A family of virtual contraction based controllers for tracking of flexible-joints port-Hamiltonian robots:Theory and experiments

In this work, we present a constructive method to design a family of virtual contraction based controllers that solve the standard trajectory tracking problem of flexible-joint robots in the port-Hamiltonian framework. The proposed design method, called virtual contraction based control, combines the concepts of virtual control systems and contraction analysis. It is shown that under potential energy matching conditions, the closed-loop virtual system is contractive and exponential convergence to a predefined trajectory is guaranteed. Moreover, the closed-loop virtual system exhibits properties such as structure preservation, differential passivity, and the existence of (incrementally) passive maps. The method is later applied to a planar RR robot, and two nonlinear tracking control schemes in the developed controllers family are designed using different contraction analysis approaches. Experiments confirm the theoretical results for each controller

A general dissipativity constraint for feedback system design, with emphasis on MPC

A ‘General Dissipativity Constraint’ (GDC) is introduced to facilitate the design of stable feedback systems. A primary application is to MPC controllers when it is preferred to avoid the use of ‘stabilising ingredients’ such as terminal constraint sets or long prediction horizons. Some very general convergence results are proved under mild conditions. The use of quadratic functions, replacing GDC by ‘Quadratic Dissipation Constraint’ (QDC), is introduced to allow implementation using linear matrix inequalities. The use of QDC is illustrated for several scenarios: state feedback for a linear time-invariant system, MPC of a linear system, MPC of an input-affine system, and MPC with persistent disturbances. The stability that is guaranteed by GDC is weaker than Lyapunov stability, being ‘Lagrange stability plus convergence’. Input-to-state stability is obtained if the control law is continuous in the state. An example involving an open-loop unstable helicopter illustrates the efficacy of the approach in practice.National Research Foundation Singapor

Adaptive Horizon Model Predictive Control and Al'brekht's Method

A standard way of finding a feedback law that stabilizes a control system to an operating point is to recast the problem as an infinite horizon optimal control problem. If the optimal cost and the optmal feedback can be found on a large domain around the operating point then a Lyapunov argument can be used to verify the asymptotic stability of the closed loop dynamics. The problem with this approach is that is usually very difficult to find the optimal cost and the optmal feedback on a large domain for nonlinear problems with or without constraints. Hence the increasing interest in Model Predictive Control (MPC). In standard MPC a finite horizon optimal control problem is solved in real time but just at the current state, the first control action is implimented, the system evolves one time step and the process is repeated. A terminal cost and terminal feedback found by Al'brekht's methoddefined in a neighborhood of the operating point is used to shorten the horizon and thereby make the nonlinear programs easier to solve because they have less decision variables. Adaptive Horizon Model Predictive Control (AHMPC) is a scheme for varying the horizon length of Model Predictive Control (MPC) as needed. Its goal is to achieve stabilization with horizons as small as possible so that MPC methods can be used on faster and/or more complicated dynamic processes.Comment: arXiv admin note: text overlap with arXiv:1602.0861

Weak exponential stability for time-periodic differential inclusions via first approximation averaging

Published online: 20 June 2012In this work we propose a method to study a weak exponential stability for time-varying differential inclusions applying an averaging procedure to a first approximation. Namely, we show that a weak exponential stability of the averaged first approximation to the differential inclusion implies the weak exponential stability of the original time-varying inclusion. The result is illustrated by an example.FC

Gyroless Spin-Stabilization Controller and Deorbiting Algorithm for CubeSats

CubeSats are becoming increasingly popular in the scientific community. While they provide a whole new range of opportunities for space exploration, they also come with their own challenges. One of the main concerns is the negative impact which they can have in the space debris problem. Commonly lacking from attitude determination and propulsion capabilities, it has been difficult to provide CubeSats with means for active deorbiting. While electric propulsion technology has been emerging for its application in CubeSats, little or no literature is available on methods to enable it to be used for deorbiting purposes, especially within the tight constraints faced by these nanosatellites. We present a new and simple algorithm for CubeSat deorbiting, which proposes the use of novel electric propulsion technology with minimum sensing and actuation capabilities. The algorithm is divided into two stages: a spin-stabilization control; and a deorbiting-phase detection. The spin-stabilization control is inspired by the B-dot controller. It does not require gyroscopes, but only requires magnetometers and magnetorquers as sensors and actuators, respectively. The deorbiting-phase detection is activated once the satellite is spin-stabilized. The algorithm can be easily implementable as it does not require any attitude information other than the orbital information, e.g., from the Global Positioning System receiver, which could be easily installed in CubeSats. The effectiveness of each part of the algorithms is validated through numerical simulations. The proposed algorithms outperform the existing approaches such as deorbiting sails, inflatable structures, and electrodynamic tethers in terms of deorbiting times. Stability and robustness analysis are also provided. The proposed algorithm is ready to be implemented with minimal effort and provides a robust solution to the space junk mitigation efforts

Stability of quantized time-delay nonlinear systems: A Lyapunov-Krasowskii-functional approach

Lyapunov-Krasowskii functionals are used to design quantized control laws for nonlinear continuous-time systems in the presence of constant delays in the input. The quantized control law is implemented via hysteresis to prevent chattering. Under appropriate conditions, our analysis applies to stabilizable nonlinear systems for any value of the quantization density. The resulting quantized feedback is parametrized with respect to the quantization density. Moreover, the maximal allowable delay tolerated by the system is characterized as a function of the quantization density.Comment: 31 pages, 3 figures, to appear in Mathematics of Control, Signals, and System

Sensitivity analysis of circadian entrainment in the space of phase response curves

Sensitivity analysis is a classical and fundamental tool to evaluate the role of a given parameter in a given system characteristic. Because the phase response curve is a fundamental input--output characteristic of oscillators, we developed a sensitivity analysis for oscillator models in the space of phase response curves. The proposed tool can be applied to high-dimensional oscillator models without facing the curse of dimensionality obstacle associated with numerical exploration of the parameter space. Application of this tool to a state-of-the-art model of circadian rhythms suggests that it can be useful and instrumental to biological investigations.Comment: 22 pages, 8 figures. Correction of a mistake in Definition 2.1. arXiv admin note: text overlap with arXiv:1206.414

Phase synchronization of autonomous AC grid system with passivity-based control

This paper discusses a ring‐coupled buck‐type inverter system to harness energy from direct current (DC) sources of electricity. The DC‐DC buck converter circuit is modified with an H‐bridge to convert the DC input voltage to a usable alternating current (AC) output voltage. Passivity‐based control (PBC) with port‐controlled Hamiltonian modelling (PCHM) is a method where the system is controlled by considering not only the energy properties of the system but also the inherent physical structure. PBC is applied to achieve stabilization of the AC output voltage to a desired amplitude and frequency. Unsynchronized output voltages in terms of phase angle or frequency can cause detrimental effects on the system. Phase‐locked loop (PLL) is employed in the ring structure to maintain synchronization of the AC output voltage of all inverter units in the ring‐coupled system

Non-overshooting stabilisation via state and output feedback

The concept of “strong stability” of LTI systems has been introduced in a recent paper [KHP2]. This is a stronger notion of stability compared to alternative definitions (e.g. stability in the sense of Lyapunov, asymptotic stability), which allows the analysis and design of control systems with non-overshooting response in the state-space for arbitrary initial conditions. The paper reviews the notion of “strong stability” [KHP2] and introduces the problem of non-overshooting stabilization. It is shown that non-overshooting stabilization under dynamic and static output feedback are, in a certain sense, equivalent problems. Thus, we turn our attention to static non-overshooting stabilization problems under state-feedback, output injection and output feedback. After developing a number of preliminary results, we give a geometric interpretation to the problem in terms of the intersection of an affine hyperplane and the interior of an open convex cone. A solution to the problem is finally obtained via Linear Matrix Inequalities, along with the complete parametrization of the optimal solution set

Decentralized sliding mode control for a class of nonlinear interconnected systems by static state feedback

In this paper, a class of interconnected systems is considered, where the nominal isolated systems are fully nonlinear. A robust decentralized sliding mode control based on static state feedback is developed. By local coordinate transformation and feedback linearization, the interconnected system is transformed to a new regular form. A composite sliding surface which is a function of the system state variables is proposed and the stability of the corresponding sliding mode dynamics is analyzed. A new reachability condition is proposed and a robust decentralized sliding mode control is then designed to drive the system states to the sliding surface in finite time and maintain a sliding motion thereafter. Both uncertainties and interconnections are allowed to be unmatched and are assumed to be bounded by nonlinear functions. The bounds on the uncertainties and interconnections have more general forms when compared with existing work. A MATLAB simulation example is used to demonstrate the effectiveness of the proposed method