Number Of Control Inputs Research Articles

Cheap control performance of a class of nonright-invertible nonlinear systems

For strict-feedback nonlinear systems, this paper shows that it is impossible to reduce to zero the optimal cost in the regulation of more states than the number of control inputs in the system, even using an unrestricted control effort. By constructing a near-optimal cheap control law, we characterize the infimum value of the optimal regulation cost as the optimal value of a reduced-order regulator problem. We illustrate our results with an example on the optimal control of a magnetic suspension system.

Structural vibration control

Undesirable time-variable motions of dynamical structures (e.g. scales, balances, vibratory platforms, bridges and buildings) are mainly caused by unknown or uncertain excitations. In a variety of applications it is desirable or even necessary to attenuate these disturbances in an effective way and with moderate effort. Hence, several passive as well as active methods and techniques have been developed in order to treat these problems. However, employment of active techniques often fails because of their considerable financial costs. We propose an affordable control scheme which accounts for the above-mentioned deficiencies. In addition, we allow constraints on control actions. Furthermore, the number of control inputs (actuators) may be arbitrary, i.e., the system may be mismatched. The scheme is based on Lyapunov stability theory and, provided that the bounds of the uncertainties are a priori known, a stable attractor (ball of ultimate boundedness) of the structure can be computed. In case measurement errors or uncertainties, respectively, are significant, it is shown how the Lyapunov-based control scheme may be combined with a fuzzy control concept. The effectiveness and behavior of the control scheme is demonstrated on two simplified models of elastic structures such as a two story building and a bridge subjected to a moving truck.

Partially Adaptive Control of an Inverted Pendulum and Cart System

It is difficult to apply the existing adaptive control methods to an inverted pendulum and cart system if it is assumed that all physical parameters are unknown, because the number of control inputs is less than that of outputs. Regarding the inverted pendulum system, the parameter uncertainties of the cart are larger than those of the pendulum. In this paper, the partially adaptive control system is designed considering that the parameter uncertainties exist only in the cart. The inverted pendulum and cart system is divided into the known part which includes only the parameters of the pendulum and the unknown part which includes the parameters of the cart. Therefore, LQ control is applied to the known part and adaptive control treats the unknown part based on the backgtepping technique. Finally, the experimental results are provided and the usefulness of this technique is confirmed.

Linear Time-Varying Dynamic Systems Optimization via Higher-Order Method: A Sub-Domain Approach

A new procedure for optimization of linear time-varying dynamic systems has been proposed that uses transformations to embed the dynamic equations explicitly into the cost functional. This leads to elimination of Lagrange multipliers and characterization of the optimality equations by high-order differential equations in the same number of variables as number of control inputs. This procedure requires that the transformation matrix be nonsingular at all time within the domain. This paper extends this procedure to problems where a single nonsingular transformation matrix does not exist over the entire domain. In this paper, the time domain is partitioned into intervals such that a nonsingular transformation exists over each interval. The transformations are used to embed the dynamic equations into the cost functional. Variational analysis of the unconstrained cost functionals results in the optimality equations, which are solved efficiently by weighted residual methods. [S0739-3717(00)00601-2]

Neural adaptive regulation of unknown nonlinear dynamical systems

With this paper we extend our previous work on the subject, by including the case where the number of control inputs is different from the number of states which is frequently faced in control engineering problems. Uniform ultimate boundedness of the state and uniform boundedness of all other signals in the closed loop is guaranteed. Robustness of our algorithm due to the presence of a modeling error term which has linear growth with unknown growth coefficient is also established. Finally, the applicability of our control scheme is highlighted via simulation results.

Design of Constant Gain Dissipative Controllers for Eigensystem Assignment in Passive Systems

Partial eigensystem assignment with output feedback can lead to an unstable closed-loop system. However, output feedback with passive linear time-invariant systems, such as flexible space structures, is guaranteed to be stable if the controller is dissipative. This paper presents a novel approach for synthesis of dissipative output feedback gain matrices for assigning a selected number of closed-loop poles. Dissipativity of a gain matrix is known to be equivalent to positive semidefiniteness of the symmetric part of the matrix. A sequential procedure is presented to assign one self-conjugate pair of closed-loop eigenvalues at each step using dissipative output feedback gain matrices, while ensuring that the eigenvalues assigned in the previous steps are not disturbed. The problem of assigning one closed-loop pair is reduced to a constrained solution of a system of quadratic equations, and necessary and sufficient conditions for the existence of a solution are presented. A minimax approach is presented for determining parameters which satisfy these conditions. This method can assign as many closed-loop system poles as the number of control inputs. A numerical example of damping enhancement for a flexible structure is presented to demonstrate the approach.

Efficient modelling and synthesis procedure of asynchronous sequential logic elements

A model and procedure are developed for synthesising asynchronous sequential logic elements (ASLEs). This model represents the functional behaviour with a more compact form, and the procedure can synthesise them more efficiently than the traditional one. With the delineation of inputs as mode inputs,level inputs and edge inputs from the design specification, a set of equations can be generated which describes the logic module's functional behaviour. The calculated states from these equations have bipartite adjacency relationships, which can easily be mapped onto an n-cube to obtain race-free state assignments. This procedure can also be applied for the synthesis of an asynchronous sequential logic circuit (ASLC) which has many data inputs and a small number of control inputs.

Analysis of function duplicating capabilities of fuzzy controllers

Abstract Fuzzy controllers have been successfully applied to many cases to which conventional control algorithms are difficult to be applied. Even though the representations and the processings of data and information in the fuzzy controller are quite different from other control algorithms, the information processing operation that it carries out is basically a function f:A ⊂ Rn→Rm, from a bounded subset A of n-dimensional Euclidean space to a bounded subset f[A] of m-dimensional Euclidean space, where n and m are the number of measured states and the number of control inputs of controlled system, respectively. Under the assumptions of Mamdani's direct reasoning method, and C.O.G. (center of gravity) defuzzification method, the fuzzy controllers are proven to perform the mappings of any given functions with appropriately defined fuzzy sets. The mapping capabilities of the fuzzy controllers are analyzed in detail for two cases; f:R1 → R1 and g:R2 → R1. Also, it will be shown that the results can be extended to multiple dimensional cases.

Robust adaptive control of revolute flexible-joint manipulators using sliding technique

In this paper, we present a 3-step procedure to robustly control the revolute flexible-joint manipulator in the presence of parameter variations and bounded input disturbances such as torque ripples. By treating the difference of motor angle and link angle as the input to the rigid link part of the manipulator dynamics, our first step is to design a smooth adaptive reference signal for this input to globally stabilize the rigid subsystem. The second step is to drive the difference of motor and link angles to this desired reference signal exponentially by using sliding control. In the third step we exploit the model reduction capability of sliding control to perform the stability analysis. It is well-known that sliding control can reduce the system order by n if the number of control inputs is n. The exploitation of this property of sliding control makes our stability analysis a lot simpler than other approaches. Global stability in the sense of Lyapunov can be guaranteed and errors in link position and velocity are driven to zero when the system is in sliding mode. No weak elasticity assumption is needed.

Local observability and controllability of stirred tank reactors

Abstract This paper deals with the observability and controllability properties of the linearized tangent dynamic model of (bio)chemical processes in isothermal stirred tank reactors (STRs). It is shown that a necessary condition for the observability (controllability) of isothermal (bio)chemical processes is that the number of measured components (the number of control inputs) is larger than or equal to the number of process components minus the number of reactions involved in the process. This gives a simple test for detecting possible lack of observability and/or controllability of isothermal STRs.

Composite Computed Torque Control of Robots with Elastic Motor Transmissions

Abstract The main problem in the control of robots with elastic transmissions between the actuators and the rigid links is caused by the number of control inputs being less than the number of degrees of freedom. This problem has been faced by a composite control law consisting of the conventional ’rigid’ computed torque controller for link-based trajectory tracking and a ’flexible’ computed torque part multiplicated with the inverse of the stiffness matrix for stabilization of the elastic deflections. The resultant control system resembles the socalled ’two-time scale sliding control’ technique of Slotine and Hong (1987), but in our approach the stiffnesses of the elastic motor transmissions do not have to be relatively large neither is there the restriction that there have to be as many motor inputs as elastic transmissions. The goal of the composite controller is that the individual link trajectories will follow the desired trajectories while the elastic-transmission forces/torques, which are not directly constrained by the output specifications, remain on a certain ’manifold’ due to the natural flexibility behavior of the system. The key concept is illustrated with simulation results of a translation-rotation robot with one torsional-elastic motor transmission.

Design of crosspoint-irredundant PLAs using minimal number of control inputs

The problem of determining a minimal number of control inputs for converting a programmable logic array (PLA) with undetectable faults to crosspoint-irredundant PLA for testing has been formulated as a nonstandard set covering problem. By representing subsets of sets as cubes, this problem has been reformulated as familiar problems. It is noted that this result has significance because a crosspoint-irredundant PLA can be converted to a completely testable PLA in a straightforward fashion, thus achieving very good fault coverage and easy testability. >

A Design for Testability of Undetectable Crosspoint Faults in Programmable Logic Arrays

In this paper, the validity of single fault assumption in deriving diagnostic test sets is examined with respect to crosspoint faults in programmable logic arrays (PLA's). The control input procedure developed here can be used to convert PLA's having undetectable crosspoint faults to crosspoint-irredundant PLA's for testing purposes. All crosspoints will be testable in crosspoint-irredundant PLA's. The control inputs are used as extra variables during testing. They are maintained at logic 1 during normal operation. A useful heuristic for obtaining a near-minimal number of control inputs is suggested. Expressions for calculating bounds on the number of control inputs have also been obtained.

The Assessment of Rotary Wing Aviator Precision Performance during Extended Helicopter Flights

To insure the most effective utilization of his aviation resources, the rotary wing flight commander requires information which describes how extended flight time affects the operational capability of his flight crews. In response to this requirement, the US Army Aeromedical Research Laboratory has conducted an investigation of the man-helicopter system performance during five days of extended flight. The current report describes the changes in pilot performance and aircraft stability on one of the maneuvers performed during the large scale fatigue investigation, the stabilized three-foot (.91 meter) precision hover. The results obtained during the current examination strongly suggest the occurrence of a learning effect across the first day of extended flight. The most stable hover performance was observed during the second flight day. By the third flight day, pilots attempted to maintain high quality precision hovers through an increase in the number of control inputs. Results obtained on the fourth day of flight suggest that the pilots have shifted their control technique from active control of the helicopter to a more passive strategy of responding to observed error.