Minimum Control Effort Research Articles

Design of an optimal feedback linearizing-based controller for an experimental flexible-joint robot manipulator

This paper presents the design of an optimal non-linear position tracking controller for a two-link flexible joint robot manipulator. The controller is designed based on the concept of exact feedback linearization and LQG/LTR techniques. It is shown that the non-linear robot model is feedback linearizable and a characterization of the set, over which the linearizing transformation is diffeomorphic, is provided. The proposed control approach reduces the number of required measurement sensors and takes into account the effects of measurement noises. A new method for computing the non-linear state estimate is also presented. It takes advantage of the linear structure of the transformed system. Simulation results demonstrate the potential benefits of the proposed control approach in reaching the desired performance with minimum control effort. Copyright © 1999 John Wiley & Sons, Ltd.

Robust H∞ Static Output Feedback Control with Actuator Saturation

There are several key issues to be considered in the design of active control systems for civil structures, including robustness to perturbations of the structural parameters stability in the presence of nonlinear actuator saturation effects and the use of output feedback methods when it is either impossible or impractical to obtain the full state of the system. This research presents a design algorithm to create robust \iH∞ static output feedback controllers for seismically excited civil structures, which account for all these effects in a single design. Robust static acceleration feedback \iH∞ controllers are created for a five-story structure with a bounded, structural parameter uncertainty model. A nonconvex optimization problem is formulated and solved using an iterative solution method to obtain the desired control gains. A primary advantage of this method is that an intuitive, feasible starting point is available using the open loop (uncontrolled) system and the worst case attenuation constant for the uncertain system. Simulation results using seismic excitations show controllers obtained using this design method to be effective with minimal control effort.

On the Robust Nonlinear Motion Position and Force Control of Flexible Joints Robot Manipulators

The design of a robust nonlinear position and force controller for a flexible joints robot manipulator interacting with a rigid environment is presented. The controller is designed using the concept of feedback linearization, sliding mode techniques, and LQE estimation methodologies. It is shown that the nonlinear robot manipulator model is feedback linearizable. A robust performance of the proposed control approach is achieved by accounting for the system parameters uncertainties in the derivation of the nonlinear control law. An upper bound of the error introduced by parametric uncertainties in the system is computed. Then, the feedback linearizing control law is modified by adding a switching action to compensate the errors and to guarantee the achievement of the desired tracking performance. The relationship between the minimum achievable boundary layer thickness and the parametric uncertainties is derived. The proposed controller is tested using an experimental flexible joints robot manipulator, and the results demonstrate its potential benefits in reducing the number of sensors required and the complexity of the design. This is achieved by eliminating the need for nonlinear observers. A robust performance is obtained with minimum control effort by taking into account the effect of system parameter uncertainties and measurement noise.

Optimal control of first-order plants by dead-beat techniques

The design of optimal dead-beat controllers for first-order plants is considered. The simple nature of these plants leads to ripple-free step response, a property that is highly desirable. The minimum energy and minimum effort control problems are formulated and solved with an analytical and generalized approach. Analytical expressions for the digital controller pulse transfer functions along with the resulting control sequences are derived. Generalized curves for the maximum control signals appearing in the system are also presented. The latter can be used for the determination of the minimum sampling period when the maximum control signal is specified. © 1997 John Wiley & Sons, Ltd.

Optimal control of first‐order plants by dead‐beat techniques

The design of optimal dead-beat controllers for first-order plants is considered. The simple nature of these plants leads to ripple-free step response, a property that is highly desirable. The minimum energy and minimum effort control problems are formulated and solved with an analytical and generalized approach. Analytical expressions for the digital controller pulse transfer functions along with the resulting control sequences are derived. Generalized curves for the maximum control signals appearing in the system are also presented. The latter can be used for the determination of the minimum sampling period when the maximum control signal is specified. © 1997 John Wiley & Sons, Ltd.

A Convergent Algorithm for the Output Covariance Constraint Control Problem

This paper considers the optimal control problem of minimizing control effort subject to multiple performance constraints on output covariance matrices $Y_i$ of the form $Y_i \leq \overline{Y}_i$, where $\overline{Y}_i$ is given. The contributions of this paper are a set of conditions that characterize global optimality, and an iterative algorithm for finding a solution to the optimality conditions. This iterative algorithm is completely described up to a user-specified parameter. We show that, under suitable assumptions on problem data, the iterative algorithm converges to a solution of the optimality conditions, provided that this parameter is properly chosen. Both discrete- and continuous-time problems are considered.

Dominant mode method for the minimum time design of slewing flexible structures

This paper presents a dominant mode method for minimum-time design of slewing flexible structures. The involved nonlinear two-point boundary problem incorporating rigid slewing manoeuvre and flexibility of the structure is linearized and then decoupled using eigenmode-based transformation. Slewing mode of the structure is chosen as the dominant mode which dominates the slew manoeuvre of the structure, and used to minimize the time of slewing manoeuvre from initial to final desired states subject to constrained input. Quadratic control input is suggested for the remaining flexible modes. It follows a mixture of bang-bang and quadratic feedback control law for the structure. Minimum control effort measured by quadratic formula is derived. Using the present method, a smooth and precise positioning for a slewing flexible beam is obtained.

Minimum fuel spacecraft reorientation

Fuel optimal solutions for the reorientation of an inertially symmetric rigid spacecraft with independent three-axes controls are investigated. All possible optimal control strategies are identified. These include bangbang solutions, finite-order singular arcs, and infinite-order singluar arcs. Higher order necessary conditions for optimality of finite-order singular arcs are presented. Numerical examples of fuel optimal solutions with fixed maneuver time are presented involving all of the theoretically possible control logics. I. Introduction O PTIMAL rigid body rotational maneuvers have been studied by many researchers in the context of spacecraft attitude control systems.15 Minimum time problems with bounded control energy and/or minimum control effort problems subject to fixed maneuver time have been the main objectives in these studies. In a recent study Bilimoria and Wie1 were the first to successfully solve minimum time 180-deg rest-to-rest reorientation problems subject to bounded control torques through a rigorous optimal control approach. Later, Seywald and Kumar6 gave a complete analysis of all possible control logics associated with the same dynamical system and performance index. Besides the nonsingular control solutions found in Ref. 1, finite- and infinite-order singular control strategies were derived and numerical examples involving these control logics were presented. In the present paper, the authors investigate the problem of reorienting an inertially symmetric spacecraft with minimum fuel expenditure from given initial angular position and velocity to fully or partly prescribed final positions. Three bounded independent control torques are assumed with the control axes aligned along prescribed principal axes. The mass of fuel burned is ignored in that the moments of inertia are unchanged during the maneuver. Except for an additional mass differential equation, the dynamical system used here is the same as in Refs. 1 and 6. The identification of all possible optimal control logics for the problem stated is emphasized. To avoid absolute values in the right-hand side of the fuel mass differential equation, each control torque is divided into its positive and its negative component, thus giving rise to six mathematical controls instead of the three physical controls. For each of the six mathematical controls, the possible optimal control logics are either bangbang type, or of finite/infinite-order singular type. Higher order necessary conditions for optimality of finiteorder singular arcs are examined using Goh transformations of the associated accessory minimum problem. Numerical examples of optimal solutions with bang-bang structure as well as finite- and infinite-order singular arcs are presented.

Minimum effort factor approach for sensor-based control of a four-joint 6-dof redundant manipulator

A sensor-driven control model and a minimum effort control algorithm in terms of time and energy expended during the execution of a movement strategy are described and validated for a multijointed cooperating robotic manipulator. Considering smooth, human-like (anthropomorphic) movements, using joint motion profiles achievable in real time as well as sensory information from all joints, and evaluating the total work expended by each manipulator joint during the execution of a movement strategy, a minimum effort motion trajectory is synthesized to precisely and efficiently position the robotic arm end-effector. This sensor-based approach significantly reduces the computational requirements for such cooperative motion. The minimum effort control algorithm generates several human-like arm movement strategies and selects the best strategy on the basis of expendable effort. The algorithm has an inherent basis to deal with obstacles in an efficient way. Detailed examples are described from the simulation studies. © 1994 John Wiley & Sons, Inc.

Optimal control law synthesis for flutter suppression using active acoustic excitations

This paper describes a development of the optimal control law design procedure for the flutter suppression of airfoils using active acoustic excitations. A bending-torsion typical section and a two-dimensional incompressible aerodynamic model are adopted for the present analysis. An irreducible state-space description of the aeroservoelastic system is constructed via the use of Hankel matrices and the singular value decomposition method. The evaluation of the degree of controllability/observability and the synthesis of the optimal control law using steady-state linear quadratic regulator theory accompanied by an asymptotic state observer are performed. This optimal control law design enables the search of the most effective position to locate the sound wave generator. The trailing edge is shown to be the best region for installing the sound wave generator, where the highest degree of controllability and the minimal control effort are attained. A case study shows that approximately 20 dB reduction in sound pressure level can be achieved using this optimal control law design.

Equilibrium-point hypothesis, minimum effort control strategy and the triphasic muscle activation pattern

Equilibrium-point hypothesis, minimum effort control strategy and the triphasic muscle activation pattern

Synthesis of Statistical Quality Control and Optimal Control

In this paper it is argued that a combination of SQC methods with Optimal Control technology (such as LQG or H ∞ ) yields a novel on-line quality control method, A solution is presented for the “design” problem of weighting matrix selection, which has hampered the success of potentially powerful optimal control techniques. Optimal selection of these weighting matrices results in sufficient contraction of quality variance to meet “on-spec” probabilities, with minimal control effort. Practical issues are being addressed, such as design transparency, the “best” control target, mininlally required variance contraction, highest achievable quality specs, observability of disturbances and feedforward techniques. The attractiveness of the concept is illustrated with a numerical design example, applying SQC/LQG to a fifth-order unstable plant

The utilization of international joint ventures by United States firms in high technology industries

Although international joint ventures have been widely studied for many years, very little is known about such alliances as used by high technology firms based in the United States. Therefore, this study surveys 9 U.S. high technology firms regarding 14 of their international joint ventures. The rationale for these alliances, the control of key resources, and the successfulness of high tech international joint ventures are explored. Based on this preliminary study, it appears that these operations, if established with a trustworthy partner, can be successful while requiring only minimal transaction costs and minimal control efforts.

Optimal placement of controllers for seismic structures

Active control devices can be implemented on seismic structures to reduce structural response from earthquakes. Certain locations of the structure are advantageous for placement of the controllers in the sense that these locations effectively reduce structural response while using the minimum control effort. A method is proposed which uses an empirical procedure to find the optimal locations by maximizing an optimal locations index. The method takes into consideration the modal responses and earthquake spectra for two different earthquake records. The proposed method is compared to two methods; in the first method a control energy performance index is minimized; the second method uses a minimum response performance index as the criterion. The proposed method is found to agree with the two alternative methods and saves computation time.

An investigation of the time required for control of structures

The minimum time required for accomplishing a rigid-body maneuver of a flexible structure by means of a finite number of unbounded inputs is investigated. The control task is accomplished by driving a finite number of structure modes from an initial state of zero to a desired final state in a given time interval. A minimum-effort control strategy is used so that uncontrolled higher modes will not be excited excessively by the control inputs. It is found that for less than a certain time interval for control, it is not possible to decrease the amount of spillover energy in uncontrolled modes at the end of the control interval by driving more flexible modes to zero. This time interval is identified as the minimum time required for control of flexible structures, and it is related to the time required for waves to travel through the structure. For one-dimensional second-order systems, the minimum time is equal to the time required for waves to travel between adjacent pairs of actuators. A similar result is found for fourth-order systems. Because the period of the lowest flexible mode is equal to the time required for a wave to make a round trip throughout the structure, the minimum time for control is in general some fraction of the period of the lowest flexible mode, which is determined by the number and placement of actuators.

Optimal feedback slewing of flexible spacecraft

A method is presented for maneuvering a flexible spacecraft from one position to another while leaving an arbitrary number of bending modes inactive at the end of the maneuver. The method combines standard fixedtime linear quadratic Gaussian regulator control theory with a modal decomposition of a flexible body. Further features of the method are that it uses minimum control effort and it can be converted to a feedback form to deal with random disturbances and parameter uncertainties. Several examples are given to demonstrate the efficacy of the method, and results from a hardware experiment are presented.

Prediction of Pilot-Aircraft Stability Boundaries and Performance Contours

Control-theoretic pilot models can provide important new insights regarding the stability and performance characteristics of the pilot-aircraft system. Optimal-control pilot models can be formed for a wide range of flight conditions, suggesting that the human pilot can maintain stability if he adapts his control strategy to the aircraft's changing dynamics. Of particular concern is the effect of suboptimal pilot adaptation as an aircraft makes transitions from low to high angles of attack during rapid maneuvering, as the changes in aircraft stability and control response can be extreme. The effects of optimal and suboptimal effort during a typical "high-g" maneuver are examined, and the concept of minimum-control effort (MCE) adaptation is introduced. Limited experimental results tend to support the MCE adaptation concept.

Optimal control of linear continuous systems with multiple control constraints

Abstract The present paper deals with a minimum effort control problem with a control performance index and a time optimal control problem with multiple control constraints of linear continuous systems. The problems are reduced to finding the predual norms and an L-problem in the theory of moments is used to obtained the solutions.

The geometry of the minimum cost problem

In recent years considerable attention has been given to a class of linear control problems known as minimum effort problems. There are various approaches to the problem and many generalizations. In 1962, Neustadt [l] formulated the minimum effort problem, and in 1964 he extended this problem to a formulation in Lebesque spaces. Also in 1962, Reid [2] con- sidered a problem of this type and again the setting was in Lebesque spaces. Reid and Neustadt both attacked the problem by transforming the mini- mum norm problem to an equivalent finite moment problem. In 1966, Porter and Williams [3] formulated the minimum effort control problem in an abstract Banach space and applied classical techniques of functional analysis to analyze the problem. In [4], Minamide and Nakamura considered a problem which includes as special cases the minimum effort problems and a class of approximation problems. The method of Minamide and Nakamura is very geometric and informative. In this paper, we present a problem which is a direct generalization of Problem (P) in [4], and an existence result. The problem is formulated without any references to topological structure, and we prove the existence of an optimal solution by applying an affine separation theorem. We take this abstract approach for two reasons. The abstract approach is geometric and provides insight into the structure of the problem. Also, this geometric approach illustrates that affine separation is sufficient in many existence proofs while, in general, continuous supporting functionals are needed to discuss necessary conditions. Moreover, there is no requirement that the operators be continuous, and hence the results obtained may be applied without “solving” the “state equations.”

Minimum-effort time-optimal control of linear discrete systems†

An iterative algorithm based on linear programming for solving the minimum-time minimum-effort discrete control problem for linear time-invariant systems is presented. The algorithm is based on transforming the minimum-effort problem to an equivalent linear programming one. Some interesting properties of the iterative linear programming algorithm are shown which result in reducing the computational time and storage memory required. Numerical examples are provided to indicate the efficiency of the proposed method.