A new family of interconnection and damping assignment passivity‐based controllers

The by‐now standard formulation of interconnection and damping assignment passivity‐based control (for input‐affine systems) proposes the solution of a partial differential equation (PDE) that defines the assignable energy functions and computes the control using the input matrix pseudo‐inverse. However, in its original formulation—a more general design procedure was proposed, which was essentially abandoned because of the difficulties in solving the PDE. In this note, a new family of interconnection and damping assignment passivity‐based controls is proposed by extending this method in the following directions: (i) It allows the desired interconnection and damping matrices to depend on the control signal, giving the possibility to shape the PDE to ensure its solvability; (ii) the PDE directly generates the control signal that have, in general, simpler expressions; and (iii) it is applicable for general nonlinear systems possibly not affine in the control. The technique is illustrated with three examples, including the well‐known boost power converter for which it yields a simple, high‐performance controller. Copyright © 2016 John Wiley & Sons, Ltd.     

Stabilization of an underactuated bottom‐heavy airship via interconnection and damping assignment

This paper focuses on feedback stabilization of a neutrally buoyant and bottom‐heavy airship actuated by only five independent controls (with the rolling motion underactuated). The airship is modelled as an eudipleural submerged rigid body whose dynamics is formulated as a Hamiltonian system with respect to a Lie–Poisson structure. By exploiting the geometrical structure and using the so‐called interconnection and damping assignment (IDA) passivity‐based methodology for port‐controlled Hamiltonian systems, state feedback control laws asymptotically stabilizing two typical motions are designed via La Salle invariance principle and Chetaev instability theorem. Simulation results verify the control laws. Copyright © 2007 John Wiley & Sons, Ltd.     

Stabilization of electromechanical systems via interconnection and damping assignment

In this article, we propose a general controller structure for asymptotic position regulation of electromechanical systems derived using the Interconnection and Damping Assignment Passivity‐Based Control methodology recently proposed in the literature. The controller is applicable to arbitrary fully actuated electromechanical systems with linear magnetic materials consisting of inductances, permanent magnets, and one mechanical co‐ordinate. We assume linear magnetic materials and fully actuated electrical dynamics; however, no restrictions are imposed on the particular form of the parameters that define the system dynamics, i.e. the inductance matrix, the magnetic coupling or the potential energy function. This allows us to treat—in a unified framework and without any additional simplifying assumptions—very diverse applications, including magnetic suspensions, and stepper and permanent magnet synchronous motors. Instrumental for our developments is the inclusion of ‘virtual’ couplings between the electrical and the mechanical subsystem, which is naturally suggested in this control methodology. Copyright © 2003 John Wiley & Sons, Ltd.     

Pole assignment for linear time-invariant systems by periodic memoryless output feedback

It is well known that the poles of a linear time-invariant controllable and observable system can be assigned arbitrarily by state feedback. When only the output is available, pole assignment is still possible by means of dynamic output feedback. In this paper the potential of time-varying memoryless output feedback is considered. It is shown that, up to some technical conditions, it is indeed possible to allocate the poles of a linear time-invariant discrete-time system by memoryless output feedback with periodic gains. The period of the gains is (n + 1) with n the order of the system. The power of the design technique is proved to be comparable to what can be achieved by the classical dynamic feedback approach.     

基于PI 控制器的线性系统的鲁棒耗散控制

针对参数具有确定性及不确定性的连续系统,给出两种严格耗散PI控制器的设计方法.首先,系统参数确定时,采用线性矩阵不等式方法,导出了类状态反馈和静态输出反馈严格耗散PI控制器存在的充要条件,并由线性矩阵不等式的可行解构造出严格耗散PI控制器增益的显式表达式;然后,考虑系数矩阵均具有范数有界不确定性时的鲁棒严格耗散控制问题,得到相似的结果;最后,通过数值算例表明了所给方法的有效性.     

Observer-based fault detection and isolation filter design for linear time-invariant systems

In this paper we consider a model-based fault detection and isolation problem for linear time-invariant dynamic systems subject to faults and disturbances. We use a state observer scheme that cancels the system dynamics and defines a residual vector signal that is sensitive only to faults and disturbances. We then design a stable fault detection and isolation filter such that the ?_∞-norm of the transfer matrix function from disturbances to the residual is minimised (for fault detection) subject to the constraint that the transfer matrix function from faults to residual is equal to a pre-assigned diagonal transfer matrix (for isolation of possibly simultaneous occurring faults). Our solution is given in the form of linear matrix inequalities using state-space techniques, as well as a model matching problem using matrix factorisation techniques. A numerical example is given to illustrate the efficiency of the fault detection and isolation filter.     

An efficient LMI approach for the quadratic stabilisation of a class of linear,uncertain, time-varying systems

The purpose of this article is to provide a numerically efficient method for the quadratic stabilisation of a class of linear, discrete-time, uncertain, time-varying systems. The considered class of systems is characterised by an interval time-varying (ITV) matrix and constant sensor and actuator matrices. It is required to find a linear time-invariant (LTI) static output feedback controller yielding a quadratically stable closed-loop system independently of the parameter variation rate. The solvability conditions are stated in terms of linear matrix inequalities (LMIs). The set of LMIs includes the stability conditions for the feedback connection of a unique suitably defined extreme plant with an LTI output controller and the positivity of a closed-loop extremal matrix. A consequent noticeable feature of the article is that the total number of LMIs is independent of the number of uncertain parameters. This greatly enhances the numerical efficiency of the design procedure.     

A dilated LMI approach to robust performance analysis of linear time-invariant uncertain systems

This paper studies robust performance analysis problems of linear time-invariant systems affected by real parametric uncertainties. In the case where the state-space matrices of the system depend affinely on the uncertain parameters, it is know that recently developed extended or dilated linear matrix inequalities (LMIs) are effective to assess the robust performance in a less conservative fashion. This paper further extends those preceding results and propose a unified way to obtain numerically verifiable dilated LMI conditions even in the case of rational parameter dependence. In particular, it turns out that the proposed dilated LMIs enable us to assess the robust performance via multiaffine parameter-dependent Lyapunov variables so that less conservative analysis results can be achieved. Connections among the proposed conditions and existing results are also discussed concretely. Several existing results can be viewed as particular cases of the proposed conditions.     

Robust iterative learning control for linear systems with multiple time-invariant parametric uncertainties

This article presents a novel robust iterative learning control algorithm (ILC) for linear systems in the presence of multiple time-invariant parametric uncertainties.The robust design problem is formulated as a min–max problem with a quadratic performance criterion subject to constraints of the iterative control input update. Then, we propose a new methodology to find a sub-optimal solution of the min–max problem. By finding an upper bound of the worst-case performance, the min–max problem is relaxed to be a minimisation problem. Applying Lagrangian duality to this minimisation problem leads to a dual problem which can be reformulated as a convex optimisation problem over linear matrix inequalities (LMIs). An LMI-based ILC algorithm is given afterward and the convergence of the control input as well as the system error are proved. Finally, we apply the proposed ILC to a generic example and a distillation column. The numerical results reveal the effectiveness of the LMI-based algorithm.     

Dilated LMI characterisations for linear time-invariant singular systems

This article explores, based on projection lemma, dilated linear matrix inequality (LMI) characterisations for linear time-invariant singular systems. The deduced formulations cover not only the existing results reported in the literature, but also complete some missing LMI conditions. This article also lightens the mutual relations of these characterisations and clarifies the relation between the dilated LMIs for the conventional state-space systems and those for singular systems. The well-known results for the state-space setting reported in the literature can be reviewed as special cases.     

Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment

We consider the application of a formulation of passivity-based control (PBC), known as interconnection and damping assignment (IDA) to the problem of stabilization of underactuated mechanical systems, which requires the modification of both the potential and the kinetic energies. Our main contribution is the characterization of a class of systems for which IDA-PBC yields a smooth asymptotically stabilizing controller with a guaranteed domain of attraction. The class is given in terms of solvability of certain partial differential equations. One important feature of IDA-PBC, stemming from its Hamiltonian formulation, is that it provides new degrees of freedom for the solution of these equations. Using this additional freedom, we are able to show that the method of "controlled Lagrangians"-in its original formulation-may be viewed as a special case of our approach. As illustrations we design asymptotically stabilizing IDA-PBCs for the classical ball and beam system and a novel inertia wheel pendulum.     

四倾转旋翼无人机无源控制与飞行实验

倾转旋翼无人机以低速悬停以及快速巡航能力得到了大量的关注,但是其变化的飞行器结构(旋翼的倾转)以及较强的非线性特性(飞行速度的大范围变化)都增大了飞行控制的难度.针对一种四倾转旋翼无人机的飞行控制问题,本文中的研究内容主要基于无源性概念,改进了互联和阻尼分配无源控制以提出此飞行器的姿态与高度控制方法.通过对于飞行器动力...     

Stabilisation of large-scale nonlinear systems by modifying the interconnection network

In this article, we develop a new strategy for the robust stabilisation of large-scale singular systems. The models that we will be concerned with consist of a large number of nonlinear subsystems, which are linked through a linear interconnection network. This approach does not require the availability of control inputs, and focuses instead on variable parameters in the interconnection network. It is shown that the determination of appropriate parameter values reduces to a constrained static output feedback problem, which can be solved using linear matrix inequalities. The proposed method is designed to minimise the number of optimisation variables, and is therefore suitable for large-scale applications. It can also incorporate information structure constraints and uncertainties in the system model.     

不确定状态滞后线性跳跃系统的时滞相关鲁棒非脆弱H∞控制

讨论了一类具有Markov跳跃参数的不确定混合线性时滞系统的鲁棒非脆弱控制问题.给出了使系统鲁棒随机稳定并具有给定的H∞性能的充分条件.并且通过参数变换和Schur补定理,将已得出的充分条件转化成一系列耦合的线性矩阵不等式形式以便于控制器参数的求解.仿真结果表明了本文提出的鲁棒非脆弱控制方法的有效性.     

Control of a class of patterned systems

Engineering systems are often architected to consist of a number of interconnected parts that interact in distinct patterns. Because most control design methods only provide general, unpatterned control laws, a compelling open question is how to synthesise distributed control laws that adhere to a system's interconnection pattern. This paper addresses patterned control synthesis for systems with interconnection patterns. The pattern is encoded algebraically through commuting relationships of the system's state space matrices. We show that several classic control problems are amenable to a patterned synthesis. Moreover, we show that these patterned control problems have the same solvability conditions as their unpatterned counterparts. That is, a patterned control law can be found whenever any control law can be found. Our findings suggest that patterned systems naturally admit patterned controllers.     

Robust performance of linear parametrically varying systems using parametrically-dependent linear feedback

In this paper a parameter-dependent control problem for linear parametrically varying (LPV) systems is presented. Sufficient conditions are given that guarantee an LPV system is exponentially stable and achieves an induced L₂-norm performance objective from the disturbance to error signals. The usefulness of parameter-dependent controllers is motivated from a gain-scheduling viewpoint. The resulting synthesis problem is reformulated into a convex optimization problem, which can be solved using efficient new algorithms.     

Some issues of structure and control for linear time-invariant systems

The objective of this paper is to emphasise the role played by particular structures in the solution of some control problems. The so-called “structural approach” relies on various indicators of dynamical systems such as, for instance, finite and infinite zeros, kernel indices, …. The fundamental invariance properties of these structures under the action of some transformations groups (e.g. feedback) are at the origin of their key role. Structural solutions to “classical” control problems, such as disturbance rejection, model matching and non-interaction are now rather well known: zeros at infinity play a role in the existence of “proper” solutions, while finite (invariant) zeros allow for the characterisation of “fixed poles”, whose location in the complex plane gives answer to pole placement limitations (including stability). Among the recent contributions to this structural approach, a particular attention is here devoted to:

- “Partial” versions of some of these control problems: The control objective only concerns a finite number of (and not necessarily all) the first Markov parameters of the transfer function matrix of the controlled system (e.g. to be zero for disturbance rejection or model matching, to be diagonal for non-interaction). Some interesting new issues in the dual context of failure detection are also sketched.

- Generalised solutions: Based on proportional and derivative feedback laws, with new issues in the context of systems with variable internal structures, and also for systems with delays.

Geometric concepts, such as invariant and almost invariant subspaces, and algebraic counterparts, such as factorisations on some special rings, are intermediary tools which support the characterisations of those particular structures and which allow for a structural treatment of the considered control and/or observation problems.

The results are here presented without proof: references are given to previous published results (in most cases in books and journals which are easily available), and some simple examples are used to illustrate non-standard notions (among which systems with variable internal structure, and time domain left invertibility).

Most of the results here presented rely on long and intensive collaborations between the author and various colleagues.     

Passivity-based control of linear time-invariant systems modelled by bond graph

Closed-loop control systems are designed for linear time-invariant (LTI) controllable and observable systems modelled by bond graph (BG). Cascade and feedback interconnections of BG models are realised through active bonds with no loading effect. The use of active bonds may lead to non-conservation of energy and the overall system is modelled by proposed pseudo-junction structures. These structures are build by adding parasitic elements to the BG models and the overall system may become singularly perturbed. The structures for these interconnections can be seen as consisting of inner structures that satisfy energy conservation properties and outer structures including multiport-coupled dissipative fields. These fields highlight energy properties like passivity that are useful for control design. In both interconnections, junction structures and dissipative fields for the controllers are proposed, and passivity is guaranteed for the closed-loop systems assuring robust stability. The cascade interconnection is applied to the structural representation of closed-loop transfer functions, when a stabilising controller is applied to a given nominal plant. Applications are given when the plant and the controller are described by state-space realisations. The feedback interconnection is used getting necessary and sufficient stability conditions based on the closed-loop characteristic polynomial, solving a pole-placement problem and achieving zero-stationary state error.     

Output-feedback control for switched linear systems subject to actuator saturation

This article is devoted to the output-feedback ?_∞ control problem for switched linear systems subject to actuator saturation. We consider both continuous- and discrete-time switched systems. Using the minimal switching rule, nonlinear output feedbacks expressed in the form of quasi-linear parameter varying system are designed to satisfy a pre-specified disturbance attenuation level defined by the regional ?₂ (?₂)-gains over a class of energy-bounded disturbances. The conditions are expressed in bilinear matrix inequalities and can be solved by line search coupled with linear matrix inequalities optimisation. A spherical inverted pendulum example is used to illustrate the effectiveness of the proposed approach.     

Simultaneous interconnection and damping assignment passivity-based control of mechanical systems using dissipative forces

To extend the realm of application of the well known controller design technique of interconnection and damping assignment passivity-based control (IDA-PBC) of mechanical systems two modifications to the standard method are presented in this article. First, similarly to Batlle et al. (2009) and Gómez-Estern and van der Schaft (2004), it is proposed to avoid the splitting of the control action into energy-shaping and damping injection terms, but instead to carry them out simultaneously. Second, motivated by Chang (2014), we propose to consider the inclusion of dissipative forces, going beyond the gyroscopic ones used in standard IDA-PBC. The contribution of our work is the proof that the addition of these two elements provides a non-trivial extension to the basic IDA-PBC methodology. It is also shown that several new controllers for mechanical systems designed invoking other (less systematic procedures) that do not satisfy the conditions of standard IDA-PBC, actually belong to this new class of SIDA-PBC.