Admissible Reference Signals Research Articles

Funnel control of nonlinear systems

Tracking of reference signals is addressed in the context of a class of nonlinear controlled systems modelled by r-th-order functional differential equations, encompassing inter alia systems with unknown “control direction” and dead-zone input effects. A control structure is developed which ensures that, for every member of the underlying system class and every admissible reference signal, the tracking error evolves in a prescribed funnel chosen to reflect transient and asymptotic accuracy objectives. Two fundamental properties underpin the system class: bounded-input bounded-output stable internal dynamics, and a high-gain property (an antecedent of which is the concept of sign-definite high-frequency gain in the context of linear systems).

Reconstruction of admissible joint-references from a prescribed output-reference for the non-standard and generalized N-trailers

A reconstruction of admissible reference signals for the inner dynamics upon a prescribed output reference of a dynamical system is a one of the key problems stated in the control theory. We address this problem with respect to a class of driftless dynamical systems representing nonholonomic kinematics of the N-trailers equipped with the on-axle and off-axle hitching, including difficult cases of the differentially non-flat and nonminimum-phase kinematics. Given a prescribed admissible reference path or trajectory for the last trailer’s posture (treated as a reference output), we analyse possible solutions to the reconstruction problem for different types of the reference output. We propose a computational procedure to reconstruct the corresponding references (in a continuous domain of some parametrizing variable) for the joint angles of the N-trailer vehicles comprising an arbitrary number of segments interconnected by any type of hitching. In particular, we show how to find an admissible solution to the reconstruction problem, that is, the one which does not exhibit a jackknife effect, by appropriate searching in a set of all the possible (at least 2N) solutions. The proposed computational method is formally explained and numerically verified for the 3-trailer kinematics equipped with various types of hitching.

Reference Tracking With Guaranteed Error Bound for Constrained Linear Systems

We propose a control design for a constrained linear system to track reference signals within a given bounded error. The admissible reference signals are generated as output trajectories of a reference generator, which is a constrained linear system driven by unknown bounded inputs. The controller has to track the reference signals and to never violate a given tracking error bound, while satisfying state and input constraints, for any admissible reference. The design is based on a model predictive controller (MPC) enforcing a polyhedral robust control invariant set defined by the system and reference generator models and constraints. We describe an algorithm to compute the robust control invariant set and how to design the tracking MPC law that guarantees satisfaction of the tracking error bound and of the system constraints, and achieves persistent feasibility. We demonstrate the proposed method in two case studies.

A reference governor-based controller for a cable robot under input constraints

Cable-suspended robots are structurally similar to parallel actuated robots but with the fundamental difference that cables can only pull the end-effector but not push it. From a scientific point of view, this feature makes feedback control of cable-suspended robots lot more challenging than their counter- part parallel actuated robots. In this brief, we look into the control design for a nonredundant cable-suspended robot under positive input constraints. The design is based on feedback linearization controllers augmented with a reference governor (RG). This RG operates in accordance with the receding horizon strategy, by generating admissible reference signals, that do not violate the input constraints. An important issue in implementing such an algorithm for nonlinear systems is to predict the system behavior in a computationally efficient way. We show that feedback lin- earization controllers with the RG can offer an efficient way to predict the system's future states, using the error dynamics of inner feedback loop. Finally, the effectiveness of the proposed method is illustrated by numerical simulation and laboratory experiments on a 6-degree-of-freedom cable suspended robot.

Systems of Controlled Functional Differential Equations and Adaptive Tracking

An adaptive servomechanism is developed in the context of the problem of approximate or practical tracking (with prescribed asymptotic accuracy), by the system output, of any admissible reference signal (absolutely continuous and bounded with essentially bounded derivative) for every member of a class of controlled dynamical systems modelled by functional differential equations.

Any Domain of Attraction for a Linear Constrained System is a Tracking Domain of Attraction

In the stabilization problem for systems with control and state constraints a domain of attraction is a set of initial states that can be driven to the origin by a feedback control without incurring constraints violations. If the problem is that of tracking a reference signal, that converges to a constant constraint-admissible value, a tracking domain of attraction is a set of initial states from which the reference signal can be asymptotically approached without constraints violation during the transient. Clearly, since the zero signal is an admissible reference signal, any tracking domain of attraction is a domain of attraction. We show that the opposite is also true. For constant reference signals we establish a connection between the convergence speed of the stabilization problem and tracking convergence which turns out to be independent of the reference signal. We also show that the tracking controller can be inferred from the stabilizing (possibly nonlinear) controller associated with the domain of attraction.

A nonlinear universal servomechanism

A servomechanism problem of controlling a scalar output variable to /spl lambda/-track any reference signal from some prescribed function space R, whilst maintaining internal states bounded, is addressed for a class S of uncertain nonlinearly-perturbed, single-input, single-output, minimum-phase, relative-degree-one, linear systems with nonlinear actuator characteristics (encompassing, for example, hysteresis and dead-zone effects). The actuator characteristics are required only to be contained in the graph of a suitably regular set-valued map. The terminology "/spl lambda/-tracking" is used in the following sense: for arbitrary prescribed /spl lambda/>0, an (adaptive) feedback strategy is sought which, for every reference signal of class R and every system (unknown to the controller) of class S, ensures that the tracking error is asymptotic to the interval /spl lsqb//spl minus//spl lambda/,/spl lambda//spl rsqb//spl sub/R. The instantaneous values of the reference signal and scaler output only are available for feedback. Adopting the space W/sup 1,/spl infin//(R) as the set R of admissible reference signals and under fairly weak assumptions on the nature of the system nonlinearities, one such (R, S)-universal adaptive feedback solution to this servomechanism problem is constructed. The feedback is continuous and its construction does not invoke an internal model principle.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>