. Because of heterogeneous nature of cell populations, the cell population balance equation (PBE) can be used to capture the dynamic behavior of such cultures. In this work, an unstructured- segregated model is used for dynamic simulation and controller synthesis. The mathematical model consists of a partial integro-differential equation describing the dynamics of the cell mass distribution (PBE) and an ordinary integro-differential equation accounting for substrate consumption. In order to solve the mathematical model, three methods, finite difference, orthogonal collocation on finite elements and Galerkin finite element are used to approximate the PBE model by a coupled set of nonlinear ordinary differential equations (ODEs). Then the resulted ODEs are solved by 4 th order Rung-Kutta method. The results indicated that the orthogonal collocation on finite element not only is able to predict the oscillating behavior of the cell culture but also needs much little time for calculations. Therefore this method is preferred in comparison with other methods. In the next step two controllers, a globally linearizing control (GLC) and a conventional proportional-integral (PI) controller are designed for controlling the total cell mass per unit volume, and performances of these controllers are compared through simulation. The results showed that although the PI controller has simpler structure, the GLC has better performance.

Dynamic Analysis and Control Synthesis of a Link-Based Dolphin-Like Robot Capable of Three-Dimensional Movements

This paper presents a three-dimensional (3-D) dynamic model for a self-propelled, multilink dolphin-like robot to predict the dynamic behaviors of the bio-inspired artificial dolphin system within the framework of multibody dynamics. The propulsive structure mimicking dorsoventral motion includes a multilink tail and a flexibly oscillating fluke moving in coordination, as well as a pair of mechanical flippers performing flapping movements. This configuration can practically be simplified as an open-chain, tree-like multibody with a mobile base. The Schiehlen method is then employed to formulate the equations of motion based on the well-integrated kinematic and dynamic analyses of propulsive elements. Several locomotor behaviors, via coordinated control of the propulsors, can be principally replicated and numerically evaluated. Comparative results between simulations and experiments on forward swimming and combined motions are shown to demonstrate the effectiveness of the created model and locomotion control methods for dolphin-like swimming.

LMI-based Periodically Time-Varying Dynamical Controller Synthesis for Discrete-Time Uncertain Linear Systems

In this paper, we propose a new LMI-based method for robust state-feedback controller synthesis of discrete-time linear periodic/time-invariant systems subject to polytopic uncertainties. In stark contrast with existing approaches that are confined to static controller synthesis, we explore dynamic controller synthesis and reveal a particular periodically time-varying dynamical controller structure that allows LMI-based synthesis. In particular, we prove rigorously that the proposed design method encompasses the well-known extended-LMI-based design methods as particular cases. Through numerical experiments, we demonstrate that the suggested design method is indeed effective to achieve less conservative results.

Dynamic Analysis and Control Synthesis of Grasping and Slippage of an Object Manipulated by a Robot

Grasping an object by a cooperating system such as multi-fingered hands and multi-manipulator robotic system has received much attention. Research has focused on analysis of force-closure grasps and the synthesis of optimal grasping, when there is no slipping condition. Although the control system is designed to keep the contact force in the friction cone and avoid the slipping condition, slippage can occur for many reasons. In this research, dynamics analysis and control synthesis of a manipulator moving an object on a horizontal surface using the contact force of an end-effector are performed considering the slipping condition. Equality and inequality equations of frictional contact conditions are replaced by a single second-order differential equation with switching coefficients in order to facilitate the dynamic modeling. Accuracy of this modeling is verified by comparing the results of the model with those of SimMech. Using this modeling of friction, a set of reduced order form is obtained for equations of motion of the system. A new method is proposed to control the object motion and the end-effector undesired slippage based on the reduced form. Finally, performance of the method is evaluated both numerically and experimentally.

Cell population balance modeling and control in continuous bioreactors

In this work we address the problem of controlling different moments of the cell mass distribution using cell population balance modeling for the derivation of appropriate nonlinear feedback control laws. The mathematical model used for dynamic simulation and controller synthesis consists of a partial integro-differential equation describing the dynamics of the cell mass distribution and an ordinary integro-differential equation accounting for substrate consumption. Nonlinear feedback laws that induce a desired closed-loop response for the biomass concentration (first moment), the cell density (zeroth moment) and the second moment of the cell mass distribution are developed and their performance and robustness to parameter uncertainties are tested via numerical simulations.