Development of U-model enhansed nonlinear systems

Nonlinear control system design has been widely recognised as a challenging issue where the key objective is to develop a general model prototype with conciseness, flexibility and manipulability, so that the designed control system can best match the required performance or specifications. As a generic systematic approach, U-model concept appeared in Prof. Quanmin Zhu’s Doctoral thesis, and U-model approach was firstly published in the journal paper titled with ‘U-model based pole placement for nonlinear plants’ in 2002.The U-model polynomial prototype precisely describes a wide range of smooth nonlinear polynomial models, defined as a controller output u(t-1) based time-varying polynomial models converted from the original nonlinear model. Within this equivalent U-model expression, the first study of U-model based pole placement controller design for nonlinear plants is a simple mapping exercise from ordinary linear and nonlinear difference equations to time-varying polynomials in terms of the plant input u(t-1). The U-model framework realised the concise and applicable design for nonlinear control system by using such linear polynomial control system design approaches.Since the first publication, the U-model methodology has progressed and evolved over the course of a decade. By using the U-model technique, researchers have proposed many different linear algorithms for the design of control systems for the nonlinear polynomial model including; adaptive control, internal control, sliding mode control, predictive control and neural network control. However, limited research has been concerned with the design and analysis of robust stability and performance of U-model based control systems.This project firstly proposes a suitable method to analyse the robust stability of the developed U-model based pole placement control systems against uncertainty. The parameter variation is bounded, thus the robust stability margin of the closed loop system can be determined by using LMI (Linear Matrix Inequality) based robust stability analysis procedure. U-block model is defined as an input output linear closed loop model with pole assignor converted from the U-model based control system. With the bridge of U-model approach, it connects the linear state space design approach with the nonlinear polynomial model. Therefore, LMI based linear robust controller design approaches are able to design enhanced robust control system within the U-block model structure.With such development, the first stage U-model methodology provides concise and flexible solutions for complex problems, where linear controller design methodologies are directly applied to nonlinear polynomial plant-based control system design. The next milestone work expands the U-model technique into state space control systems to establish the new framework, defined as the U-state space model, providing a generic prototype for the simplification of nonlinear state space design approaches.The U-state space model is first described as a controller output u(t-1) based time-varying state equations, which is equivalent to the original linear/nonlinear state space models after conversion. Then, a basic idea of corresponding U-state feedback control system design method is proposed based on the U-model principle. The linear state space feedback control design approach is employed to nonlinear plants described in state space realisation under U-state space structure. The desired state vectors defined as xd(t), are determined by closed loop performance (such as pole placement) or designer specifications (such as LQR). Then the desired state vectors substitute the desired state vectors into original state space equations (regarded as next time state variable xd(t) = x(t) ). Therefore, the controller output u(t-1) can be obtained from one of the roots of a root-solving iterative algorithm.A quad-rotor rotorcraft dynamic model and inverted pendulum system are introduced to verify the U-state space control system design approach for MIMO/SIMO system. The linear design approach is used to determine the closed loop state equation, then the controller output can be obtained from root solver. Numerical examples and case studies are employed in this study to demonstrate the effectiveness of the proposed methods

On Stabilization of Cart-Inverted Pendulum System: An Experimental Study

The Cart-Inverted Pendulum System (CIPS) is a classical benchmark control problem. Its dynamics resembles with that of many real world systems of interest like missile launchers, pendubots, human walking and segways and many more. The control of this system is challenging as it is highly unstable, highly non-linear, non-minimum phase system and underactuated. Further, the physical constraints on the track position control voltage etc. also pose complexity in its control design. The thesis begins with the description of the CIPS together with hardware setup used for research, its dynamics in state space and transfer function models. In the past, a lot of research work has been directed to develop control strategies for CIPS. But, very little work has been done to validate the developed design through experiments. Also robustness margins of the developed methods have not been analysed. Thus, there lies an ample opportunity to develop controllers and study the cart-inverted pendulum controlled system in real-time. The objective of this present work is to stabilize the unstable CIPS within the different physical constraints such as in track length and control voltage. Also, simultaneously ensure good robustness. A systematic iterative method for the state feedback design by choosing weighting matrices key to the Linear Quadratic Regulator (LQR) design is presented. But, this yields oscillations in cart position. The Two-Loop-PID controller yields good robustness, and superior cart responses. A sub-optimal LQR based state feedback subjected to H∞ constraints through Linear Matrix Inequalities (LMIs) is solved and it is observed from the obtained results that a good stabilization result is achieved. Non-linear cart friction is identified using an exponential cart friction and is modeled as a plant matrix uncertainty. It has been observed that modeling the cart friction as above has led to improved cart response. Subsequently an integral sliding mode controller has been designed for the CIPS. From the obtained simulation and experiments it is seen that the ISM yields good robustness towards the output channel gain perturbations. The efficacies of the developed techniques are tested both in simulation and experimentation. It has been also observed that the Two-Loop PID Controller yields overall satisfactory response in terms of superior cart position and robustness. In the event of sensor fault the ISM yields best performance out of all the techniques

Dynamic balance and walking control of biped mechanisms

The research presented here focuses on the development of a feedback control systems for locomotion of two and three dimensional, dynamically balanced, biped mechanisms. The main areas to be discussed are: development of equations of motion for multibody systems, balancing control, walking cycle generation, and interactive computer graphics. Additional topics include: optimization, interface devices, manual control methods, and ground contact force generation;Planar (2D) and spatial (3D) multibody system models are developed in this thesis to handle all allowable ground support conditions without system reconfiguration. All models consist of lower body segments only; head and arm segments are not included. Model parameters for segment length, mass, and moments of inertia are adjustable. A ground contact foot model simulates compression compliance and allows for non-uniform surfaces. In addition to flat surfaces with variable friction coefficients, the systems can adapt to inclines and steps;Control techniques are developed that range from manual torque input to automatic control for several types of balancing, walking, and transitioning modes. Balancing mode control algorithms can deal with several types of initial conditions which include falling and jumping onto various types of surfaces. Walking control state machines allow selection of steady-state velocity, step size, and/or step frequency;The real-time interactive simulation software developed during this project allows the user to operate the biped systems within a 3D virtual environment. In addition to presenting algorithms for interactive biped locomotion control, insights can also be drawn from this work into the levels of required user effort for tasks involving systems controlled by simultaneous user inputs;Position and ground reaction force data obtained from human walking studies are compared to walking data generated by one of the more complex biped models developed for this project

Vibration, Control and Stability of Dynamical Systems

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

A MECHANISTIC APPROACH TO POSTURAL DEVELOPMENT IN CHILDREN

Upright standing is intrinsically unstable and requires active control. The central nervous system's feedback process is the active control that integrates multi-sensory information to generate appropriate motor commands to control the plant (the body with its musculotendon actuators). Maintaining standing balance is not trivial for a developing child because the feedback and the plant are both developing and the sensory inputs used for feedback are continually changing. Knowledge gaps exist in characterizing the critical ability of adaptive multi-sensory reweighting for standing balance control in children. Furthermore, the separate contributions of the plant and feedback and their relationship are poorly understood in children, especially when considering that the body is multi-jointed and feedback is multi-sensory. The purposes of this dissertation are to use a mechanistic approach to study multi-sensory abilities of typically developing (TD) children and children with Developmental Coordination Disorder (DCD). The specific aims are: 1) to characterize postural control under different multi-sensory conditions in TD children and children with DCD; 2) to characterize the development of adaptive multi-sensory reweighting in TD children and children with DCD; and, 3) to identify the plant and feedback for postural control in TD children and how they change in response to visual reweighting. In the first experiment (Aim 1), TD children, adults, and 7-year-old children with DCD are tested under four sensory conditions (no touch/no vision, with touch/no vision, no touch/with vision, and with touch/with vision). We found that touch robustly attenuated standing sway in all age groups. Children with DCD used touch less effectively than their TD peers and they also benefited from using vision to reduce sway. In the second experiment (Aim 2), TD children (4- to 10-year-old) and children with DCD (6- to 11-year-old) were presented with simultaneous small-amplitude touch bar and visual scene movement at 0.28 and 0.2 Hz, respectively, within five conditions that independently varied the amplitude of the stimuli. We found that TD children can reweight to both touch and vision from 4 years on and the amount of reweighting increased with age. However, multi-sensory fusion (i.e., inter-modal reweighting) was only observed in the older children. Children with DCD reweight to both touch and vision at a later age (10.8 years) than their TD peers. Even older children with DCD do not show advanced multisensory fusion. Two signature deficits of multisensory reweighting are a weak vision reweighting and a general phase lag to both sensory modalities. The final aim involves closed-loop system identification of the plant and feedback using electromyography (EMG) and kinematic responses to a high- or low-amplitude visual perturbation and two mechanical perturbations in children ages six and ten years and adults. We found that the plant is different between children and adults. Children demonstrate a smaller phase difference between trunk and leg than adults at higher frequencies. Feedback in children is qualitatively similar to adults. Quantitatively, children show less phase advance at the peak of the feedback curve which may be due to a longer time delay. Under the high and low visual amplitude conditions, children show less gain change (interpreted as reweighting) than adults in the kinematic and EMG responses. The observed kinematic and EMG reweighting are mainly due to the different use of visual information by the central nervous system as measured by the open-loop mapping from visual scene angle to EMG activity. The plant and the feedback do not contribute to reweighting

Probabilistic models for data efficient reinforcement learning

Trial-and-error based reinforcement learning (RL) has seen rapid advancements in recent times, especially with the advent of deep neural networks. However, the standard deep learning methods often overlook the progress made in control theory by treating systems as black-box. We propose a model-based RL framework based on probabilistic Model Predictive Control (MPC). In particular, we propose to learn a probabilistic transition model using Gaussian Processes (GPs) to incorporate model uncertainty into long-term predictions, thereby, reducing the impact of model errors. We provide theoretical guarantees for first-order optimality in the GP-based transition models with deterministic approximate inference for long-term planning. We demonstrate that our approach not only achieves the state-of-the-art data efficiency, but also is a principled way for RL in constrained environments. When the true state of the dynamical system cannot be fully observed the standard model based methods cannot be directly applied. For these systems an additional step of state estimation is needed. We propose distributed message passing for state estimation in non-linear dynamical systems. In particular, we propose to use expectation propagation (EP) to iteratively refine the state estimate, i.e., the Gaussian posterior distribution on the latent state. We show two things: (a) Classical Rauch-Tung-Striebel (RTS) smoothers, such as the extended Kalman smoother (EKS) or the unscented Kalman smoother (UKS), are special cases of our message passing scheme; (b) running the message passing scheme more than once can lead to significant improvements over the classical RTS smoothers. We show the explicit connection between message passing with EP and well-known RTS smoothers and provide a practical implementation of the suggested algorithm. Furthermore, we address convergence issues of EP by generalising this framework to damped updates and the consideration of general -divergences. Probabilistic models can also be used to generate synthetic data. In model based RL we use ’synthetic’ data as a proxy to real environments and in order to achieve high data efficiency. The ability to generate high-fidelity synthetic data is crucial when available (real) data is limited as in RL or where privacy and data protection standards allow only for limited use of the given data, e.g., in medical and financial data-sets. Current state-of-the-art methods for synthetic data generation are based on generative models, such as Generative Adversarial Networks (GANs). Even though GANs have achieved remarkable results in synthetic data generation, they are often challenging to interpret. Furthermore, GAN-based methods can suffer when used with mixed real and categorical variables. Moreover, the loss function (discriminator loss) design itself is problem specific, i.e., the generative model may not be useful for tasks it was not explicitly trained for. In this paper, we propose to use a probabilistic model as a synthetic data generator. Learning the probabilistic model for the data is equivalent to estimating the density of the data. Based on the copula theory, we divide the density estimation task into two parts, i.e., estimating univariate marginals and estimating the multivariate copula density over the univariate marginals. We use normalising flows to learn both the copula density and univariate marginals. We benchmark our method on both simulated and real data-sets in terms of density estimation as well as the ability to generate high-fidelity synthetic data.Open Acces

Computational methods and software systems for dynamics and control of large space structures

Two key areas of crucial importance to the computer-based simulation of large space structures are discussed. The first area involves multibody dynamics (MBD) of flexible space structures, with applications directed to deployment, construction, and maneuvering. The second area deals with advanced software systems, with emphasis on parallel processing. The latest research thrust in the second area involves massively parallel computers

Control Engineering

Control means a speci?c action to reach the desired behavior of a system. In the control of industrial processes generally technological processes, are considered, but control is highly required to keep any physical, chemical, biological, communication, economic, or social process functioning in a desired manner