On the design of optimal linear systems using only output-variable feedback.
Optimal control of linear systems with state variables generated by linear feedback from output variables, considering time variance
Athans, M.↗
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Concepts for the design of a completely active helicopter isolation system using output vector feedback
The theory of output vector feedback (a few measured quantities) is used to derive completely active oscillation isolation functions for helicopters. These feedback controller concepts are tested with various versions of the BO 105 helicopter and their performance is demonstrated. A compensation of the vibrational excitations from the rotor and harmonics of the number of blades are considered. There is also a fast and automatic trim function for maneuvers.
Schulz, G.↗
Minimal complexity control law synthesis
A paradigm for control law design for modern engineering systems is proposed: Minimize control law complexity subject to the achievement of a specified accuracy in the face of a specified level of uncertainty. Correspondingly, the overall goal is to make progress towards the development of a control law design methodology which supports this paradigm. Researchers achieve this goal by developing a general theory of optimal constrained-structure dynamic output feedback compensation, where here constrained-structure means that the dynamic-structure (e.g., dynamic order, pole locations, zero locations, etc.) of the output feedback compensation is constrained in some way. By applying this theory in an innovative fashion, where here the indicated iteration occurs over the choice of the compensator dynamic-structure, the paradigm stated above can, in principle, be realized. The optimal constrained-structure dynamic output feedback problem is formulated in general terms. An elegant method for reducing optimal constrained-structure dynamic output feedback problems to optimal static output feedback problems is then developed. This reduction procedure makes use of star products, linear fractional transformations, and linear fractional decompositions, and yields as a byproduct a complete characterization of the class of optimal constrained-structure dynamic output feedback problems which can be reduced to optimal static output feedback problems. Issues such as operational/physical constraints, operating-point variations, and processor throughput/memory limitations are considered, and it is shown how anti-windup/bumpless transfer, gain-scheduling, and digital processor implementation can be facilitated by constraining the controller dynamic-structure in an appropriate fashion.
Bernstein, Dennis S.↗
Optimal output fast feedback in two-time scale control of flexible arms
Control of lightweight flexible arms moving along predefined paths can be successfully synthesized on the basis of a two-time scale approach. A model following control can be designed for the reduced order slow subsystem. The fast subsystem is a linear system in which the slow variables act as parameters. The flexible fast variables which model the deflections of the arm along the trajectory can be sensed through strain gage measurements. For full state feedback design the derivatives of the deflections need to be estimated. The main contribution of this work is the design of an output feedback controller which includes a fixed order dynamic compensator, based on a recent convergent numerical algorithm for calculating LQ optimal gains. The design procedure is tested by means of simulation results for the one link flexible arm prototype in the laboratory.
Siciliano, B.↗
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.
Maghami, Peiman G.↗
Choosing Sensor Configuration for a Flexible Structure Using Full Control Synthesis
Optimal locations and types for feedback sensors which meet design constraints and control requirements are difficult to determine. This paper introduces an approach to choosing a sensor configuration based on Full Control synthesis. A globally optimal Full Control compensator is computed for each member of a set of sensor configurations which are feasible for the plant. The sensor configuration associated with the Full Control system achieving the best closed-loop performance is chosen for feedback measurements to an output feedback controller. A flexible structure is used as an example to demonstrate this procedure. Experimental results show sensor configurations chosen to optimize the Full Control performance are effective for output feedback controllers.
Lind, Rick↗
Space shuttle active-pogo-suppressor control design using linear quadratic regulator techniques
Two methods of active pogo suppression (stabilization) for the space shuttle vehicle were studied analytically. The basis for both approaches was the linear quadratic regulator, state space technique. The first approach minimized root-mean-square pump inlet pressure by using either fullstate feedback, partial-state feedback, or output feedback with a Kalman filter. The second approach increased the modal damping associated with the critical structural modes by using either full-state feedback or reconstructed state feedback. A number of implementable controls were found by both approaches. The designs were analyzed with respect to sensitivity, complexity, and controller energy requirements, as well as controller performance. Practical controllers resulting from the two design approaches tended to use pressure and flow as feedback variables for the minimum-rms method and structural accelerations or velocities for the modal control method. Both approaches are suitable for the design of active pogo-suppression controllers.
Lehtinen, B.↗
Efficient eigenvalue assignment for large space structures
A novel and efficient approach for the eigenvalue assignment of large first-order time-invariant systems is developed using full-state feedback and output feedback. First, a Schur decomposition is applied to triangularize the state matrix. Second, a series of coordinate rotations (Givens rotations) are used to move the eigenvalue to be reassigned to the end of the diagonal of its Schur form. Third, the eigenvalue is moved to the desired location by a full-state feedback, without affecting the remaining eigenvalues. The second and third step can be repeated until all the assignable eigenvalues are moved to the desired locations. Given the freedom of multiple inputs, the feedback gain matrix is calculated to minimize an objective function composed of a gain matrix norm and/or a robustness index of the closed-loop system. Numerical examples are given to demonstrate the feasibility of the proposed approach.
Maghami, Peiman G.↗
Multi-Objective Optimal Control of High Aspect Ratio Wing Wind Tunnel Model
This paper presents the design of a multi-objective optimal controller for the 13.5 aspect ratio Common Research Model (CRM) wind tunnel model. A Pareto front analysis is performed to provide the optimal tradeoff between the competing objectives - gust load alleviation, maneuver load alleviation, and drag minimization - so that the weighting matrices for the control law are selected optimally. Also presented are two formulations of the controller: a state feedback with Kalman filter design, and an output feedback form where sensors are used directly for feedback control. The controller demonstrates a reduced peak-to-peak strain of 45.78% while also reducing drag and mean bending moment. An output feedback formulation for gust load alleviation is formulated and produces a 53% reduction in the strain response due to a gust input.
Gust Load Alleviation↗
Implementation of Autonomous GPS Guidance and Control for Spacecraft Formation Flying
This paper presents the general relative orbit dynamics equations and GPS (Global Positioning System) orbit observational equations that have been developed for on-board control of spacecraft flying in formation. The approach to the implementation of the autonomous control for orbit acquisition and maintenance of spacecraft formation using GPS code pseudoranges are presented. As a practical application of the models and method provided in this paper, the orbit control of the Earth-Orbiter 1(EO-1) / Landsat 7 system has been designed, using the discrete-time linear optimal output feedback control. For the actuator of the on/off type reaction jets, the implementation problem of the pulse-amplitude modulation is also studied. Simulation results of autonomous orbit control and maintenance, for 3-dimensional initial orbit error, using optimal output feedback control are shown. These simulation results certified the feasibility of the implementation of the autonomous maintenance control for EO-1/Landsat 7 formation flying by means of the discrete-time linear optimal output feedback control.
Xing, Guang Q.↗
Integrated Control Using the SOFFT Control Structure
The need for integrated/constrained control systems has become clearer as advanced aircraft introduced new coupled subsystems such as new propulsion subsystems with thrust vectoring and new aerodynamic designs. In this study, we develop an integrated control design methodology which accomodates constraints among subsystem variables while using the Stochastic Optimal Feedforward/Feedback Control Technique (SOFFT) thus maintaining all the advantages of the SOFFT approach. The Integrated SOFFT Control methodology uses a centralized feedforward control and a constrained feedback control law. The control thus takes advantage of the known coupling among the subsystems while maintaining the identity of subsystems for validation purposes and the simplicity of the feedback law to understand the system response in complicated nonlinear scenarios. The Variable-Gain Output Feedback Control methodology (including constant gain output feedback) is extended to accommodate equality constraints. A gain computation algorithm is developed. The designer can set the cross-gains between two variables or subsystems to zero or another value and optimize the remaining gains subject to the constraint. An integrated control law is designed for a modified F-15 SMTD aircraft model with coupled airframe and propulsion subsystems using the Integrated SOFFT Control methodology to produce a set of desired flying qualities.
Halyo, Nesim↗
Optimal limited state variable feedback controllers for linear systems.
Optimized static and dynamic linear system compensator designs with a priori fixed dimensions are discussed. Expressions are derived to determine the parameters of these designs, including the fixed-gain output feedback, the time-varying output feedback, and time-invariant compensation. A relevant deterministic off-line optimization problem is formulated, and the properties of a solution to the problem are analyzed. A unified design philosophy for limited state-variable control problems of essentially deterministic systems is developed. The philosophy incorporates design constraints, a careful selection of performance criteria, and interpretation of the results.
Levine, W. S.↗
A disturbance based control/structure design algorithm
Some authors take a classical approach to the simultaneous structure/control optimization by attempting to simultaneously minimize the weighted sum of the total mass and a quadratic form, subject to all of the structural and control constraints. Here, the optimization will be based on the dynamic response of a structure to an external unknown stochastic disturbance environment. Such a response to excitation approach is common to both the structural and control design phases, and hence represents a more natural control/structure optimization strategy than relying on artificial and vague control penalties. The design objective is to find the structure and controller of minimum mass such that all the prescribed constraints are satisfied. Two alternative solution algorithms are presented which have been applied to this problem. Each algorithm handles the optimization strategy and the imposition of the nonlinear constraints in a different manner. Two controller methodologies, and their effect on the solution algorithm, will be considered. These are full state feedback and direct output feedback, although the problem formulation is not restricted solely to these forms of controller. In fact, although full state feedback is a popular choice among researchers in this field (for reasons that will become apparent), its practical application is severely limited. The controller/structure interaction is inserted by the imposition of appropriate closed-loop constraints, such as closed-loop output response and control effort constraints. Numerical results will be obtained for a representative flexible structure model to illustrate the effectiveness of the solution algorithms.
Mclaren, Mark D.↗
Alternate Forms of Relative Attitude Kinematics and Dynamics Equations
In this paper the alternate forms of the relative attitude kinematics and relative dynamics equations are presented. These developments are different from the earlier developments that have been presented in other publications. The current forms of equations have the advantage of being simpler than earlier ones. These equations are applied in developing the necessary kinematics and dynamics for relative navigation in formation flying and virtual platforms. These equations also have application in the implementation of nonlinear full state feedback and nonlinear output feedback control for large attitude angle acquisition and tracking. This paper presents simulations from such a full state feedback control application.
Xing, Guang Q.↗
Output model-following control synthesis for an oblique-wing aircraft
Recent interest in oblique-wing aircraft has focused on the potential aerodynamic performance advantage of a variable-skew oblique wing over a conventional or symmetric sweep wing. Unfortunately, the resulting asymmetric configuration has significant aerodynamic and inertial cross-coupling between the aircraft longitudinal and lateral-directional axes. Presented here is a decoupling control law synthesis technique that integrates stability augmentation, decoupling, and the direct incorporation of desired handling qualities into an output feedback controller. The proposed design technique uses linear quadratic regulator concepts in the framework of explicit model following. The output feedback strategy used is a suboptimal projection from the state space to the output space. Dynamics are then introduced into the controller to improve steady-state performance and increase system robustness. Closed-loop performance is shown by application of the control laws to the linearized equations of motion and nonlinear simulation of an oblique-wing aircraft.
Pahle, Joseph W.↗
The generalized pole assignment problem
For some linear, strictly proper system given by its transfer function, two dynamic output feedback problems can be posed. The first one is that of using dynamic-output feedback to assign the closed-loop characteristic polynomial and the second that of assigning the closed-loop invariant factors. These problems and their interrelationships are discussed. The formulation is done in the frequency domain and the investigation carried out from an algebraic point of view, in terms of linear equations over rings of polynomials. Using the notion of genericity, several necessary and sufficient conditions are expressed.
Djaferis, T. E.↗
Structure redesign for improved dynamic response
The concepts of multivariable control design are used to redesign structures represented by lumped parameter models. When the mass is held constant, the changing of passive structural members is mathematically equivalent to an output feedback decentralized control problem. When the mass is also allowed to change, a generalization of the output feedback formulation is required. The design objective is to minimize the changes in the structure required to simultaneously satisfy inequality constraints on both the root-mean-square and absolute value of the dynamic response of each output. An alternative objective treated is to minimize the root-mean-square of the dynamic response subject to inequality constraints on the changes allowed in each structural member. Examples illustrate both procedures.
Skelton, R. E.↗
Controller design via structural reduced modeling by FETM
The Finite Element - Transfer Matrix (FETM) method has been developed to reduce the computations involved in analysis of structures. This widely accepted method, however, has certain limitations, and does not directly produce reduced models for control design. To overcome these shortcomings, a modification of FETM method has been developed. The modified FETM method easily produces reduced models that are tailored toward subsequent control design. Other features of this method are its ability to: (1) extract open loop frequencies and mode shapes with less computations, (2) overcome limitations of the original FETM method, and (3) simplify the procedures for output feedback, constrained compensation, and decentralized control. This semi annual report presents the development of the modified FETM, and through an example, illustrates its applicability to an output feedback and a decentralized control design.
Yousuff, A.↗