Constrained control allocation - Three-moment problem
01 Mar 1994-Journal of Guidance Control and Dynamics (American Institute of Aeronautics and Astronautics (AIAA))-Vol. 17, Iss: 2, pp 330-336
TL;DR: In this paper, a method for the solution of the constrained control allocation problem for the case of three moments is presented, in which the number of controls is greater than the total number of moments being controlled, and the ranges of the controls are constrained to certain limits.
Abstract: This paper presents a method for the solution of the constrained control allocation problem for the case of three moments. The control allocation problem is to find the "best" combination of several flight control effectors for 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. The controls are assumed to be individually linear in their effect throughout their ranges of motion and complete in the sense that they generate moments in arbitrary combinations. The best combination of controls is taken to be an apportioning of the controls that yields the greatest total moment in a specified ratio of moments without exceeding any control constraint. The method of solving the allocation problem is presented as an algorithm and is demonstrated for a problem of seven aerodynamic controls on an F-18 airplane.
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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
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 methods from "Constrained control allocation - Th..."
...Improvements over the original algorithm (Durham, 1993) are based on various data structures, enumerations and representations (Bordignon & Durham, 1995; Durham, 1994a,b, 1999; Petersen & Bodson, 2002) as well as linear programming (Bodson, 2002; Oppenheimer et al., 2010)....
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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 - Th..."
...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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01 Jan 2003
TL;DR: In this paper, an adaptive backstepping and nonlinear observer design method is proposed for nonlinear control problems in flight control and the results are presented in a general framework and can also be applied to other areas.
Abstract: In this thesis we study a number of nonlinear control problems motivated by their appearance in flight control. The results are presented in a general framework and can also be applied to other areas. The two main topics are backstepping and control allocation.Backstepping is a nonlinear control design method that provides an alternative to feedback linearization. Here, backstepping is used to derive robust linear control laws for two nonlinear systems, related to angle of attack control and flight path angle control, respectively. The resulting control laws require less modeling information than corresponding designs based on feedback linearization, and achieve global stability in cases where feedback linearization can only be performed locally. Further, a method for backstepping control of a rigid body is developed, based on a vector description of the dynamics. We also discuss how to augment an existing nonlinear controller to suppress constant input disturbances. Two methods, based on adaptive backstepping and nonlinear observer design, are proposed.Control allocation deals with actuator utilization for overactuated systems. In this thesis we pose the control allocation problem as a constrained least squares problem to account for actuator position and rate constraints. Efficient solvers based on active set methods are developed with similar complexity to existing, approximate, pseudoinverse methods. A method for dynamic control allocation is also proposed which enables a frequency dependent control distribution among the actuators to be designed. Further, the relationship between control allocation and linear quadratic control is investigated. It is shown that under certain circumstances, the two techniques give the same freedom in distributing the control effort among the actuators. An advantage of control allocation, however, is that since the actuator constraints are considered, the control capabilities of the actuator suite can be fully exploited.
305 citations
Cites background or methods from "Constrained control allocation - Th..."
...• The choice of u∗ is not always unique (Durham 1994a)....
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...For k = dim v = 3, Durham has proposed a number of methods (Durham 1994b,a, 1999, 2001), all of which are based on the notion of an attainable moment subset (AMS)....
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...Durham (1994a) showed that this problem occurs if not all k × k submatrices of B have full rank....
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...Methods to make the choice of u∗ unique include perturbing the elements of B to avoid rank deficiency (Durham 1994a), and averaging over (a subset of) the possible control inputs (Petersen and Bodson 2000), which in our case would lead to u∗ = (0 0 1)T ....
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...Description of Method In the original papers on direct control allocation (Durham 1993, 1994b), the method was described as follows....
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TL;DR: Comparison with several other vehicle control system approaches shows how the system operational envelope for CRVDC is significantly expanded in terms of vehicle global trajectory and planar motion responses.
Abstract: A coordinated reconfigurable vehicle dynamics control (CRVDC) system is achieved by high-level control of generalized forces/moment, distributed to the slip and slip angle of each tire by an innovative control allocation (CA) scheme. Utilizing control of individual tire slip and slip angles helps resolve the inherent tire force nonlinear constraints that otherwise may make the system more complex and computationally expensive. This in turn enables a real-time adaptable, computationally efficient accelerated fixed-point (AFP) method to improve the CA convergence rate when actuation saturates. Evaluation of the overall system is accomplished by simulation testing with a full-vehicle CarSim model under various adverse driving conditions, including scenarios where vehicle actuator failures occur. Comparison with several other vehicle control system approaches shows how the system operational envelope for CRVDC is significantly expanded in terms of vehicle global trajectory and planar motion responses.
262 citations
Cites methods from "Constrained control allocation - Th..."
...1 Direct Control Allocation The direct control allocation method was mainly proposed and refined by Durham and his group [Durham 1993], [Durham 1994a], [Durham 1994b]....
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References
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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
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.
527 citations
TL;DR: This paper describes the results of recent research into the problem of allocating several flight control effectors to generate moments acting on a flight vehicle using various generalized inverse solutions and a hybrid solution utilizing daisy chaining.
Abstract: This paper describes the results of recent research into the problem of allocating several flight control effectors to generate moments acting on a flight vehicle. The results focus on the use of various generalized inverse solutions and a hybrid solution utilizing daisy chaining. In this analysis, the number of controls is greater than the number of moments being controlled, and the ranges of the controls are constrained to certain limits. The control effectors are assumed to be individually linear in their effects throughout their ranges of motion and independent of one another in their effects. A standard of comparison is developed based on the volume of moments or moment coefficients a given method can yield using admissible control deflections. Details of the calculation of the various volumes are presented. Results are presented for a sample problem involving 10 flight control effectors. The effectivenesses of the various allocation schemes are contrasted during an aggressive roll about the velocity vector at low dynamic pressure. The performance of three specially derived generalized inverses, a daisy-chaining solution, and direct control allocation are compared.
141 citations
108 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