Papers by Gerasimos Rigatos
Intelligent industrial systems, Sep 1, 2016
Controller design for autonomous 4-wheeled ground vehicles is performed with differential flatnes... more Controller design for autonomous 4-wheeled ground vehicles is performed with differential flatness theory. Using a 3-DOF nonlinear model of the vehicle's dynamics and through the application of differential flatness theory an equivalent model in linear canonical (Brunovksy) form is obtained. For the latter model a state feedback controller is developed that enables accurate tracking of velocity setpoints. Moreover, it is shown that with the use of Kalman Filtering it is possible to dynamically estimate the disturbances due to unknown forces and torques exerted on the vehicle. The processing of velocity measurements (provided by a small number of on-board sensors) through a Kalman Filter which has been redesigned in the form of a disturbance observer results in accurate identification of external disturbances affecting the vehicle's dynamic model. By including in the vehicle's controller an additional term that compensates for the estimated disturbance forces, the vehicle's motion characteristics remain unchanged. Numerical simulation confirms the efficiency of both the proposed controller and of the disturbance forces estimator. Autonomous navigation • 4-wheeled ground vehicles • Flatness-based control • Kalman Filtering • Disturbance forces/torques estimator B G. Rigatos
Journal of Artificial Intelligence and Soft Computing Research, Oct 1, 2014
An adaptive fuzzy controller is designed for spark-ignited (SI) engines, under the constraint tha... more An adaptive fuzzy controller is designed for spark-ignited (SI) engines, under the constraint that the system's model is unknown. The control algorithm aims at satisfying the H ∞ tracking performance criterion, which means that the influence of the modeling errors and the external disturbances on the tracking error is attenuated to an arbitrary desirable level. After transforming the SI-engine model into the canonical form, the resulting control inputs are shown to contain nonlinear elements which depend on the system's parameters. The nonlinear terms which appear in the control inputs are approximated with the use of neuro-fuzzy networks. It is shown that a suitable learning law can be defined for the aforementioned neuro-fuzzy approximators so as to preserve the closed-loop system stability. With the use of Lyapunov stability analysis it is proven that the proposed adaptive fuzzy control scheme results in H ∞ tracking performance. The efficiency of the proposed adaptive fuzzy control scheme is checked through simulation experiments.
Intelligent industrial systems, Oct 1, 2016
The article proposes a method for nonlinear control of the dynamical system that is formed by a D... more The article proposes a method for nonlinear control of the dynamical system that is formed by a DC-DC converter and a DC motor, making use of differential flatness theory. First it is proven that the aforementioned system is differentially flat which means that all its state vector elements and its control inputs can be expressed as differential functions of primary state variables which are defined to be the system's flat outputs. By exploiting the differential flatness properties of the model its transformation to a linearized canonical (Brunovsky) form becomes possible. For the latter description of the system one can design a stabilizing feedback controller. Moreover, estimation of the nonmeasurable state vector elements of the system is achieved by applying a new nonlinear Filtering method which is known as Derivative-free nonlinear Kalman Filter. This filter consists of the Kalman Filter recursion applied on the linearized equivalent model of the system and of an inverse transformation that is based on differential flatness theory and which B G. Rigatos
Research Square (Research Square), May 22, 2023
The article proposes a nonlinear optimal control method for the dynamic model of the parallel dou... more The article proposes a nonlinear optimal control method for the dynamic model of the parallel double inverted pendulum. Three different forms of this system are considered: (i) two poles mounted on the same cart resulting into a model with four state variables and one control input, (ii) two poles mounted on the same cart resulting into a model with six state variables and one control input, (iii) two different cart-pole systems connected through an elastic link, resulting into a model with eight state variables and two control inputs. To implement the proposed nonlinear optimal control method the dynamic model of the parallel double pendulum undergoes approximate linearization around a temporary operating point which is updated at each sampling instance. This operating point is defined within each sampling period by the present value of the state vector of the parallel double inverted pendulum and by the last sampled value of the control inputs vector. The linearization process is based on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. For the approximately linearized model of the parallel double inverted pendulum a stabilizing H-infinity feedback controller is designed. To compute the feedback gains of this controller an algebraic Riccati equation is also being solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. First it is demonstrated that the H-infinity tracking performance criterion holds, which signifies robustness of the control method under model uncertainty and external perturbations. Moreover, under moderate conditions it is proven that the control loop of the parallel double inverted pendulum is globally asymptotically stable. To implement state estimation-based control the H-infinity Kalman Filter is used as a robust observer. The nonlinear optimal control scheme for the parallel double inverted pendulum achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs.
Autonomous Intelligent Systems, Aug 30, 2022
Tower cranes find wide use in construction works, in ports and in several loading and unloading p... more Tower cranes find wide use in construction works, in ports and in several loading and unloading procedures met in industry. A nonlinear optimal control approach is proposed for the dynamic model of the 4-DOF underactuated tower crane. The dynamic model of the robotic crane undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the system a stabilizing optimal (H-infinity) feedback controller is designed. To compute the controller's feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed control approach is advantageous because: (i) unlike the popular computed torque method for robotic manipulators, the new control approach is characterized by optimality and is also applicable when the number of control inputs is not equal to the robot's number of DOFs, (ii) it achieves fast and accurate tracking of reference setpoints under minimal energy consumption by the robot's actuators, (iii) unlike the popular Nonlinear Model Predictive Control method, the article's nonlinear optimal control scheme is of proven global stability and convergence to the optimum.
Intelligent industrial systems, Feb 4, 2016
Control of the heat diffusion in the welded metal is of primary importance for successful welding... more Control of the heat diffusion in the welded metal is of primary importance for successful welding of high quality (the latter being a prerequisite for efficient ship building). The paper proposes a distributed parameter systems control method that is based on differential flatness theory, aiming at solving the problem of heat distribution control in the arcwelding process. Besides it proposes a nonlinear filtering method, under the name Derivative-free nonlinear Kalman Filtering for reducing the number of real-time control measurements needed to implement the feedback control loop. The stability of the control method is confirmed analytically, while its efficiency is also evaluated through simulation experiments. Ship-building • Arc welding • Heat diffusion • Differential flatness theory • Nonlinear control • Nonlinear Kalman Filtering B G. Rigatos
Journal of energy and power technology, May 11, 2023
The article aims at optimizing six-phase induction generator-based renewable energy systems (6-ph... more The article aims at optimizing six-phase induction generator-based renewable energy systems (6-phase IGs or dual star induction generators) through a novel nonlinear optimal control method. Six-phase induction generators appear to be advantageous compared to three-phase synchronous or asynchronous power generators, in terms of fault tolerance and improved power generation rates. The dynamic model of the six-phase induction generator is first written in a nonlinear and multivariable state-space form. It is proven that this model is differentially flat. The 6-phase IG is approximately linearized around a temporary operating point recomputed at each sampling interval to design the optimal controller. The linearization is based on first-order Taylor series expansion and the Jacobian matrices of the state-space model of the 6-phase IG. A stabilizing optimal (H-infinity) feedback controller is designed for the linearized state-space description of the six-phase IG. The feedback gains of the controller are computed by solving an algebraic Riccati equation at each iteration of the control method. Lyapunov analysis is used to demonstrate global stability for the control loop. The H-infinity Kalman Filter is also used as a robust state estimator, which allows for implementing sensorless control for 6-phase IG-based renewable energy systems. The nonlinear optimal control method achieves fast and accurate tracking of setpoints by the state variables of the 6-phase IG, under moderate variations of the control inputs.
International Journal of Humanoid Robotics, Oct 1, 2021
This paper proposes a nonlinear optimal control approach for mulitple degrees of freedom (DOF) br... more This paper proposes a nonlinear optimal control approach for mulitple degrees of freedom (DOF) brachiation robots, which are often used in inspection and maintenance tasks of the electric power grid. Because of the nonlinear and multivariable structure of the related state-*Corresponding author.
Intelligent industrial systems, Feb 5, 2016
The paper is concerned with proving differential flatness of the three-phase voltage source conve... more The paper is concerned with proving differential flatness of the three-phase voltage source converter (VSC) model and its resulting description in the Brunovsky (canonical) form. For the linearized canonical model of the converter a feedback controller is designed. At a second stage, a novel Kalman Filtering method (Derivative-free nonlinear Kalman Filtering) is introduced. The proposed Kalman Filter is redesigned as disturbance observer for estimating additive input disturbances to the VSC model. These estimated disturbance terms are finally used by a feedback controller that enables the DC output voltage track desirable setpoints. The efficiency of the proposed state estimation-based control scheme is tested through simulation experiments. Differential flatness theory • Observer-based control • Nonlinear dynamical systems • Disturbance estimator • Derivative-free nonlinear Kalman Filter B G. Rigatos
Advanced control for applications, Mar 15, 2022
The article proposes flatness-based control and a Kalman Filter-based disturbance observer for so... more The article proposes flatness-based control and a Kalman Filter-based disturbance observer for solving the control problem of a robotic exoskeleton under time-delayed exogenous disturbances. A two-link lower-limb robotic exoskeleton is used as a case study. It is proven that this robotic system is differentially flat. The robot is considered to be subject to unknown contact forces at its free-end which in turn generate unknown disturbance torques at its joints. It is shown that the dynamic model of the robotic exoskeleton can be transformed into the input-output linearized form and equivalently into the linear canonical Brunovsky form. This linearized description of the exoskeleton's dynamics is both controllable and observable. It allows for designing a stabilizing feedback controller with the use of the pole-placement (eigenvalues assignment) method. Moreover, it allows for solving the state estimation problem with the use of Kalman Filtering (the use of the Kalman Filter on the flatness-based linearized model of nonlinear dynamical systems is also known as Derivative-free nonlinear Kalman Filtering). Furthermore, (i) by extending the state vector of the exoskeleton after considering as additional state variables the additive disturbance torques which affect its joints and (ii) by redesigning the Kalman Filter as a disturbance observer, one can achieve the real-time estimation of the perturbations that affect this robotic system. Finally, by including in the controller of the exoskeleton additional terms that compensate for the estimated disturbance torques, the perturbations' effects can be eliminated and the precise tracking of reference trajectories by the joints of this robot can be ensured.
Intelligent industrial systems, Jun 3, 2016
An adaptive fuzzy controller is designed for a class of underactuated nonlinear robotic manipulat... more An adaptive fuzzy controller is designed for a class of underactuated nonlinear robotic manipulators, under the constraint that the system's model is unknown. The control algorithm aims at satisfying the H ∞ tracking performance criterion, which means that the influence of the modeling errors and the external disturbances on the tracking error is attenuated to an arbitrary desirable level. After transforming the robotic system into the canonical form, the resulting control inputs are shown to contain nonlinear elements which depend on the system's parameters. The nonlinear terms which appear in the control inputs are approximated with the use of neuro-fuzzy networks. It is shown that a suitable learning law can be defined for the aforementioned neuro-fuzzy approximators so as to preserve the closed-loop system stability. With the use of Lyapunov stability analysis it is proven that the proposed adaptive fuzzy control scheme results in H ∞ tracking performance. The efficiency of the proposed adaptive fuzzy control scheme is checked in the case of a 2-DOF planar robotic manipulator that has the structure of a closed-chain mechanism. Adaptive fuzzy control • Differential flatness theory • Nonlinear control • Closed-chain mechanisms • Underactuated robotic manipulators • Disturbances compensation B G. Rigatos
Robotica, 2021
The article proposes a nonlinear optimal (H-infinity) control approach for a type of underactuate... more The article proposes a nonlinear optimal (H-infinity) control approach for a type of underactuated power-line inspection robots. To implement this control scheme, the state-space model of the power-line inspection robots undergoes first approximate linearization around a temporary operating point, through first-order Taylor series expansion and through the computation of the associated Jacobian matrices. To select the feedback gains of the controller an algebraic Riccati equation is solved at each time step of the control method. The global stability properties of the control loop are proven through Lyapunov analysis. The significance of the article’s results is outlined in the following: (i) the proposed control method is suitable for treating underactuated robotic systems and in general nonlinear dynamical systems with control inputs gain matrices which are in a nonquadratic form, (ii) by achieving stabilization of the power-line inspection robots in underactuation conditions the ...
Nonlinear optimal control for Synchronous Reluctance Machines
2017 11th IEEE International Conference on Compatibility, Power Electronics and Power Engineering (CPE-POWERENG), 2017
A nonlinear H-infinity (optimal) control approach is proposed for the problem of control of Synch... more A nonlinear H-infinity (optimal) control approach is proposed for the problem of control of Synchronous Reluctance Machines (SRMs). Approximate linearization is applied to the dynamic model of the Synchronous Reluctance Machine, round a local operating point. To accomplish this linearization Taylor series expansion and the computation of the associated Jacobian matrices are performed. The robustness of the control scheme assures that the modelling error due to truncation of higher order terms from the Taylor expansion will be compensated. Next, an H-infinity feedback controller is designed. After solving an algebraic Riccati equation at each iteration of the control algorithm, the feedback gain is computed. Lyapunov stability analysis proves that the control loop satisfies an H-infinity tracking performance criterion. This in turn signifies elevated robustness to model uncertainty and external perturbations. Moreover, under moderate conditions it is proven that the control loop is globally asymptotically stable.
IET Collaborative Intelligent Manufacturing, 2021
The mechanical pulping process is non-linear and multivariable. To solve the related control prob... more The mechanical pulping process is non-linear and multivariable. To solve the related control problem, the dynamic model of the pulping process undergoes first approximate linearization around a temporary operating point which is updated at each iteration of the control algorithm. The linearization process relies on first-order Taylor series expansion and on the computation of the Jacobian matrices of the state-space model of the pulping process. For the approximately linearized description of the pulping process, a stabilizing H-infinity feedback controller is designed. To compute the controller's feedback gains, an algebraic Riccati equation is solved at each time-step of the control method. The stability properties of the control scheme are proven through Lyapunov analysis. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.
International Journal of Humanoid Robotics, 2020
The use of robotic limb exoskeletons is growing fast either for rehabilitation purposes or in an ... more The use of robotic limb exoskeletons is growing fast either for rehabilitation purposes or in an aim to enhance human ability for lifting heavy objects or for walking for long distances without fatigue. The paper proposes a nonlinear optimal control approach for a lower-limb robotic exoskeleton. The method has been successfully tested so far on the control problem of several types of robotic manipulators and this paper shows that it can also provide an optimal solution to the control problem of limb robotic exoskeletons. To implement this control scheme, the state-space model of the lower-limb robotic exoskeleton undergoes first approximate linearization around a temporary operating point, through first-order Taylor series expansion and through the computation of the associated Jacobian matrices. To select the feedback gains of the H-infinity controller an algebraic Riccati equation is solved at each time-step of the control method. The global stability properties of the control loo...
Intelligent Industrial Systems, 2016
The new issue of the Journal of Intelligent Industrial Systems presents research findings in sign... more The new issue of the Journal of Intelligent Industrial Systems presents research findings in significant areas of industrial systems technology, that is modelling, control and fault diagnosis. In the new issue, the problem of controller design for industrial systems is solved in several nontrivial cases: (i) under uncertainty about the measurements of the system's state vector elements as well as under uncertainty about disturbance inputs which are exerted on the system (ii) under uncertainty about the entire dynamical model of the system jointly with underactuation and (iii) under PDE dynamics. Differential flatness theory is the main constituent of the control approaches developed for treating the aforementioned control problems (i) to (iii). In all cases the global asymptotic stability of the control loop is demonstrated. Moreover, in this issue the problems of probabilistic modelling and neural networks-based fault diagnosis in industrial systems are also explored. It is shown that probabilistic modelling, that is description of the system's model through known statistical distributions can be used in certain cases for representing key features of industrial systems. Alternatively it is proposed to apply non-parametric estimators of the neural network type so as to extract the model of industrial systems out of data sets. Moreover, it is proposed to exploit neural networks for accomplishing fault diagnosis tasks, In such an approach the neural network is used for assigning the industrial systems' output to fault classes.
Aerospace Systems, 2019
The article proposes a nonlinear optimal (H-infinity) control method for a hypersonic aerial vehi... more The article proposes a nonlinear optimal (H-infinity) control method for a hypersonic aerial vehicle (HSV). The dynamic model of the hypersonic vehicle undergoes approximate linearization around a temporary operating point which is recomputed at each iteration of the control method. This operating point consists of the present value of the system's state vector and of the last value of the control inputs vector that was applied on the HSV. The linearization relies on Taylor series expansion and on the computation of the associated Jacobian matrices. For the approximately linearized model of the hypersonic aerial vehicle, an optimal (H-infinity) feedback controller was designed. To compute the controller's feedback gains, an algebraic Riccati equation had to be repetitively solved at each iteration of the control algorithm. The global asymptotic stability of the control method is proven through Lyapunov analysis. The control scheme remains robust against model uncertainties an external perturbations.
MATEC Web of Conferences, 2018
The problem of statistical fault diagnosis for the quadruple watertanks system is examined. The s... more The problem of statistical fault diagnosis for the quadruple watertanks system is examined. The solution of the fault diagnosis problem for the dynamic model of the four-water tanks system is a non-trivial case, due to nonlinearities and the system's multivariable structure. In the article's approach, the system's dynamic model undergoes first approximate linearization around a temporary operating point which is recomputed at each sampling period. The linearization procedure relies on Taylor series expansion and on the computation of the Jacobian matrices of the state-space description of the system. The H-infinity Kalman Filter is used as a robust state estimator for the approximately linearized model of the quadruple water tanks system. By comparing the outputs of the H-infinity Kalman Filter against the outputs measured from the real water tanks system the residuals sequence is generated. It is concluded that the sum of the squares of the residuals' vectors, being weighted by the inverse of the associated covariance matrix, stands for a stochastic variable that follows the χ 2 distribution. As a consequence, a statistical method for condition monitoring of the quadruple water tanks system is drawn, by using the properties of the χ 2 distribution and the related confidence intervals. Actually, normal functioning can be ensured as long as the value of the aforementioned stochastic variable stays within the previously noted confidence intervals. On the other side, one can infer the malfunctioning of the quadruple water tanks system with a high level of certainty (e.g. of the order of 96% to 98%), when these confidence intervals are exceeded. The article's method allows also for fault isolation, that is for identifying the specific component of the quadruple water tanks system that has been subject to fault or cyber-attack.
AIP Conference Proceedings, 2017
A flatness-based adaptive fuzzy control is applied to the problem of stabilization of the dynamic... more A flatness-based adaptive fuzzy control is applied to the problem of stabilization of the dynamics of a chaotic finance system, describing interaction between the interest rate, the investment demand and the price exponent. First it is proven that the system is differentially flat. This implies that all its state variables and its control inputs can be expressed as differential functions of a specific state variable, which is a so-called flat output. It also implies that the flat output and its derivatives are differentially independent which means that they are not connected to each other through an ordinary differential equation. By proving that the system is differentially flat and by applying differential flatness diffeomorphisms, its transformation to the linear canonical (Brunovsky) is performed. For the latter description of the system, the design of a stabilizing state feedback controller becomes possible. A first problem in the design of such a controller is that the dynamic model of the finance system is unknown and thus it has to be identified with the use of nonlinear regressors, among which neurofuzzy approximators are known to be very accurate. The estimated dynamics provided by the approximators is used in the computation of the control input, thus establishing an indirect adaptive control scheme. The learning rate of the approximators is chosen from the requirement the system's Lyapunov function to have always a negative first-order derivative. Another problem that has to be dealt with is that the control loop is implemented only with the use of output feedback. To estimate the nonmeasurable state vector elements of the finance system, a state observer is implemented in the control loop. The computation of the feedback control signal requires the solution of two algebraic Riccati equations at each iteration of the control algorithm. Lyapunov stability analysis demonstrates first that an H-infinity tracking performance criterion is satisfied. This signifies elevated robustness against modelling errors and external perturbations. Moreover, the global asymptotic stability is proven for the control loop.
Intelligent Industrial Systems, 2016
The use of efficient embedded control systems in the transportation industry and particularly in ... more The use of efficient embedded control systems in the transportation industry and particularly in turbocharged Diesel engines requires the programming of elaborated nonlinear control and filtering methods. To this end, in this paper nonlinear control for turbocharged Diesel engines is developed with the use of Differential flatness theory and adaptive fuzzy control. It is shown that the dynamic model of the turbocharged Diesel engine is differentially flat and admits dynamic feedback linearization. It is also shown that the dynamic model can be written in the linear Brunovsky canonical form for which a state feedback controller can be easily designed. To compensate for modeling errors and external disturbances an adaptive fuzzy control scheme is implemented making use of the transformed dynamical system of the diesel engine that is obtained through the application of differential flatness theory. The control algorithm aims at satisfying the H ∞ tracking performance criterion, which means that the influence of the modeling errors and the external disturbances on the tracking error is attenuated to an arbitrary desirable level. After transforming the MIMO diesel engine system into the canonical form, the resulting control inputs are shown to contain nonlinear elements which depend on the system's parameters. The nonlinear terms which appear in the control inputs are approximated with the use of neuro-B G. Rigatos
Uploads
Papers by Gerasimos Rigatos