Dissertation•
Constrained control allocation for systems with redundant control effectors
19 Dec 1996-
TL;DR: The Null-Space Intersection method was derived from the same principles used to compute for a generalized inverse, the principles involved in finding the intersection of a subspace with a higher dimensional polytope.
Abstract: The Null-Space Intersection method was derived from the same principles used to compute for a generalized inverse. Specifically, the principles involved in finding the intersection of a subspace with a higher dimensional polytope are used. When calculating , the subspace represents directions in which the controls should be deflected to generate specified moments. The Null-Space Intersection method involves the use of a subspace which represents directions in which the controls can be deflected without changing the moment generated.
Citations
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Proceedings Article•
01 Jan 2005
TL;DR: In this article, the authors investigate the relationship between optimal control design and control allocation when the performance indexes are quadratic in the control input and show that for a particular class of nonlinear systems, they give exactly the same design freedom in distributing the control effort among the actuators.
Abstract: This paper considers actuator redundancy management for a class of overactuated nonlinear systems. Two tools for distributing the control effort among a redundant set of actuators are optimal control design and control allocation. In this paper, we investigate the relationship between these two design tools when the performance indexes are quadratic in the control input. We show that for a particular class of nonlinear systems, they give exactly the same design freedom in distributing the control effort among the actuators. Linear quadratic optimal control is contained as a special case. A benefit of using a separate control allocator is that actuator constraints can be considered, which is illustrated with a flight control example.
341 citations
TL;DR: In this article, the authors investigate the relationship between optimal control design and control allocation when the performance indexes are quadratic in the control input and show that for a particular class of nonlinear systems, they give exactly the same design freedom in distributing the control effort among the actuators.
340 citations
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 for ..."
...Thus, if CGI is considered a viable alternative for real-time applications, then so should SLS, MLS, and definitely WLS be....
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...However, in case 2, the CGI solution is rather degraded....
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...Further, our simulations show that the timing properties of the proposed methods proposed are similar to those of the comparison methods—the cascaded generalized inverse method of Bordignon (1996) and the fix-point method of Burken et al. (2001)—and that the solutions produced are in general of the same or better quality....
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...Note that if k actuators are placed in each group, and the resulting square submatrices Bi have full rank, each Pi is uniquely determined by BiPi = I. • The method may fail to produce virtual control inputs which are indeed feasible (Bordignon 1996, chap....
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...Note that the CGI solution fails to meet the virtual control demand and only achieves v = Bu = 3....
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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 for ..."
...However, Bordignon pointed out that the method could fail to produce virtual controls that are actually feasible [Bordignon, 1996]....
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...2 Daisy Chain Control Allocation The main idea of daisy chain control allocation method is to distribute the virtual control among the redundant actuators in a series by grouping the actuators [Buffington and Enns, 1996], [Bordignon, 1996]....
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TL;DR: In this article, an adaptive backstepping flight control law for the F-16/MATV (multi-axis thrust vectoring) aircraft is discussed, which tracks reference trajectories with the angle of attack a, the stability-axes roll rate p s, and the total velocity V T. Furthermore, the sideslip angle β has to be kept at zero.
Abstract: The design of an adaptive backstepping flight control law for the F-16/MATV (multi-axis thrust vectoring) aircraft is discussed. The control law tracks reference trajectories with the angle of attack a, the stability-axes roll rate p s , and the total velocity V T . Furthermore, the sideslip angle β has to be kept at zero. B-spline neural networks are used inside the parameter update laws of the backstepping control law to approximate the uncertain aerodynamic forces and moments. Command filters are used to implement the constraints on the control surfaces and the virtual control states. The stability of the parameter estimation process during periods of saturation is guaranteed by using a modified tracking error definition, in which the effect of the saturation has been filtered out. The controller and its performance are evaluated on a nonlinear, six-degrees-of-freedom dynamic model of an F-16/MATV aircraft in a number of simulation scenarios.
257 citations
Cites background from "Constrained control allocation for ..."
...The pseudoinverse is the most simple way of control allocation [40,41]....
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References
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TL;DR: This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull algorithm with the general-dimension Beneath-Beyond Algorithm, and provides empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it used less memory.
Abstract: The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull algorithm with the general-dimension Beneath-Beyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it used less memory. computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floating-point arithmetic, this assumption can lead to serous errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of “thick” facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions.
5,050 citations
Book•
01 Jan 1980
TL;DR: This well-respected, market-leading text discusses the use of digital computers in the real-time control of dynamic systems and thoroughly integrates MATLAB statements and problems to offer readers a complete design picture.
Abstract: From the Publisher:
This well-respected, market-leading text discusses the use of digital computers in the real-time control of dynamic systems The emphasis is on the design of digital controls that achieve good dynamic response and small errors while using signals that are sampled in time and quantized in amplitude Both classical and modern control methods are described and applied to illustrative examples The strengths and limitations of each method are explored to help the reader develop solid designs with the least effort Two new chapters have been added to the third edition offering a review of feedback control systems and an overview of digital control systems Updated to be fully compatible with MATLAB versions 4 and 5, the text thoroughly integrates MATLAB statements and problems to offer readers a complete design picture The new edition contains up-to-date material on state-space design and twice as many end-of-chapter problems to give students more opportunities to practice the material
3,756 citations
01 Apr 1983
TL;DR: Kinematically redundant manipulators have a number of potential advantages over current manipulator designs and velocity control through pseudoinverses is suggested for this type of arm.
Abstract: Kinematically redundant manipulators have a number of potential advantages over current manipulator designs. For this type of arm, velocity control through pseudoinverses is suggested. Questions associated with pseudoinverse control are examined in detail and show that in some cases this control leads to undesired arm configurations. A method for distributing joint angles of a redundant arm in a good approximation to a true minimax criterion is described. In addition several numerical considerations are discussed.
1,007 citations
Posted Content•
TL;DR: Gale as mentioned in this paper provides a complete and lucid treatment of important topics in mathematical economics which can be analyzed by linear models, including games, linear programming, and the Neumann model of growth.
Abstract: In the past few decades, methods of linear algebra have become central to economic analysis, replacing older tools such as the calculus. David Gale has provided the first complete and lucid treatment of important topics in mathematical economics which can be analyzed by linear models. This self-contained work requires few mathematical prerequisites and provides all necessary groundwork in the first few chapters. After introducing basic geometric concepts of vectors and vector spaces, Gale proceeds to give the main theorems on linear inequalities—theorems underpinning the theory of games, linear programming, and the Neumann model of growth. He then explores such subjects as linear programming; the theory of two-person games; static and dynamic theories of linear exchange models, including problems of equilibrium prices and dynamic stability; and methods of play, optimal strategies, and solutions of matrix games. This book should prove an invaluable reference source and text for mathematicians, engineers, economists, and those in many related areas.
731 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