Unified control/structure design and modeling research

To demonstrate the applicability of the control theory for distributed systems to large flexible space structures, research was focused on a model of a space antenna which consists of a rigid hub, flexible ribs, and a mesh reflecting surface. The space antenna model used is discussed along with the finite element approximation of the distributed model. The basic control problem is to design an optimal or near-optimal compensator to suppress the linear vibrations and rigid-body displacements of the structure. The application of an infinite dimensional Linear Quadratic Gaussian (LQG) control theory to flexible structure is discussed. Two basic approaches for robustness enhancement were investigated: loop transfer recovery and sensitivity optimization. A third approach synthesized from elements of these two basic approaches is currently under development. The control driven finite element approximation of flexible structures is discussed. Three sets of finite element basic vectors for computing functional control gains are compared. The possibility of constructing a finite element scheme to approximate the infinite dimensional Hamiltonian system directly, instead of indirectly is discussed

H infinity control design for generalized second order systems based on acceleration sensitivity function

This article presents an Hinfinty control design method based on the Acceleration Sensitivity (AS) function. This approach can be applied to any fully actuated generalized second order system. In this framework, classical modal specifications(pulsations / damping ratios) are expressed in terms of Hinfinty templates allowing other frequency domain specifications to betaken into account. Finally, a comparison between AS with a more classical Hinfinty approach and with the Cross Standard Form(CSF) is presented. A 2 degrees of freedom spring-damper-mass academic example is used to illustrate the properties of the AS,though this method was developed and is used for atmospheric reentry control design

Lateral fligh control design for a highly flexible aircraft using a nonsmooth method

This paper describes a nonsmooth optimization technique for designing a lateral flight control law for a highly flexible aircraft. Flexible modes and high-dimensional models pose a major challenge to modern control design tools. We show that the nonsmooth approach offers potent and flexible alternatives in this difficult context. More specifically, the proposed technique is used to achieve a mix of frequency domain as well as time domain requirements for a set of different flight conditions

Gain scheduling of aircraft pitch attitude and control of discrete, affine, linear parametrically varying systems

This research is motivated by gain scheduling, a technique which has been successfully applied to many nonlinear control problems. In flight controls, the wide variations in the characteristics of the aircraft dynamics throughout the flight envelope make gain scheduling a particularly suitable design strategy. This research consists of two parts: (1) aircraft pitch attitude scheduling scheme designs, and (2) control of a class of linear parametrically varying (LPV) systems.;In the first part, the classical gain scheduling technique and the single quadratic Lyapunov function (SQLF) based LPV technique are investigated. In the classical gain scheduling design, the Hinfinity mixed sensitivity GS/T method is chosen for local linear time invariant (LTI) designs to provide robustness to unmodeled dynamics and parametric uncertainties. Following a model reduction procedure that exploits the optimal controller structure, LTI controllers designed at the selected equilibrium points are reduced to second order controllers and realized in a feedback path configuration. Such controllers are shown to retain the superior robust performance at each flight condition, while having a low order that is amenable to scheduling. A gain-scheduling law is developed and simulation results verify that the closed-loop performance specifications are met. In the LPV design, the mixed sensitivity S/KS/T design setup is used. An approximation to the original LPV controller using the linear fractional transformation (LFT) representation is constructed. Our design exhibits potential applications of the LPV technique to commercial aircraft gain scheduling designs.;In the second part, we consider a class of discrete, affine, linear parametrically varying (DALPV) systems. For this type of systems, the parameters are assumed to vary in a polytope and the state space matrices are assumed to depend affinely on the varying parameters. A sufficient condition is derived to analyze the stability and the ℓinfinity to ℓinfinity performance of a DALPV system. For an open-loop DALPV system, a procedure is proposed to design a gain-scheduled controller such that the closed-loop system is asymptotically stable and achieves a certain level of ℓinfinity to ℓinfinity performance

Mixed sensitivity control: a non-iterative approach

Recent analytical solutions to Mixed Sensitivity Control (MSC) are developed and compared with standard MSC based on γ -iteration. The proposed MSC solution gives conditions for strong stability and overcomes the pole-zero cancellations between the plant and the controller of non-iterative solutions, keeping the low-computational effort advantage of non-iterative solutions. The proposed MSC is based on the minimization of the most common closed-loop sensitivity functions in low frequencies and the free-parameters of the stabilizing-controllers solve an algebraic equation of restriction that assigns the same value to the infinity-norms of the sensitivity functions at low and high-frequencies, guaranteeing robust stability and robust performance. It is assumed that the plant state dimension is double the plant input dimension and that the linear time-invariant nominal plant has a stabilizable and detectable realization and is strongly stabilizable. This MSC problem is solved in a one-parameter observer-controller configuration and reference tracking-control of positions is realized on a two-degrees of freedom feedback-configuration. An approximated optimal value of the location of the closed-loop poles is proposed based on Glover and McFarlane’s optimal stability margin [(1989)] which in turn is based on Nehari’s Theorem. Simulations of a mechanical system illustrate the results

A flexible mixed-optimization with H∞ control for coupled twin rotor MIMO system based on the method of inequality (MOI)- An Experimental Study

This article introduces a cutting-edge H∞ model-based control method for uncertain Multi Input Multi Output (MIMO) systems, specifically focusing on UAVs, through a flexible mixed-optimization framework using the Method of Inequality (MOI). The proposed approach adaptively addresses crucial challenges such as unmodeled dynamics, noise interference, and parameter variations. Central to the design is a two-step controller development process. The first step involves Nonlinear Dynamic Inversion (NDI) and system decoupling for simplification, while the second step integrates H∞ control with MOI for optimal response tuning. This strategy is distinguished by its adaptability and focus on balancing robust stability and performance, effectively managing the intricate cross-coupling dynamics in UAV systems. The effectiveness of the proposed approach is validated through simulations conducted in MATLAB/Simulink environment. Results demonstrated the efficiency of the proposed robust control approach as evidenced by reduced steady-state error, diminished overshoot, and faster system response times, thus significantly outperforming traditional control methods

Controller Design with Real Parametric Uncertainty

A number of techniques have been developed in recent years for the analysis and design of controllers which are robust with respect to structured complex uncertainty. In particular the complex μ synthesis procedure has been successfully applied to a number of engineering problems. However the presence of real parametric uncertainty in the problem description substantially complicates matters, so that standard complex μ synthesis techniques are no longer adequate. In this paper we develop a procedure to tackle the mixed (real and complex) μ synthesis problem. This procedure involves a "D,G-K iteration" between computing the mixed μ upper bound and solving an H∞ optimal control problem, and has guaranteed convergence to a local minimum of the (nonconvex) problem. The procedure has been implemented in software, and several controller designs are compared with the corresponding complex μ synthesis designs

A Unified Framework for the H∞ Mixed-Sensitivity Design of Fixed Structure Controllers through Putinar Positivstellensatz

In this paper, we present a novel technique to design fixed structure controllers, for both continuous-time and discrete-time systems, through an H∞ mixed sensitivity approach. We first define the feasible controller parameter set, which is the set of the controller parameters that guarantee robust stability of the closed-loop system and the achievement of the nominal performance requirements. Then, thanks to Putinar positivstellensatz, we compute a convex relaxation of the original feasible controller parameter set and we formulate the original H∞ controller design problem as the non-emptiness test of a set defined by sum-of-squares polynomials. Two numerical simulations and one experimental example show the effectiveness of the proposed approach