A new control approach for switching shunt damping

This paper presents a survey of the most recent literature developments in the field of computational guidance and control for space applications. In recent years, the space sector has changed significantly, shifting towards solutions requiring increased performance and autonomy. This change has also been accelerated by the technical and economic needs of the new space approach. However, traditional guidance and control techniques cannot always meet the increasing requirements of autonomy and performance. For this reason, computational guidance and control has become of increasing interest to the aerospace sector. In contrast to traditional guidance and control, computational guidance and control generates commands in real time by using on-board numerical computation. It represents, therefore, a fundamental step on the way to system autonomy and autonomous operations, with the potential to increase system capabilities and reduce operational costs. On-board computation introduces, however, a series of challenges, including the need to develop algorithms which are computationally efficient, reliable and robust. The literature has classified computational guidance and control techniques into two major categories, namely model-based and data-based. The model-based category encompasses all techniques in which the guidance and control laws are explicitly related to the system dynamic and kinematic models. On the contrary, data-based techniques infer guidance and control laws from a set of data, derived from the models, but do not explicitly use such models in the algorithm itself. Model-based guidance and control includes optimal control, model predictive control and convex optimisation. For the specific case of space attitude re-orientation manoeuvres, additional techniques are path planning and artificial potential functions. The general concept behind the Model Predictive Control (MPC) framework is to solve an optimal control problem repeatedly, for example whenever new measurements are available. The MPC implements only the first element of the returned solution, and the process is then repeated. By doing so, the system is better able to cope autonomously with model uncertainties, failures, or errors. For spacecraft with limited on-board capability, having to repeatedly solve an optimisation problem on-board could represent a challenge. In this case, explicit implementations of the MPC have been proposed, in which the guidance and control laws are precomputed offline and implemented on-board using look-up tables or simple functions. If the optimal control problem of the MPC is convex, or if it can be convexified, convex optimisation can be used directly. If the problem cannot be convexified, the solution can be found by sequentially solving a convex approximation of the original non-convex problem. Convex optimisation can be used either repeatedly in the context of an MPC framework, or as a single function call to generate guidance and control laws, e.g. at the beginning of an attitude re-orientation manoeuvre. Convex optimisation has received increased attention in recent years, also due to its suitability to on-board implementation. In fact, if the optimal control problem is convex, it can be solved reliably and efficiently on-board. Convex optimisation has been successfully applied to the space sector with the notable examples of the SpaceX rocket booster landing and of the Mars pinpoint landing demonstration aboard the Masten Xombie sounding rocket. Model-based guidance techniques, not based on optimisation, have been increasingly explored in recent years, as guidance strategies employed in other engineering fields, such as robotics, are being applied to spacecraft. Among these strategies, of particular importance are path planning and artificial potential field methods, due to their applicability to spacecraft autonomous attitude manoeuvres. Path planning algorithms have been applied for decades to ground vehicles and robotic manipulators. These algorithms consist of techniques to find the best route between two points of a graph representing the search space of a problem. For spacecraft re-orientation applications, the literature has proposed different attitude representation conventions and various cost functions associated to the graph search algorithm. Each approach comes with advantages and disadvantages, which will be analysed in the paper. Along with path planning, Artificial Potential Function (APF) techniques have been developed in the field of robotics, and are now also considered for space applications, to track or maintain a specific reference under a set of constraints. The main idea behind these methods is to synthetise the controller using a potential function. This function is specifically built to grant asymptotic stability to the system, according to Lyapunov’s second stability theorem. This formulation grants flexibility to accommodate system constraints, in a computationally light-weight and efficient manner. Data-based guidance and control laws are mainly based on Artificial Intelligence (AI) technologies, and generate guidance commands after training an algorithm with a large set of data. The interest of the space sector towards AI has accelerated in the last years due to the greater maturity of the technology. Some of the most powerful examples lie in the area of machine learning, like reinforcement learning, supervised learning and deep learning. These algorithms are used to extract patterns from large amounts of data derived from complex nonlinear dynamical and kinematical models. Examples of such data can be numerical solutions of an optimal control problem. The patterns extracted from the data allow the system to identify, in a short computational time, the critical parameters needed to relate the state and control variables. Creating a sufficiently large dataset for training the algorithm requires a considerable computational effort, though, and for certain methods optimality cannot be guaranteed due to the lack of theoretical support derived from the optimality conditions. Advancements made in the last years span several research directions and open a wide variety of opportunities and challenges, which need to be examined to guide further exploration. In this paper, both model-based and data-based techniques and applications are presented. The considered techniques include model predictive control, convex optimisation and machine learning. In addition, for the implementation of autonomous attitude manoeuvres, path planning methods and artificial potential function methods are analysed. These techniques have been applied, in the literature, to a range of different applications. The applications discussed in this paper include, in addition to attitude manoeuvres, powered descent landing guidance, low-thrust orbital transfers, proximity operations and station keeping.

This thesis focuses on Model Predictive Control (MPC) of discrete-time hybrid systems. Hybrid systems contain continuous and discrete valued components, and are located at the intersection between the fields of control theory and computer science. MPC uses an internal model of the controlled plant to predict the future evolution of the controlled variables over a prediction horizon. A cost function is minimized to obtain the optimal control input sequence, which is applied to the plant by means of a receding horizon policy. The latter implies that only the first control input of the input sequence is implemented, the horizon is shifted by one time-step and the above procedure is repeated at the next sampling instant. Most importantly, theory and tools are available to off-line derive the piecewise affine (PWA) state-feedback control law. Hence, any time-consuming on-line computation of the control input is avoided and plants with high sampling frequencies can be controlled. The thesis is divided into two parts: The first part is devoted to theory and algorithms, whereas the second part tackles applications in the fields of power electronics and power systems. In the first part, using the notion of cell enumeration in hyperplane arrangements from computational geometry, we propose an algorithm that efficiently enumerates all feasible modes of a composition of hybrid systems. This technique allows the designer to evaluate the complexity of the compound model, to efficiently translate the model into a PWA representation, and to reduce the computational burden of optimal control schemes by adding cuts that prune infeasible modes from the model. With respect to implementation, an important issue is the complexity reduction of PWA state-feedback controllers. Hence, we propose two algorithms that solve the problem of deriving a PWA representation that is both equivalent to the given one and minimal in the number of regions. As both algorithms refrain from solving additional Linear Programs, they are not only optimal but also computationally feasible. In many cases, the optimal complexity reduction constitutes an enabling technique when implementing the optimal controllers as look-up tables in hardware. In the second part of the thesis, we consider the field of power electronics that is intrinsically hybrid, since the positions of semiconductor switches are described by binary variables. The fact that the methodologies of MPC and hybrid systems are basically unknown in the power electronics community has motivated us to consider such problems, namely

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.

ABSTRACTFor unknown continuous‐time nonlinear systems with multiple equilibrium points, this article proposes a robust adaptive optimal tracking switching controller. The controller integrates multiple nonlinear approximate optimal tracking controllers, an optimal switching sequence, and a robust compensator. First, multiple nonlinear neural network models are established to construct a controller design model, whose unknown parameters are online estimated by resorting to Lyapunov stability theory. Then, at every instant, the optimal switching sequence and approximate optimal tracking controller are obtained by using embedding transformation and approximate dynamic programming technology. After that, according to the error between the nonlinear system and the given input, a robust compensator is designed. Finally, stability and convergence of the control system are verified, and the simulations are conducted to validate the effectiveness and superiority.

Optimal channel switching in multiuser systems under average capacity constraints

This paper treats the vibration surpression by piezoelectric shunt damping. Use of a piezoelectric element to which a shunt circuit composed of a resistor and an inductor are connected is one of the efficient techniques of vibration control. Recently, to improve the performance of the shunt damping, switching of the shunt circuit was attempted. In previous works, one of the authors found in the study of elastic impact dampers that the switch of the dynamic characteristics of the damper gives good perfomance for vibration surpression in some condisions. In this paper, the possibility of improvement of vibration surpression by switching the dynamic characteristics in the shunt circuits is discussed based on the results of numerical simulation.

In this paper an effective direct torque control (DTC) for a 5-phase induction motor with sinusoidally distributed windings is developed. First by coordinate transformation, the converter/motor models are represented by two independent equivalent d-q circuit models; and the 5-phase VSI input are decoupled into the torque producing and non-torque producing harmonics sets. Then with the torque production component of the induction motor model, the space vector modulation (SVM) can be applied to the five-phase induction motor DTC control, resulting in considerable torque ripple reduction over the lookup table method. Based on the decoupled system model, the current distortion issue due to lack of back EMF for certain harmonics is analyzed. Two equally effective SVM schemes with the harmonic cancellation effect are introduced to solve this problem. To analyze the DTC control torque ripple, an insightful perspective (also applicable to 3-phase analysis) is introduced to predict the torque ripple pattern evolution with changing motor speed and stator flux angular position. Therefore the switching sequence for lowest torque ripple can be determined and re-arranged online. Finally, with the overall optimal switching scheme adopted, detailed simulations verify the effectiveness of the new control.

This brief studies the linear quadratic regulation problem of discrete-time switched linear systems via dynamic programming. Discrete decision variables (referred as switch inputs) are introduced to represent the subsystem selection. This formulation leads to a mixed integer quadratic programming problem, which is known to be computationally hard in general. Instead of deriving suboptimal policies with analytical bounds on its optimality, the optimal switching sequence is computed in a computationally efficient manner when the input matrix is restricted as a vector. The unique contribution of this brief is an analytical expression of both the optimal switching condition (determining the subsystem selection) and the optimal control law. Proof of optimality is presented by fractional optimization and the practical merits of our approach is validated through simulations on a second-order system in comparison with recent pruning methods.

This paper presents a new method for the design of control laws for systems with on-off nonlinear actuators. The new methodology improves the design of control laws for pulse-modulated systems by allowing the use of continuous-time multi-inputlmultioutput design procedures. Discrete-time state feedback control gains are developed from the of continuous-time feedback gains, based on a geometric series approximation, to closely match the states of the closed-loop hybrid system to those of the original designed closed-loop continuous-time system at each sampling instant. A delay is then incorporated into a pulse-width modulator design to closely match the states of the modulated system to those of the discrete-time pulse-amplitude modulated system. The delay time is improved from previous work to provide a close match between the states for pulse durations of all sizes, in effect matching the states of the pulse-width modulated system to those of the closed-loop continuous-time system. The new control law design is applied to the problem of attitude control of the Space Shuttle Orbiter with the Hubble Space Telescope deployed on its remote manipulator. * Senior Member Technical Staff. Member A I M . t Professor, Electrical Engineering. Member AIAA. tt Aerospace Engineer. Member AIAA. Copyright O 1995 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Many paradigms are available for the synthesis of control laws for continuous-time systems, and though many methods also exist for developing discrete-time or digital controllers, it is often desirable to design a control law for the continuous-time plant. It is often more direct to determine the control specifications in the continuous-time or frequency domain. Also, direct digital control law design has difficulty in predetermining the hybrid control specifications and ignores inter sampling effects. Yet, these continuoustime control laws are generally implemented via discrete-time computer control, requiring that a discrete-time control, equivalent to the continuous-time control, be developed. The process of developing discrete-time control laws that provide closed-loop performance of the hybrid system equivalent to the performance of the designed closed-loop continuoustime system is known as redesign. Several techniques have been developed to digitally redesign continuous-time feedback controllers[l] ,[2] ,[3]. Unfortunately, the principal applied for the design of discrete-time control laws, i.e., that the amplitude of the control signal can take any finite value, which is why discrete-time control is often referred to as pulse-amplitude control (PAM), is not valid for all computer controlled systems. Systems that utilize onoff control devices, such as the reaction jet or electronic relay, can only provide a single finite value of control. To provide control with these types of actuator, either complex non-linear algorithms[4] must be developed or the control must be applied by modulating the pulse width, the pulse frequency or both the pulse width and frequency. These modulation techniques, in particular pulse-width modulation (PWM), allow the design of linear control laws to control non-linear systems. Although methods exist for the design of linear control laws for pulse width modulation systems[5], they still

This paper proposes a hybrid control algorithm with sliding sectors for the control of a wheeled mobile robot (WMR), which is a non-holonomic system. The WMR control system with a set of available or pre-designed control laws is considered as a hybrid system with a set of subsystems. The WMR with one of control laws forms a non-linear subsystem of the hybrid system. The subsystems may be unstable but for each subsystem of the hybrid system, a stable subset called a sliding sector is designed such that a Lyapunov function candidate decreases inside the sliding sector. The hybrid control rule is used to stabilize the WMR control system by switching the hybrid system among its subsystems such that the system is always inside a sliding sector of some subsystem. The proposed hybrid sliding sector control algorithm has been successfully implemented to the real-time control of WMR with good control performance.

This article addresses the event-triggered consensus problem of multiagent systems (MASs) with packet losses. The packet losses are not restricted to be identical, and a hybrid systems framework is proposed to handle the considered problem with or without leader in a unified framework. Distributed control law is constructed based on an estimator, whose dynamics are related to whether packet losses occur. A novel hybrid event-triggering mechanism (ETM) is proposed, and a lower bound of the interevent times is enforced to guarantee Zeno-freeness. For stability analysis, a unified hybrid model is constructed to describe the dynamics of MAS with or without leader. In accordance to this model, how to design the hybrid ETM and consensus analysis are formally developed, and the maximum allowable successive packet losses can be explicitly computed. Moreover, even if there exist nonlinearities and disturbances in system dynamics, and the leader has nonzero input, the proposed method can still be applied. Finally, examples are provided to illustrate the superiority of the proposed method.

A study on interaction control for seismic response of parallel structures

A key challenge of cyber physical system is how to design the communication system. In this paper, the framework of hybrid system which consists of both continuous and discrete system states is adopted for the communication system design, particularly on the routing problem. The mapping between the routing scheme and the system dynamics mode is established by analyzing the impact of delay on the system dynamics. A heuristic algorithm is then proposed to choose the set of routing schemes, based on a sufficient condition of the stability of hybrid systems. The proposed approach is then applied in the voltage control of distributed energy generations in microgrids, whose validity is demonstrated by numerical simulations.

In the high-precision application of Global Navigation Satellite System (GNSS), integer ambiguity resolution is the key step to realize precise positioning and attitude determination. As the necessary part of quality control, integer aperture (IA) ambiguity resolution provides the theoretical and practical foundation for ambiguity validation. It is mainly realized by acceptance testing. Due to the constraint of correlation between ambiguities, it is impossible to realize the controlling of failure rate according to analytical formula. Hence, the fixed failure rate approach is implemented by Monte Carlo sampling. However, due to the characteristics of Monte Carlo sampling and look-up table, we have to face the problem of a large amount of time consumption if sufficient GNSS scenarios are included in the creation of look-up table. This restricts the fixed failure rate approach to be a post process approach if a look-up table is not available. Furthermore, if not enough GNSS scenarios are considered, the table may only be valid for a specific scenario or application. Besides this, the method of creating look-up table or look-up function still needs to be designed for each specific acceptance test. To overcome these problems in determination of critical values, this contribution will propose an instantaneous and CONtrollable (iCON) IA ambiguity resolution approach for the first time. The iCON approach has the following advantages: (a) critical value of acceptance test is independently determined based on the required failure rate and GNSS model without resorting to external information such as look-up table; (b) it can be realized instantaneously for most of IA estimators which have analytical probability formulas. The stronger GNSS model, the less time consumption; (c) it provides a new viewpoint to improve the research about IA estimation. To verify these conclusions, multi-frequency and multi-GNSS simulation experiments are implemented. Those results show that IA estimators based on iCON approach can realize controllable ambiguity resolution. Besides this, compared with ratio test IA based on look-up table, difference test IA and IA least square based on the iCON approach most of times have higher success rates and better controllability to failure rates.

This paper presents a computational framework for modeling hybrid systems in discrete-time. We introduce the class of discrete hybrid automata (DHA) and show its relation with several other existing model paradigms: piecewise affine systems, mixed logical dynamical systems, (extended) linear complementarity systems, min-max-plus-scaling systems. We present HYSDEL (hybrid systems description language), a high-level modeling language for DHA, and a set of tools for translating DHA into any of the former hybrid models. Such a multimodeling capability of HYSDEL is particularly appealing for exploiting a large number of available analysis and synthesis techniques, each one developed for a particular class of hybrid models. An automotive example shows the modeling capabilities of HYSDEL and how the different models allow to use several computational tools.