Adaptive feedback control of time varying structures utilizing dual-core wireless sensing and actuation nodes

A nonlinear energy-based control law was flight tested on a small, fixed-wing unmanned aircraft. This paper summarizes the selected aircraft, instrumentation system, data processing techniques, system identification methods, and the control laws that were implemented. The flight test campaign used a build up approach with increasingly complex computer generated system identification excitations and then increasingly complex control laws. This build up approach allowed the team to overcome technical challenges in a progressive manner and then finally test an advanced nonlinear control law in flight. Automated multistep, frequency sweep, and multisine excitation inputs were implemented for system identification. System identification methods were leveraged to develop linear and nonlinear aerodynamic models. A servoactuator model was developed from ground test data and data processing techniques were used to condition the flight test data for analysis. A proportional-derivative attitude commanded system was implemented and tuned using pilot comments, without the use of an a priori model. A linear quadratic regulator was tuned using the linear aerodynamic model, and refined during flight tests to improve handling qualities. A port-Hamiltonian energy-based nonlinear control law was tuned in simulation using the nonlinear model, and gains refined during flight tests to improve directional tracking and perturbation response. Implementation techniques for automated system identification maneuvers, as well as feedback control using a Pixhawk and Raspberry Pi co-computer are documented and made available by means of a publicly accessible web repository. Flight test results illustrate the utility of the experimental data collection and analysis methods for testing advanced flight control schemes.

This paper focuses on the adaptive control problems for a class of interconnected systems. The nonLinear uncertainties of the systems under study are bounded by polynomial functions with unknown gains. Firstly, the adaptive feedback controller is proposed to guarantee the stabiLity of the closed-loop system. Then the proposed adaptive idea is extended to robust stabiLizing designing method for a class of large-scale interconnected systems. Based on Lyapunov's theory and LMI method, we can deal with the time-delay term in the system and construct the corresponding adaptive control and state feedback controller. Finally, an illustrative example is given to show the vaLidity of the proposed approach.

Robust Adaptive Control

In this work, an Adaptive Linear Quadratic Regulator (LQR) is proposed for the tracking control of a 3 DOF articulated robotic manipulator. The main objective of this work is to drive the robotic manipulator to its equilibrium point from any initial position of the end effector of a robotic manipulator in an adaptive way even if the system dynamics consist of modelling uncertainties. The conventional LQR is able to provide a good measure of robustness against disturbances and achieve good tracking performance. However, it will give degraded tracking performance in case of the presence of model uncertainties. Therefore LQR tracking performance is enhanced by using a Model Reference Adaptive Controller (MRAC) in the literature for enabling a 2 DOF system to achieve good tracking against modelling uncertainties. But it has not been applied for a 3 DOF system till date. Therefore in this work, it is proposed to be applied for such a system for the first time to realize an adaptive control. The forward and inverse kinematics level equations are formulated using an indirect form of the Denavit Hartenberg (DH) convention. The dynamics of robotic manipulator are derived using the Euler-Lagrange formulation. The dynamics of manipulator with the LQR control are considered to be the reference dynamics for the MRAC control and the modelling uncertainty will be added to the system dynamics to test its performance. The MRAC augmented LQR provides faster convergence with improved stability against modelling uncertainties.

Critical non-structural equipment, including life-saving equipment in hospitals, circuit breakers, computers, high technology instrumentations, etc., is vulnerable to strong earthquakes, and on top of that, the failure of the vibration-sensitive equipment will cause severe economic loss. In order to protect vibration-sensitive equipment or machinery against strong earthquakes, various innovative control algorithms are developed to compensate the internal forces that to be applied. These new or improved control strategies, such as the control algorithms based on optimal control theory and sliding mode control (SMC), are also developed for structures engineering as a key element in smart structure technology. The optimal control theory, one of the most common methodologies in feedback control, finds control forces through achieving a certain optimal criterion by minimizing a cost function. For example, the linear-quadratic regulator (LQR) was the most popular control algorithm over the past three decades, and a number of modifications have been proposed to increase the efficiency of classical LQR algorithm. However, except to the advantage of simplicity and ease of implementation, LQR are susceptible to parameter uncertainty and modeling error due to complex nature of civil structures. Different from LQR control, a robust and easy to be implemented control algorithm, SMC has also been studied. SMC is a nonlinear control methodology that forces the structural system to slide along surfaces or boundaries; hence this control algorithm is naturally robust with respect to parametric uncertainties of a structure. Early attempts at protecting vibration-sensitive equipment were based on the use of existing control algorithms as described above. However, in recent years, researchers have tried to renew the existing control algorithms or developing a new control algorithm to adapt the complex nature of civil structures which include the control of both structures and non-structural components. The aim of this paper is to develop a hybrid control algorithm on the control of both structures and equipments simultaneously to overcome the limitations of classical feedback control through combining the advantage of classic LQR and SMC. To suppress vibrations with the frequency contents of strong earthquakes differing from the natural frequencies of civil structures, the hybrid control algorithms integrated with the wavelet-base vibration control algorithm is developed. The performance of classical, hybrid, and wavelet-based hybrid control algorithms as well as the responses of structure and non-structural components are evaluated and discussed through numerical simulation in this study.

A scheduling strategy of multiple semi-active control laws for various earthquake disturbances is proposed to maximize the control performance. Generally, the semi-active controller for a given structural system is designed as a single control law and the single control law is used for all the forthcoming earthquake disturbances. It means that the general semi-active control should be designed to achieve a certain degree of the control performance for all the assumed disturbances with various time and/or frequency characteristics. Such requirement on the performance robustness becomes a constraint to obtain the optimal control performance. We propose a scheduling strategy of multiple semi-active control laws. Each semi-active control law is designed to achieve the optimal performance for a single earthquake disturbance. Such optimal control laws are scheduled with the available data in the control system. As the scheduling mechanism of the multiple control laws, a command signal generator (CSG) is defined in the control system. An artificial neural network (ANN) is adopted as the CSG. The ANN-based CSG works as an interpolator of the multiple control laws. Design parameters in the CSG are optimized with the genetic algorithm (GA). Simulation study shows the effectiveness of the approach.

The mutual impacts between adjacent buildings caused large-scale damage during past major earthquakes sparking interest in examining the reliability and effectiveness of various control devices for alleviating the seismic responses of adjacent buildings. In this study, seismic response attenuation of multi-story adjacent buildings connected with MR dampers is examined using the Simple Adaptive Control (SAC) method. The use of the adaptive controller is advantageous as it can cope with the structural characteristics change during the severe events such as earthquakes. The simple Bouc-Wen model is considered in the analysis to model the highly nonlinear behavior of the MR damper. The Linear Quadratic Regulator (LQR) is used to design the reference model with desired trajectories. The change in the structural characteristics is reflected as a reduction in the plant's mass and stiffness as a result of the damage in the structural system. The efficacy of the simple adaptive controller is investigated in the presence of damage and in case where the system still undamaged. The results show that connecting adjacent buildings with MR dampers driven by the Simple Adaptive Control method is quite effective in mitigating the seismic responses.

It is well known that highly volatile control laws, while theoretically optimal for certain systems, are undesirable from an engineering perspective, being generally deleterious to the controlled system. In this article we are concerned with the temporal volatility of the regulator's control process in discrete time Linear Quadratic Regulators (LQRs). Our investigation in this paper unearths a surprising connection between the cost functional that an LQR is tasked with minimizing and the temporal variations of its control laws. We first show that optimally controlling the system always implies high levels of control volatility, i.e., it is impossible to reduce volatility in the optimal control process without sacrificing cost. We also show that, akin to communication systems, every LQR has a Capacity Region associated with it, that dictates and quantifies how much cost is achievable at a given level of control volatility. This additionally establishes the fact that no admissible control policy can simultaneously achieve low volatility and low cost. We then employ this analysis to explain the phenomenon of extreme temporal price volatility, frequently observed in deregulated electricity markets. We model the suppliers and consumers in the market as strategic, price-anticipating participants who submit bids, in the form of price-quantity graphs, to the market operator. We then show that in any such market, at the Nash-Walras equilibrium, improving social welfare must necessarily be traded off with volatility in prices, i.e., it is impossible to reduce volatility in the price of electricity without sacrificing social welfare. Our investigation in this paper unearths a surprising connection between the cost functional that an LQR is tasked with minimizing and the temporal variations of its control laws. We first show that optimally controlling the system always implies high levels of control volatility, i.e., it is impossible to reduce volatility in the optimal control process without sacrificing cost. We also show that, akin to communication systems, every LQR has a Capacity Region associated with it, that dictates and quantifies how much cost is achievable at a given level of control volatility. This additionally establishes the fact that no admissible control policy can simultaneously achieve low volatility and low cost. We then employ this analysis to explain the phenomenon of extreme temporal price volatility, frequently observed in deregulated electricity markets. We model the suppliers and consumers in the market as strategic, price-anticipating participants who submit bids, in the form of price-quantity graphs, to the market operator. We then show that in any such market, at the Nash-Walras equilibrium, improving social welfare must necessarily be traded off with volatility in prices, i.e., it is impossible to reduce volatility in the price of electricity without sacrificing social welfare. We then employ this analysis to explain the phenomenon of extreme temporal price volatility, frequently observed in deregulated electricity markets. We model the suppliers and consumers in the market as strategic, price-anticipating participants who submit bids, in the form of price-quantity graphs, to the market operator. We then show that in any such market, at the Nash-Walras equilibrium, improving social welfare must necessarily be traded off with volatility in prices, i.e., it is impossible to reduce volatility in the price of electricity without sacrificing social welfare.

A EROSPACE engineering applications greatly stimulated the development of optimal control theory during the 1950s and 1960s, where the objective was to drive the system states in such a way that some defined cost was minimized. This turned out to have very useful applications in the design of regulators (where some steady state is to be maintained) and in tracking control strategies (where some predetermined state trajectory is to be followed). Among such applications was the problem of optimal flight trajectories for aircraft and space vehicles. Linear optimal control theory in particular has been very well documented and widely applied, where the plant that is controlled is assumed linear and the feedback controller is constrained to be linear with respect to its input. However, the availability of powerful low-cost microprocessors has spurred great advantages in the theory and applications of nonlinear control. The competitive era of rapid technological change, particularly in aerospace exploration, now demands stringent accuracy and cost requirements in nonlinear control systems. This has motivated the rapid development of nonlinear control theory for application to challenging, complex, dynamical real-world problems, particularly those that bear major practical significance in aerospace, marine, and defense industries. Infinite-time horizon nonlinear optimal control (ITHNOC) presents a viable option for synthesizing stabilizing controllers for nonlinear systems by making a state-input tradeoff, where the objective is to minimize the cost given by a performance index. The original theory of nonlinear optimal control dates from the 1960s. Various theoretical and practical aspects of the problem have been addressed in the literature over the decades since. In particular, the continuous-time nonlinear deterministic optimal control problem associated with autonomous (time-invariant) nonlinear regulator systems that are affine (linear) in the controls has been studied by many authors. The long-established theory of optimal control offers quite mature and well-documented techniques for solving this control-affine nonlinear optimization problem, based on dynamic programming or calculus of variations, but their application is generally a very tedious task. Bellman’s dynamic programming approach reduces to solving a nonlinear first-order partial differential equation (PDE), expressed by the Hamilton–Jacobi–Bellman (HJB) equation. The solution to the HJB equation gives the optimal performance/cost value (or storage) function and determines an optimal control in feedback form under some smoothness assumptions. Alternatively, in the classical calculus of variations, optimal control problems can be characterized locally in terms of the Hamiltonian dynamics arising from Pontryagin’s minimum principle. These are the characteristic equations of the HJB PDE, which result in a nonlinear, constrained two-point boundary value problem (TPBVP) that, in general, can only be solved by successive approximation of the optimal control input using iterative numerical techniques for each set of initial conditions. Numerically, even though the nonlinear TPBVP is somewhat easier to solve than the HJBPDE, control signals can only be determined offline and are thus best suited for feedforward control of plants for which the state trajectories are known a priori. Therefore, contrary to the dynamic programming approach, the resultant control law is not generally in feedback form. Open-loop control, however, is sensitive to random disturbances and requires that the initial state be on the optimal trajectory. In contrast, nonlinear optimal feedback has inherent robustness properties (inherent in the sense that it is obtained by ignoring uncertainty and disturbances). The potential difficulty with the HJB approach is that no efficient algorithm is available to solve the PDE when it is nonlinear and the problem dimension is high, making it impossible to derive exact expressions for optimal controls for most nontrivial problems of interest. The optimal can only be computed in special cases, such as linear dynamics and quadratic cost, or very low-dimensional systems. In particular, if the plant is linear time invariant (LTI) and the (infinite-time) performance index is quadratic, then the corresponding HJB equation for this infamous linear-quadratic regulator (LQR) problem reduces to an algebraic Riccati equation (ARE). Contrary to the well-developed and widely applied theory and computational tools for theRiccati equation (for example, see [1]), theHJB equation is difficult, if not impossible, to solve for most practical applications. The exact solution for the optimal control policies is very complex

Generation of control torque for highly agile satellite missions is generally achieved with momentum exchange devices, such as reaction wheels and control moment gyros (CMGs) with high slew maneuverability. However, the generation of a high control torque from the respective actuators requires high power and thus a large mass. The work presented here proposes a novel type of control actuator that generates torques in all three principal axes of a rigid satellite using only a spinning wheel and a simple tilt mechanism. This newly proposed actuator has several distinct advantages including less mass and more simplicity than a conventional CMG and no singularities being experienced during nominal wheel operation. A new high performance bounded (HPB) linear quadratic regulator (LQR) control law has been presented that extends classical LQR by providing faster settling times, gain-scheduling the control input weightings to optimize its performance, and has much quicker computation times than classical LQR. This work derives a fundamental mathematical model of the actuator and demonstrates feasibility by providing three degree of freedom high fidelity simulations for the actuator using both classical LQR and HPB LQR.

With the increasing complexity of control systems in industrial process control, traditional controllers are greatly limited in many occasions, so the development of new controller is extremely urgent. This paper combines adaptive feedback control with PID control, and designs a new type of adaptive PID feedback controller. The designed controller is verified by establishing a physical model of the 6-DOF collaborative robot. On the basis of improved adaptive PID feedback control, precise tracking control of multi-DOF cooperative robots is achieved, which improves response speed and eliminates steady-state errors. The designed controller is compared with classical PID control and adaptive control. The steady-state performance, dynamic performance, and anti-interference performance of position control and velocity control are analyzed. The improved adaptive PID feedback control has better control performance. The feasibility and reliability of the adaptive PID feedback controller for collaborative robots are verified.

A parameter dependent Riccati equation approach is taken to analyze the stability properties of an output feedback adaptive control law design. The adaptive controller is intended to augment a nominal, fixed gain, observer based output feedback control law. Although the formulation is in the setting of model following adaptive control, the realization of the adaptive controll er does not require implementing the reference model. In this regard, the cost of implementing the adaptive controller above that of a fixed gain control law is far less than that of other methods. The error signals are shown to be uniformly ultimately bounded and an expression for the ultimate bound is provided. The control design process and theoretical results are illustrated using a model for wing-rock dynamics. Research in adaptive output feedback control of uncertain nonlinear systems is motivated by the many emerging applications that employ novel actuation devices for active control of flexible structures and fluid flows. These applications include actuators such as piezo-electric films and s ynthetic jets, which are typically nonlinearly coupled to t he plant dynamics they are intended to control. Models for these applications vary from accurate low frequency models to models that crudely approximate the true dynamics even at low frequencies. Examples of applications include active damping of flexible structures, control of aeroservoelasti c aircraft, and active control of flows. Adaptive control can be used to satisfy performance requirements in the presence of large scale parameter uncertainty, and improved safety in the event of actuator failure.

A typical section analysis is employed to provide an understanding of the fundamental mechanisms and limitations involved in performing aeroelastic control. The effects of both articulated aerodynamic control surfaces and induced strain actuators are included in the model. The ability of these actuators to effect aeroelastic control is studied for each actuator individually as well as in various combinations. The control options available are examined for single-input, single-output (SISO) and multiple-input, multiple-output (MIMO) classical and optimal control laws. A state-cost-vs-control-cost analysis is performed to assess the effectiveness of optimal linear quadratic regulator (LQR) control laws for different actuators and actuator combinations. The cost comparisons show that strain actuation is an effective means of achieving aeroelastic control and a viable alternative to articulated control surface methods. In addition, the advantages of using multiple actuators to avoid limitations associated with single-actuator systems are demonstrated.

Integral Q-learning and explorized policy iteration for adaptive optimal control of continuous-time linear systems

Rapid advances in information processing, communication and sensing technologies have enabled more and more devices to be provided with embedded processors, networking capabilities and sensors. For the field of estimation and control, it is now possible to consider an architecture in which many simple components communicate and cooperate to achieve a joint team goal. This distributed (or networked) architecture promises much in terms of performance, reliability and simplicity of design; however, at the same time, it requires extending the traditional theories of control, communication and computation and, in fact, looking at a unified picture of the three fields. A systematic theory of how to design distributed systems is currently lacking. This dissertation takes the first steps towards understanding the effects of imperfect information flow in distributed systems from an estimation and control perspective and coming up with new design principles to counter these effects. Designing networked systems is difficult because such systems challenge two basic assumptions of traditional control theory - presence of a central node with access to all the information about the system and perfect transmission of information among components. We formulate and solve many problems that deal with the removal of one, or both, of these assumptions. The chief idea explored in this dissertation is the joint design of information flow and the control law. While traditional control design has concentrated on calculating the optimal control input by assuming a particular information flow between the components, our approach seeks to synthesize the optimal information flow along with the optimal control law that satisfies the constraints of the information flow. Thus besides the question of 'What should an agent do?', the questions of 'Whom should an agent talk to?', 'What should an agent communicate?', 'When should an agent communicate?' and so on also have to be answered. The design of the information flow represents an important degree of freedom available to the system designer that has hitherto largely been ignored. As we demonstrate in the dissertation, the joint design of information flow and the optimal control input satisfying the constraints of that information flow yields large improvements in performance over simply trying to fit traditional design theories on distributed systems. We begin by formulating a distributed control problem in which many agents in a formation need to cooperate to minimize a joint cost function. We provide numerical algorithms to synthesize the optimal constrained control law that involve solving linear equations only and hence are free from numerical issues plaguing the other approaches proposed in the literature. We then provide and analyze a model to understand the issue of designing the topology according to which the agents interact. The results are very surprising since there are cases when allowing communication to happen between two agents may, in fact, be detrimental to the performance. We then move on to consider the effects of communication channels on control performance. To counter such effects, we propose the idea of encoding information for the purpose of estimation and control prior to transmission. Although information theoretic techniques are not possible in our problem, we are able to solve for a recursive yet optimal encoder / decoder structure in many cases. This information flow design oriented approach has unique advantages such as being optimal for any packet drop pattern, being able to include the effect of known but random delays easily, letting us escape the limits set by reliability for transmission of data across a network by using intermediate nodes as 'repeaters' similar to a digital communication network and so on. We finally take a look at combining the effects of multiple sources of information and communication channels on estimation and control. We look at a distributed estimation problem in which, at every time step, only a subset out of many sensors can transmit information to the estimator. This is also a representative resource allocation problem. We propose the idea of stochastic communication patterns that allows us to include the effects of communication channels explicitly during system design. Thus, instead of tree-search based algorithms proposed in the literature, we provide stochastic scheduling algorithms that can take into account the random packet drop effect of the channels. We also consider a distributed control problem with switching topologies and solve for the optimal controller. The tools that we develop are applicable to many other scenarios and we demonstrate some of them in the dissertation. Along the way, we look at many other related problems in the dissertation. As an example, we provide initial results about the issue of robustness of a distributed system design to a malfunctioning agent. This notion is currently lacking in the control and estimation community, but has to be a part of any effective theory for designing networked or distributed systems.