Page 60 - ASME DSCC 2015 Program

Technical Program

Stabilization of nonlinear Systems By Switched lyapunov function
ConTRIBuTED SESSIon
1-9-1 TP3 Advances in non-linear and optimal Control Contributed regular paper. DSCC2015-9650
George Bellows E 4:00pm–6:00pm Andy Zelenak, The University of Texas at Austin, Fort Collins, CO, United
States, Mitch Pryor, The University of Texas at Austin, XX, TX, United States
Session Chair: Warren White, Kansas State University
Stabilization of Nonlinear Systems By Switched Lyapunov Function
Session Co-Chair: Atul Kelkar, Iowa State University
Model free Approaches Applied to the Control of nonlinear Systems: A
Combined Input Shaping and feedback Control of a Double-Pendulum Brief Survey With Special Attention to Intelligent PID Iterative learning
System Subject to External Disturbances Control
Contributed regular paper. DSCC2015-9849 Contributed regular paper. DSCC2015-9721
Robert Mar, Anurag Goyal, Vinh nguyen, Tianle Yang, William Singhose, Elmira Madadi, Duisburg-Essen University, Duiburg, Germany, dirk Söffker,
Georgia Institute of Technology, Atlanta, GA, United States University of Duisburg-Essen, Duisburg, Germany
A control system combining input shaping and feedback is applied to a dou- Model-based control is one of the popular solutions for designing a control-
ble-pendulum bridge crane subjected to external disturbances. The external ler used to control nonlinear systems. However, the difficulty of obtaining
disturbances represent naturally occurring forces, such as gusting winds. an accurate model is a challenge for control designers. For this reason
The proposed control method achieves fast point-to-point response similar model-free control (MFC) methods are attractive. This contribution gives an
to open-loop input-shaping control. It also minimizes transient deflections overview on different types of model-free control. It includes an investiga-
and disturbance-induced residual swing using the feedback control. Effects tion about model-free techniques applied to nonlinear systems. In detail the
of parameters such as the mass ratio of the double-pendulum, suspension iPID iterative learning-based method is expressed more detailed. Simula-
length ratio, and the traveled distance were studied via numerical simulation tion results also illustrate a successful application and performance of the
and hardware experiments. The controller effectively suppresses the distur- proposed method.
bances and is robust to modeling uncertainties and task variations.
long Time Average Cost Control of Polynomial Systems: A Sum-of-
Tracking Control of non-Minimum Phase Systems using filtered Basis Squares-Based Small-feedback approach
functions: A nuRBS-Based Approach Contributed regular paper. DSCC2015-9684
Contributed regular paper. DSCC2015-9859 deqing huang, Sergei chernyshenko, Imperial College London, London,
Molong Duan, Keval Ramani, Chinedum okwudire, University of Michigan, United Kingdom
Ann Arbor, MI, United States
This paper provides a proof of concept of the recent novel idea in the area
This paper proposes an approach for minimizing tracking errors in systems with of long-time average cost control. Meanwhile, a new method of
non-minimum phase (NMP) zeros by using filtered basis functions. The output of overcoming the well-known difficulty of non-convexity of simultaneous
the tracking controller is represented as a linear combination of basis functions optimization of a control law and an additional tunable function is given.
having unknown coefficients. The basis functions are forward filtered using the First, a recently-proposed method of obtaining rigorous bounds of
dynamics of the NMP system and their coefficients selected to minimize the long-time average cost is outlined for the uncontrolled system with
errors in tracking a given trajectory. The control designer is free to choose any polynomials of system state on the right-hand side. In this method the
suitable set of basis functions but, in this paper, a set of basis functions derived polynomial constraints are relaxed to be sum-of-squares and formulated
from the widely-used non uniform rational B-spline (NURBS) curve is employed. as semi-definite programs. It was proposed to use the upper bound of
Analyses and illustrative examples are presented to demonstrate the effective- long-time average cost as the objective function instead of the time-
ness of the proposed approach in comparison to popular approximate model average cost itself in controller design. In the present paper this
inversion methods like zero phase error tracking control. suggestion is implemented for a particular system and is shown to give
good results.
escape regions of the active Target defense differential game
Designing the optimal controller by this method requires optimising simulta-
Contributed regular paper. DSCC2015-9628
neously both the control law and a tunable function similar to the Lyapunov
Eloy Garcia, Infoscitex Corp., Dayton, OH, United States, David W. Casbeer, function. The new approach proposed and implemented in this paper for
AFRL Aerospace Systems Directorate, Wright-Patterson AFB, OH, United overcoming the inherent non-convexity of this optimisation is based on a
States, Meir Pachter, Air Force Institute of Technology, Dayton, OH, United
States formal assumption that the amplitude of control is small. By expanding the
tunable function and the bound in the small parameter, the long-time aver-
The active target defense differential game is addressed in this paper. In this age cost is reduced by minimizing the respective bound in each term of the
differential game an Attacker missile pursues a Target aircraft. The aircraft is series. The derivation of all the polynomial coefficients in controller is given
however aided by a Defender missile launched by, say, the wingman, to inter- in terms of the solvability conditions of state-dependent linear and bilinear
cept the Attacker before it reaches the Target aircraft. Thus, a team is formed inequalities. The resultant sum-of-squares problems are solved in sequence,
by the Target and the Defender which cooperate to maximize the separation thus avoiding the non-convexity in optimization.
between the Target aircraft and the point where the Attacker missile is intercept-
ed by the Defender missile, while the Attacker simultaneously tries to minimize
said distance. This paper focuses on characterizing the set of coordinates such
60 that if the Target’s initial position belong to this set then its survival is guaranteed
if both the Target and the Defender follow their optimal strategies. Such optimal
strategies are presented in this paper as well.