9,192 research outputs found
Optimal control and robust estimation for ocean wave energy converters
This thesis deals with the optimal control of wave energy converters and some associated
observer design problems. The first part of the thesis will investigate model
predictive control of an ocean wave energy converter to maximize extracted power.
A generic heaving converter that can have both linear dampers and active elements
as a power take-off system is considered and an efficient optimal control algorithm
is developed for use within a receding horizon control framework. The optimal
control is also characterized analytically. A direct transcription of the optimal control
problem is also considered as a general nonlinear program. A variation of
the projected gradient optimization scheme is formulated and shown to be feasible
and computationally inexpensive compared to a standard nonlinear program solver.
Since the system model is bilinear and the cost function is not convex quadratic, the
resulting optimization problem is shown not to be a quadratic program. Results are
compared with other methods like optimal latching to demonstrate the improvement
in absorbed power under irregular sea condition simulations.
In the second part, robust estimation of the radiation forces and states inherent in
the optimal control of wave energy converters is considered. Motivated by this, low
order H∞ observer design for bilinear systems with input constraints is investigated
and numerically tractable methods for design are developed. A bilinear Luenberger
type observer is formulated and the resulting synthesis problem reformulated as that
for a linear parameter varying system. A bilinear matrix inequality problem is then
solved to find nominal and robust quadratically stable observers. The performance
of these observers is compared with that of an extended Kalman filter. The robustness
of the observers to parameter uncertainty and to variation in the radiation
subsystem model order is also investigated.
This thesis also explores the numerical integration of bilinear control systems with
zero-order hold on the control inputs. Making use of exponential integrators, exact
to high accuracy integration is proposed for such systems. New a priori bounds
are derived on the computational complexity of integrating bilinear systems with a
given error tolerance. Employing our new bounds on computational complexity, we
propose a direct exponential integrator to solve bilinear ODEs via the solution of
sparse linear systems of equations. Based on this, a novel sparse direct collocation
of bilinear systems for optimal control is proposed. These integration schemes are
also used within the indirect optimal control method discussed in the first part.Open Acces
A Robust Constrained Reference Governor Approach using Linear Matrix Inequalities
The purpose of this paper is to examine and provide a solution to the output reference tracking problem for uncertain systems subject to input saturation. As well-known, input saturation and modelling errors are very common problems at industry, where control schemes are implemented without accounting for such problems. In many cases, it is sometimes difficult to modify the existing implemented control schemes being necessary to provide them with external supervisory control approaches in order to tackle problems with constraints and modelling errors. In this way, a cascade structure is proposed, combining an inner loop containing any proper controller with an outer loop where a generalized predictive controller (GPC) provides adequate references for the inner loop considering input saturations and uncertainties. Therefore, the contribution of this paper consists in providing a state space representation for the inner loop and using linear matrix inequalities (LMI) to obtain a predictive state-vector feedback in such a way that the input reference for the inner loop is calculated to satisfy robust tracking specifications considering input saturations. Hence, the final proposed solution consists in solving a regulation problem to a fixed reference value subjected to a set of constraints described by several LMI and bilinear matrix inequalities (BMI). The main contribution of the paper is that the proposed solution is a non-linear setpoint tracking approach, that is, it is allowed that the system goes into saturation facing the problem of setpoint tracking instead of regulating to the origin. An illustrative numerical example is presented.Ministerio de Ciencia y Tecnología DPI2004-07444-C04-01/0
Sequential Convex Programming Methods for Solving Nonlinear Optimization Problems with DC constraints
This paper investigates the relation between sequential convex programming
(SCP) as, e.g., defined in [24] and DC (difference of two convex functions)
programming. We first present an SCP algorithm for solving nonlinear
optimization problems with DC constraints and prove its convergence. Then we
combine the proposed algorithm with a relaxation technique to handle
inconsistent linearizations. Numerical tests are performed to investigate the
behaviour of the class of algorithms.Comment: 18 pages, 1 figur
On Time Optimization of Centroidal Momentum Dynamics
Recently, the centroidal momentum dynamics has received substantial attention
to plan dynamically consistent motions for robots with arms and legs in
multi-contact scenarios. However, it is also non convex which renders any
optimization approach difficult and timing is usually kept fixed in most
trajectory optimization techniques to not introduce additional non convexities
to the problem. But this can limit the versatility of the algorithms. In our
previous work, we proposed a convex relaxation of the problem that allowed to
efficiently compute momentum trajectories and contact forces. However, our
approach could not minimize a desired angular momentum objective which
seriously limited its applicability. Noticing that the non-convexity introduced
by the time variables is of similar nature as the centroidal dynamics one, we
propose two convex relaxations to the problem based on trust regions and soft
constraints. The resulting approaches can compute time-optimized dynamically
consistent trajectories sufficiently fast to make the approach realtime
capable. The performance of the algorithm is demonstrated in several
multi-contact scenarios for a humanoid robot. In particular, we show that the
proposed convex relaxation of the original problem finds solutions that are
consistent with the original non-convex problem and illustrate how timing
optimization allows to find motion plans that would be difficult to plan with
fixed timing.Comment: 7 pages, 4 figures, ICRA 201
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