Prescribed Stability Margin Research Articles

Sensitivity Analysis of Krasovskii Passivity-Based Controllers

In the domain of passivity theory, there were major contributions in the last decade, the most recent notion of passivity being the so-called Krasovskii passivity. This framework offers the possibility of designing a controller which ensures the passivity of the resulting closed-loop system. The current paper proposes a solution to design the parameters of Krasovskii passivity-based controllers (K-PBCs) in order to ensure small sensitivity of the closed-loop systems. As such, after the initial construction of the passivity output, the controller parameters are designed in order to impose the dominant eigenvalues of the Jacobian of the resulting closed-loop system with the smallest deviation around the given forced equilibrium point which is, additionally, smaller than a prescribed stability margin. The resulting optimization problem is non-convex by nature, and a metaheuristic approach is proposed to design these parameters. Moreover, in order to impose an extra set of performances, the control system contains an outer loop where dynamical path planning is used to impose the additional requirements. All mentioned results are developed for processes modeled as bilinear systems. In order to illustrate the proposed control method, a numerical example consisting of a single-ended primary inductor DC-DC converter (SEPIC) process is presented.

Analytic Solutions for Wheeled Mobile Manipulator Supporting Forces

When a mobile manipulator’s wheel loses contact with the ground, the manipulator may overturn, causing material damage, and in the worst case, putting human lives in danger. The overturning stability of wheeled mobile manipulators must not be overlooked at any stage of the mobile manipulator’s life, starting from the design phase, continuing through the commissioning period and extending to the operational phase. The various overturning stability criteria formulated throughout the years do not explicitly consider normal wheel loads, with most of them relying on the prescribed stability margins in terms of overturning moments. These formulations commonly consider the overturning moments regarding axes connecting the adjacent manipulator’s contact points with the ground and could be notably restrictive. Explicit expressions for the supporting forces of the manipulator provide the best insights into the relevant affecting terms that contribute to the overturning (in)stability. They also reduce the necessity for considering about which axis the manipulator could overturn and simultaneously enable the formulation of more intuitive stability margins and on- line overturning prevention techniques. The present study presents a general dynamics modelling approach in the Newton–Euler framework using 6D vectors and provides normal wheel load equations for a typical 4-wheeled rigid-chassis mobile manipulator traversing uneven terrain. The given expressions are expected to become the standard guidelines in considered wheeled mobile manipulators and to provide a basis for effective overturning stability criteria and overturning avoidance techniques. Based on the presented results, specific improvements of the state-of-the-art criteria are discussed.

Phase-compensating-system design using generalised stability-triangle

ABSTRACT This paper develops a new method for the design of a recursive allpass phase-compensating system (PCS) with an arbitrarily prescribed stability margin (SM). The design methodology comes from the generalised stability-triangle (GST) that defines a closed stability region for the second-order system, and the closed stability region is described by a pair of parameterised inequalities. Since the GST is developed for the second-order recursive system, to design a high-order PCS, we first construct a high-order PCS using the cascade of a set of second-order systems (sections), and then apply the GST to each of the second-order sections. The two coefficients of each second-order section are first transformed into two new variables by employing a coefficient-transformation technique, and then all the new variables are optimised in such a way that a given phase specification is best approximated. Thanks to both the coefficient transformations and the general stability condition from the GST, the resulting high-order PCS is not only stable, but also satisfies a prescribed SM design specification. This paper includes two examples to illustrate the usefulness of the GST-based PCS design.

Practical Sample-and-Hold Stabilization of Nonlinear Systems Under Approximate Optimizers

It is a known fact that not all controllable systems can be asymptotically stabilized by a continuous static feedback. Several approaches have been developed throughout the last decades, including time-varying, dynamical and even discontinuous feedbacks. In the latter case, the sample-and-hold framework is widely used, in which the control input is held constant during sampling periods. Consequently, only practical stability can be achieved at best. Existing approaches often require solving optimization problems for finding stabilizing control actions exactly. In practice, each optimization routine has a finite accuracy which might influence the state convergence. This work shows, what bounds on optimization accuracy are required to achieve prescribed stability margins. Simulation studies support the claim that optimization accuracy has high influence on the state convergence.

Stability Margins in Adaptive Mixing Control Via a Lyapunov-Based Switching Criterion

This paper proposes a Lyapunov-based switching logic within the framework of adaptive mixing control (AMC), where a weighted combination of a family of candidate controllers can be inserted in the loop to regulate the output of an uncertain plant. The proposed AMC scheme employs a bank of parallel estimators, or multiple estimators, together with a switching logic that orchestrates which estimate should be evaluated by the mixer. The switching logic is driven by input/output data and uses Lyapunov-based criteria to assess the best estimate among the bank of parallel estimates. The resulting scheme guarantees convergence of the switching signal in finite time to a controller that satisfies a Lyapunov inequality implying a prescribed stability margin. The problem of convergence to the desired controller is addressed both analytically and numerically. In contrast, most classes of continuous tuning adaptive control or switching adaptive control schemes do not guarantee that after the switching stops or the adaptation is switched off the resulting closed loop linear time-invariant (LTI) system is stable, unless there is sufficient plant excitation that guarantees convergence to the desired fixed parameter controller. The proposed scheme guarantees that if the desired controller is switched on, it will never be switched off thereafter. Furthermore, simulations demonstrate that while alternative adaptation methods can converge to an LTI unstable feedback loop, the proposed scheme consistently converges to the desired controller.

A backstepping approach to the output regulation of boundary controlled parabolic PDEs

In this article the output regulation problem for boundary controlled parabolic systems with spatially varying coefficients is solved by applying the backstepping approach. Thereby, the outputs to be controlled are not required to be measurable and can be pointwise, distributed or boundary quantities, whereas the measurement is located at the boundary. By solving the state feedback regulator problem in the backstepping coordinates regulator equations with a simple structure result, so that their analysis and solution is facilitated. The output feedback regulator design is completed by determining a finite-dimensional reference observer and an infinite-dimensional disturbance observer. For the latter a backstepping approach is presented that consists of a triangular decoupling in the backstepping coordinates. This allows a systematic design and the explicit derivation of directly verifiable existence conditions for the disturbance observer. It is shown that for the resulting compensator the separation principle holds implying output regulation for the exponentially stable closed-loop system with a prescribed stability margin. The output regulation results of the article are illustrated by means of a parabolic system with an in-domain pointwise controlled output.

MULTI‐HOPPING INDUCED GAIN SCHEDULING FOR WIRELESS NETWORKED CONTROLLED SYSTEMS

ABSTRACTA multi‐hopping induced gain scheduler for Wireless Networked Controlled Systems (WiNCS) is proposed. The control scheme is based on a client‐server architecture. The data packets are assumed to be carried over a network composed of wireless sensor nodes running the 802.11b protocol. The number of hops necessary for packets to reach their destinations is variable and depends on current traffic conditions. Changes in the number of hops induces changes in the latency times introduced by the communication network in the feedback loop. To deal with these changes an LQR‐output feedback scheme is introduced, whose parameters are adjusted according to the number of the hops. The weights of the LQR controllers are subsequently tuned using LMIs to ensure a prescribed stability margin despite the variable latency times. The overall scheme resembles a gain scheduled controller with the number of hops playing the role of the scheduling parameter. Simulation results on the NS‐2 simulator are provided to highlight the efficacy of the proposed scheme.

LMI-BASED ANALYSIS FOR CONTINUOUS-DISCRETE LINEAR SHIFT-INVARIANT nD SYSTEMS

In this paper, we describe the Linear Matrix Inequality (LMI) approach to the analysis and the synthesis of continuous-discrete linear shift-invariant multidimensional systems presented in the Roesser form. We consider stability, stability margins, robust stability, stabilization and stabilization to the prescribed stability margins and robust stabilization. An example is included as illustrations of the obtained results.

An observer design procedure for a class of nonlinear time-delay systems

This paper considers a class of uncertain, nonlinear differential state delayed control systems and presents a reduced-order observer design procedure to asymptotically estimate any vector state functionals. The method proposed involves decomposition of the delayed portion of the system into two parts: a matched and mismatched part. Provided that the rank of the mismatched part is less than the number of the outputs, a reduced-order linear functional observer, with any prescribed stability margin, can be constructed by using a simple procedure. A numerical example is given to illustrate the new design procedure and its features.

Optimal design of IIR digital filters with robust stability using conic-quadraticprogramming updates

In this paper, minimax design of infinite-impulse-response (IIR) filters with prescribed stability margin is formulated as a conic quadratic programming (CQP) problem. CQP is known as a class of well-structured convex programming problems for which efficient interior-point solvers are available. By considering factorized denominators, the proposed formulation incorporates a set of linear constraints that are sufficient and near necessary for the IIR filter to have a prescribed stability margin. A second-order cone condition on the magnitude of each update that ensures the validity of a key linear approximation used in the design is also included in the formulation and eliminates a line-search step. Collectively, these features lead to improved designs relative to several established methods. The paper then moves on to extend the proposed design methodology to quadrantally symmetric two-dimensional (2-D) digital filters. Simulation results for both one-dimensional (1-D) and 2-D cases are presented to illustrate the new design algorithms and demonstrate their performance in comparison with several existing methods.

Linear functional state observer for time-delay systems

A new linear functional state observer for time-delay systems is introduced in this paper. It is shown that the observer converges, with any prescribed stability margin, to any number of linear functionals when some conditions are met. The design procedure is simple and can be easily implemented. Numerical examples are given to illustrate the properties of the new observer and its advantages over existing observer design techniques in the literature.

Design of recursive digital filters with prescribed stability margin: a parameterization approach

A major problem in the design of recursive digital filters is stability. Although an unstable recursive filter obtained from a design algorithm can be stabilized by reciprocal substitution of the unstable factors of the filter without changing its amplitude response, this stabilization technique cannot be applied if phase response is a part of the design specifications. In this paper, we propose a new method for the design of recursive digital filters with a prescribed stability margin by parameterizing all stable transfer functions and carrying out unconstrained optimization over this class of transfer functions. Three parameterization techniques are described, and closed-form formulas for the gradient functions and Hessian matrices of several typical objective functions are derived. The design technique is expected to be useful in the cases where both amplitude and phase specifications are required in the design.

Slenderness of Flexible Robot Links: Dynamic Model Selection

Abstract In this paper a case study for the slenderness of single-link flexible robot arms is presented for the purpose of appropriate dynamic model selection. The term of ‘slender flexible links’ is clarified by two new concepts, slenderness margin and slenderness error, which are available for selections of appropriate models. An easily checkable quatitive criterion obtained by robust control theory can be used to identify whether or not a flexible link is slender for a prescribed stability margin. Computer simulation studies are given to illustrate our useful conclusions.

On the stability properties of hexapod tripod gait

Hexapod tripod gaits for straight-line motion and crab walking are derived. Mathematical relations that express the stability margin, the stride length, and the duty factor are formulated for straight-line motion and for crab walking, respectively. The derived results provide tripod gaits of the hexapond for walking with a prescribed stability margin either over perfect terrain or constant slope terrain. >

Design of type-1 servo systems possessing prescribed stability margins using a generalized Riccati-type equation

A design method for type-1 servo systems having prescribed stability margins at the control input and error channels is presented. The former and latter stability margins affect the properties of sensitivity and robustness and the transient response characteristics, respectively. As a preliminary, a class of state feedback laws for regulators that possess a prescribed stability margin is parametrized by means of a generalized Riccati-type equation. This is applied to designing servo systems, which enables us to specify the stability margins at the above two portions. We can improve the output response of the system by the proposed design procedure and the effect is ascertained by an example. The integrity at the error channel is also investigated.

Digital computer control of large scale power systems

The problem of the control of large scale power systems is investigated in this paper. A control stategy which satisfy prescribed stability margins is developed using decomposition-coordination principles of hierarchical control. The potential application of the method is illustrated by an example consisting of three power plants.

Stabilizability of linear discrete-time dynamical systems with retarded control

Abstract In this paper, conditions for the stabilizability by linear state feedback of a class of linear discrete-time dynamical systems with retarded control are established using tho method of D-partition : in addition, conditions for the existence of prescribed stability margins in such systems are established. Typical transient response characteristics which illustrate these stabilizability conditions are presented.