Constrained Control Allocation
01 Aug 1993-Journal of Guidance Control and Dynamics (American Institute of Aeronautics and Astronautics (AIAA))-Vol. 16, Iss: 4, pp 717-725
TL;DR: In this article, the problem of the allocation of several airplane flight controls to the generation of specified body-axis moments is addressed, and a direct method of allocating these several controls is presented that guarantees the maximum possible moment can be generated within the constraints of the controls.
Abstract: This paper addresses the problem of the allocation of several airplane flight controls to the generation of specified body-axis moments. The number of controls is greater than the number of moments being controlled, and the ranges of the controls are constrained to certain limits. They are assumed to be individually linear in their effect throughout their ranges of motion and independent of one another in their effects. The geometries of the subset of the constrained controls and of its image in moment space are examined. A direct method of allocating these several controls is presented that guarantees the maximum possible moment can be generated within the constraints of the controls. It is shown that no single generalized inverse can yield these maximum moments everywhere without violating some control constraint. A method is presented for the determination of a generalized inverse that satisfies given specifications which are arbitrary but restricted in number. We then pose and solve a minimization problem that yields the generalized inverse that best approximates the exact solutions. The results are illustrated at each step by an example problem involving three controls and two moments.
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TL;DR: A bibliographical review on reconfigurable fault-tolerant control systems (FTCS) is presented, with emphasis on the reconfiguring/restructurable controller design techniques.
2,455 citations
08 Apr 2011
TL;DR: In this article, the authors present a survey of the latest tools for analysis and design of advanced guidance, navigation and control systems and present new material on underwater vehicles and surface vessels.
Abstract: The technology of hydrodynamic modeling and marine craft motion control systems has progressed greatly in recent years. This timely survey includes the latest tools for analysis and design of advanced guidance, navigation and control systems and presents new material on underwater vehicles and surface vessels. Each section presents numerous case studies and applications, providing a practical understanding of how model-based motion control systems are designed.
1,389 citations
Cites methods from "Constrained Control Allocation"
...An alternative approach to integral action is to use a state estimator to estimate the ocean currents (Encarnacao et al., 2000). Cascaded design techniques based on backstepping and Lyapunov analysis are discussed by Lapierre and Soetanto (2007) and Børhaug and Pettersen (2006), while Breivik and Fossen (2004a) present an alternative approach for Serret–Frenet path-following control where the path curvature κ is superfluous....
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TL;DR: The objective of the present paper is to survey control allocation algorithms, motivated by the rapidly growing range of applications that have expanded from the aerospace and maritime industries, where control allocation has its roots, to automotive, mechatronics, and other industries.
841 citations
Cites background or methods from "Constrained Control Allocation"
...In Durham (1993) it is shown that no single generalized inverse (i.e. weight matrix W ) can yield exact allocation whenever possible using simple saturation....
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...The direct allocation method (Durham, 1993) starts with the unconstrained control allocation computed using some pseudoinverse, e.g. ũ = B+τc ....
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...Control allocation is widely used with such designs in order to ensure optimal use of the effectors, including fault tolerant and robust control over a wide flight envelope, (Bolling & Durham, 1997; Burken et al., 2001; Davidson, Lallman, & Bundick, 2001; Durham, 1993; Huang, Liu, & Zhu, 2009)....
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...The underlying motivation for the direct control allocation method, (Durham, 1993), is that inmany applications (in particular aircraft) it is considered important to keep the direction of the allocated forces and moments equal to the command, in order to get graceful degradation of performance and…...
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...is a generalized inverse that can be derived from optimality conditions of (12) using Lagrange multipliers, see e.g. Bordignon and Durham (1995), Durham (1993), Enns (1998), Fossen and Sagatun (1991), Oppenheimer et al. (2010), Snell, Enns, andGarrard (1990) and Virnig and Bodden (1994)....
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TL;DR: The major conclusion is that constrained optimization can be performed with computational requirements that fall within an order of magnitude of those of simpler methods.
Abstract: The performanceand computational requirements ofoptimization methodsfor control allocation areevaluated Two control allocation problems are formulated: a direct allocation method that preserves the directionality of the moment and a mixed optimization method that minimizes the error between the desired and the achieved momentsaswellasthecontroleffortTheconstrainedoptimizationproblemsaretransformedinto linearprograms so that they can be solved using well-tried linear programming techniques such as the simplex algorithm A variety of techniques that can be applied for the solution of the control allocation problem in order to accelerate computations are discussed Performance and computational requirements are evaluated using aircraft models with different numbers of actuators and with different properties In addition to the two optimization methods, three algorithms with low computational requirements are also implemented for comparison: a redistributed pseudoinverse technique, a quadratic programming algorithm, and a e xed-point method The major conclusion is that constrained optimization can be performed with computational requirements that fall within an order of magnitude of those of simpler methods The performance gains of optimization methods, measured in terms of the error between the desired and achieved moments, are found to be small on the average but sometimes signie cantAvariety ofissuesthataffecttheimplementation ofthevariousalgorithmsin ae ight-controlsystem are discussed
628 citations
Cites background or methods from "Constrained Control Allocation"
...The original algorithm [4] was slow and difficult to implement, but an elegant approach [10] reduced the number of computations considerably....
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...They are implemented to solve both the direct allocation problem posed by Durham [4], and a more common error minimization objective [6]....
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...More complex methods formulate control allocation as a constrained optimization problem [3], [4]....
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...This observation was made earlier by Durham using different arguments....
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...The direct allocation problem was proposed by Durham [4]....
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TL;DR: This work considers the additional objective of singularity avoidance, which is essential to avoid loss of controllability in some applications, leading to a nonconvex nonlinear program, and suggests a sequential quadratic programming approach, solving at each sample a convex quadRatic program approximating the non linear program.
Abstract: Control allocation problems can be formulated as optimization problems, where the objective is typically to minimize the use of control effort (or power) subject to actuator rate and position constraints, and other operational constraints. Here we consider the additional objective of singularity avoidance, which is essential to avoid loss of controllability in some applications, leading to a nonconvex nonlinear program. We suggest a sequential quadratic programming approach, solving at each sample a convex quadratic program approximating the nonlinear program. The method is illustrated by simulated maneuvers for a marine vessel equipped with azimuth thrusters. The example indicates reduced power consumption and increased maneuverability as a consequence of the singularity-avoidance.
350 citations
Cites background from "Constrained Control Allocation"
...1Linear models are also common in flight control applications [2], [3]....
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...Various computational algorithms for constrained least squares control allocation, with emphasis on efficient real-time implementation without real-time optimization, are studied in [2], [3], [11]–[15]....
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References
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Book•
01 Jan 1971
TL;DR: The relationship between state variable and transfer function descriptions of linear feedback control systems is discussed in this paper, along with the relationship between the Cayley Hamilton Theorem and state variable descriptions of systems.
Abstract: 1. Background and Preview. 2. Highlights of Classical Control Theory. 3. State Variables and the State Space Description of Dynamic Systems. 4. Fundamentals of Matrix Algebra. 5. Vectors and Linear Vector Spaces. 6. Simultaneous Linear Equations. 7. Eigenvalues and Eigenvectors. 8. Functions of Square Matrices and the Cayley-Hamilton Theorem. 9. Analysis of Continuous and Discrete Time State Equations. 10. Stability. 11. Controllability and Observability for Linear Systems. 12. The Relationship between State Variable and Transfer Function Descriptions of Systems. 13. Design of Linear Feedback Control Systems. 14. An Introduction to Optimal Control Theory. 15. An Introduction to Nonlinear Control Systems.
1,419 citations
TL;DR: In this article, the authors discuss the use of nonlinear dynamic inversion in the design of a flight control system for a Superman aircraft and compare it with a more conventional, gain-scheduled system and yield better performance in terms of lateral acceleration, sideslip, and control deflections.
Abstract: Nonlinear dynamic inversion affords the control system designer a straightforward means of deriving control laws for nonlinear systems. The control inputs are used to cancel unwanted terms in the equations of motion using negative feedback of these terms. In this paper, we discuss the use of nonlinear dynamic inversion in the design of a flight control system for a Supermaneuvera ble aircraft. First, the dynamics to be controlled are separated into fast and slow variables. The fast variables are the three angular rates and the slow variables are the angle of attack, sideslip angle, and bank angle. A dynamic inversion control law is designed for the fast variables using the aerodynamic control surfaces and thrust vectoring control as inputs. Next, dynamic inversion is applied to the control of the slow states using commands for the fast states as inputs. The dynamic inversion system was compared with a more conventional, gain-scheduled system and was shown to yield better performance in terms of lateral acceleration, sideslip, and control deflections.
579 citations
01 Apr 1985
TL;DR: In this paper, a method to select optimal combinations of the control variables of a linear system is reported, where the combinations are chosen so that the control channels have their principal influences on selected fundamental modes of the system.
Abstract: A method to select optimal combinations of the control variables of a linear system is reported. The combinations are chosen so that the control channels have their principal influences on selected fundamental modes of the system. A series of algebraic maximization problems is used to maximize the effects of the control channels on selected modes while simultaneously minimizing the effects on the remaining modes. The method is applied to the lateral and directional control of a linearized airplane model having ailerons, a rudder, and differential tail surfaces. Integration of these control eliminates oscillations present in the roll rate for a step lateral-control input and improves the sideslip response with reduced rolling motions for a step directional-control input. Inclusion of thrust-vectoring engine nozzles improves the roll rate capability of the airplane.
27 citations
01 Nov 1985
TL;DR: In this article, a preliminary design of a lateral-directional control system for a fighter airplane capable of controlled operation at extreme angles of attack is developed, which is representative of a modern twin-engine high-performance jet fighter, equipped with ailerons, rudder, and independent horizontal-tail surfaces.
Abstract: A preliminary design of a lateral-directional control system for a fighter airplane capable of controlled operation at extreme angles of attack is developed. The subject airplane is representative of a modern twin-engine high-performance jet fighter, is equipped with ailerons, rudder, and independent horizontal-tail surfaces. Idealized bidirectional thrust-vectoring engine nozzles are appended to the mathematic model of the airplane to provide additional control moments. Optimal schedules for lateral and directional pseudo control variables are calculated. Use of pseudo controls results in coordinated operation of the aerodynamic and thrust-vectoring controls with minimum coupling between the lateral and directional airplane dynamics. Linear quadratic regulator designs are used to specify a preliminary flight control system to improve the stability and response characteristics of the airplane. Simulated responses to step pilot control inputs are stable and well behaved. For lateral stick deflections, peak stability axis roll rates are between 1.25 and 1.60 rad/sec over an angle-of-attack range of 10 deg to 70 deg. For rudder pedal deflections, the roll rates accompanying the sideslip responses can be arrested by small lateral stick motions.
22 citations