Polynomial interpolation for inversion-based control

To help to achieve high performances in the regulation of linear scalar (SISO) nonminimum-phase systems, an inversion-based (feedforward) control method is proposed. The aim is designing an inverse input to smoothly switch from a current, arbitrary, steady-state regime to a new, future, desired steady-state output. A new-found polynomial basis solves the related interpolation problem to join the current output to the future one while ensuring the necessary or desired smoothness. The (interpolation) transition time can be minimized in order to optimally reduce the delay with which the desired output occurs. By applying a behavioral stable inversion formula to the overall smoothed output, detailed expressions of the inverse input are finally derived. A simulation of a flexible arm rotating in the horizontal plane exemplifies the presented method

Robust two-degree-of freedom control optimally balancing feedforward plant inversion and feedforward closed loop inversion

none2openleopoldo Jetto; valentina orsiniIetto, Leopoldo; Orsini, Valentin

A Robust Offline Precomputed Optimal Feedforward Control Action for the Real Time Feedback/Feedforward Control of Double Pendulum Gantry Cranes

none1openvalentina orsiniOrsini, Valentin

Theoretical constraints in the design of multivariable control systems

The theoretical constraints inherent in the design of multivariable control systems were defined and investigated. These constraints are manifested by the system transmission zeros that limit or bound the areas in which closed loop poles and individual transfer function zeros may be placed. These constraints were investigated primarily in the context of system decoupling or non-interaction. It was proven that decoupling requires the placement of closed loop poles at the system transmission zeros. Therefore, the system transmission zeros must be minimum phase to guarantee a stable decoupled system. Once decoupling has been accomplished, the remaining part of the system exhibits transmission zeros at infinity, so nearly complete design freedom is possible in terms of placing both poles and zeros of individual closed loop transfer functions. A general, dynamic inversion model following system architecture was developed that encompasses both the implicit and explicit configuration. Robustness properties are developed along with other attributes of this type of system. Finally, a direct design is developed for the longitudinal-vertical degrees of freedom of aircraft motion to show how a direct lift flap can be used to improve the pitch-heave maneuvering coordination for enhanced flying qualities

Guidance of Nonlinear Nonminimum-Phase Dynamic Systems

The first two years research work has advanced the inversion-based guidance theory for: (1) systems with non-hyperbolic internal dynamics; (2) systems with parameter jumps; (3) systems where a redesign of the output trajectory is desired; and (4) the generation of recovery guidance maneuvers

Advanced Computational-Effective Control and Observation Schemes for Constrained Nonlinear Systems

Constraints are one of the most common challenges that must be faced in control systems design. The sources of constraints in engineering applications are several, ranging from actuator saturations to safety restrictions, from imposed operating conditions to trajectory limitations. Their presence cannot be avoided, and their importance grows even more in high performance or hazardous applications. As a consequence, a common strategy to mitigate their negative effect is to oversize the components. This conservative choice could be largely avoided if the controller was designed taking all limitations into account. Similarly, neglecting the constraints in system estimation often leads to suboptimal solutions, which in turn may negatively affect the control effectiveness. Therefore, with the idea of taking a step further towards reliable and sustainable engineering solutions, based on more conscious use of the plants' dynamics, we decide to address in this thesis two fundamental challenges related to constrained control and observation. In the first part of this work, we consider the control of uncertain nonlinear systems with input and state constraints, for which a general approach remains elusive. In this context, we propose a novel closed-form solution based on Explicit Reference Governors and Barrier Lyapunov Functions. Notably, it is shown that adaptive strategies can be embedded in the constrained controller design, thus handling parametric uncertainties that often hinder the resulting performance of constraint-aware techniques. The second part of the thesis deals with the global observation of dynamical systems subject to topological constraints, such as those evolving on Lie groups or homogeneous spaces. Here, general observability analysis tools are overviewed, and the problem of sensorless control of permanent magnets electrical machines is presented as a case of study. Through simulation and experimental results, we demonstrate that the proposed formalism leads to high control performance and simple implementation in embedded digital controllers

Energy-Optimal Control of Over-Actuated Systems - with Application to a Hybrid Feed Drive

Over-actuated (or input-redundant) systems are characterized by the use of more actuators than the degrees of freedom to be controlled. They are widely used in modern mechanical systems to satisfy various control requirements, such as precision, motion range, fault tolerance, and energy efficiency. This thesis is particularly motivated by an over-actuated hybrid feed drive (HFD) which combines two complementary actuators with the aim to reduce energy consumption without sacrificing positioning accuracy in precision manufacturing. This work addresses the control challenges in achieving energy optimality without sacrificing control performance in so-called weakly input-redundant systems, which characterize the HFD and most other over-actuated systems used in practice. Using calculus of variations, an optimal control ratio/subspace is derived to specify the optimal relationship among the redundant actuators irrespective of external disturbances, leading to a new technique termed optimal control subspace-based (OCS) control allocation. It is shown that the optimal control ratio/subspace is non-causal; accordingly, a causal approximation is proposed and employed in energy-efficient structured controller design for the HFD. Moreover, the concept of control proxy is proposed as an accurate causal measurement of the deviation from the optimal control ratio/subspace. The proxy enables control allocation for weakly redundant systems to be converted into regulation problems, which can be tackled using standard controller design methodologies. Compared to an existing allocation technique, proxy-based control allocation is shown to dynamically allocate control efforts optimally without sacrificing control performance. The relationship between the proposed OCS control allocation and the traditional linear quadratic control approach is discussed for weakly input redundant systems. The two approaches are shown to be equivalent given perfect knowledge of disturbances; however, the OCS control allocation approach is shown to be more desirable for practical applications like the HFD, where disturbances are typically unknown. The OCS control allocation approach is validated in simulations and machining experiments on the HFD; significant reductions in control energy without sacrificing positioning accuracy are achieved.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/146104/1/molong_1.pd

Robust nonlinear control of vectored thrust aircraft

An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations

Robust Adaptive Control of Linear Parameter-Varying Systems with Unmatched Uncertainties

This paper presents a robust adaptive control solution for linear parameter-varying (LPV) systems with unknown input gain and unmatched nonlinear (state- and time-dependent) uncertainties based on the $\mathcal{L}_1$ adaptive control architecture and peak-to-peak gain (PPG) analysis/minimization from robust control. Specifically, we introduce new tools for stability and performance analysis leveraging the PPG bound of an LPV system that is computable using linear matrix inequality (LMI) techniques. A piecewise-constant estimation law is introduced to estimate the lumped uncertainty with quantifiable error bounds, which can be systematically improved by reducing the estimation sampling time. We also present a new approach to attenuate the unmatched uncertainty based on the PPG minimization that is applicable to a broad class of systems with linear nominal dynamics. In addition, we derive transient and steady-state performance bounds in terms of the input and output signals of the actual closed-loop system as compared to the same signals of a virtual reference system that represents the possibly best achievable performance. Under mild assumptions, we prove that the transient performance bounds can be uniformly reduced by decreasing the estimation sampling time, which is subject only to hardware limitations. The theoretical development is validated by extensive simulations on the short-period dynamics of an F-16 aircraft