Charudatta Subhash Mehendale

A homotopy method for decentralized control design

This paper considers the design of a full order output feedback decentralized H/sub /spl infin// controller. An iterative algorithm that is based on the idea of two homotopy paths is proposed. Along one homotopy path, the decentralized control design problem, which is essentially non-convex, is locally linearized and solved. Along the other homotopy path the existing controller is deformed at each step so that in the end it attains a decentralized structure. A decentralized control design for a doubly inverted pendulum is demonstrated using the proposed algorithm.

A Linear Parameter-varying Framework for Adaptive Active Microgravity Isolation

This paper presents a novel approach to the design of adaptive active vibration isolation systems using linear parameter-varying (LPV) control techniques. The proposed LPV controller is scheduled based on the relative position of the vibrating system, as well as a parameter that characterizes the harshness of the base motion. By scheduling on relative position, the controller is able to shift its focus from a “soft” setting to a “stiff” setting depending on the need for acceleration minimization or relative displacement reduction. An outer loop that is scheduled based on a parameter that quantifies base motion harshness controls the way in which the system transitions between the “soft” and “stiff” settings. Parameter-dependent weighting functions are used to achieve these objectives. A single degree-of-freedom rack-level microgravity vibration isolation model is used to demonstrate the proposed adaptive design framework. The objective is to provide stringent closed-loop isolation characteristics and at the same time restrict the relative motion of the system, so as to prevent it from bumping into its hardstop bumpers. Simulations show that the parameter-varying controller provides excellent isolation with simultaneous position control despite the large variability in the harshness of environmental disturbances.

A double homotopy method for decentralised control design

An iterative algorithm that is based on the idea of two homotopy paths is proposed for output feedback decentralised ℋ∞ control design. The approach follows a bilinear matrix inequality (BMI) formulation of the decentralised control problem. Along one homotopy path the BMI problem, which is non-convex, is locally linearised and solved. Along the second homotopy path the controller is deformed at each step so that in the end it attains a decentralised structure. The proposed computational algorithm can also be applied to obtain reduced-order decentralised controllers. Numerical examples are used to demonstrate the efficacy of the proposed algorithm.

A new approach to LPV gain-scheduling design and implementation

A new approach for design and implementation of stabilizing gain-scheduled controllers is proposed. The scheduling variable is used to parameterize the frozen-time linearized dynamics with respect to all system trajectories. This formulation removes the restriction in traditional gain-scheduling that the initial conditions remain close to an equilibrium manifold. A new approach for LPV controller design which results in practically valid controllers is suggested. Next, a novel gain-scheduled controller implementation is proposed for a general LPV controller structure and is shown to satisfy a local linear equivalence condition at the equilibrium manifold. In addition, the novel controller implementation offers extra degrees of freedom that can be employed to maximize the parameter rate bounds. Stability analysis shows that with a bound on parameter variation rates the nonlinear closed-loop system trajectories remain bounded for initial conditions not restricted to be close to equilibrium.

Performance of LPV gain-scheduled systems

The design of nonlinear gain-scheduled controllers using linear parameter varying (LPV) systems methodology has seen a lot of development. It is known that when the LPV plant model is obtained using linearization, extra care must be taken when implementing the gain-scheduled controller from the designed LPV controller in order to guarantee stability. In this paper, we motivate and investigate guaranteed performance bounds for the nonlinear closed loop system obtained via linearization LPV gain-scheduling methods

Control of time-delayed LPV systems using delayed feedback

Abstract In this paper, the delayed (memory) feedback synthesis problem for linear parameter varying (LPV) systems with parameter-varying time delays is introduced and addressed. It is assumed that the state-space data and the time-delay depend continuously on the parameters which are measurable in real-time and vary in a compact set with bounded variation rates. Synthesis conditions for stabilization and L 2 norm performance using delayed state feedback and delayed output feedback are formulated in terms of Linear Matrix Inequalities (LMIs) that can be solved efficiently. It is shown that time-delayed feedback control provides advantages in terms of reduced conservatism, improved performance and ease of controller implementation. Numerical examples are used to demonstrate the improved performance of the proposed delayed feedback configuration compared with that of the memoryless feedback schemes.

Hysteresis Compensation Using LPV Control

The paper proposes a Linear Parameter Varying (LPV) approach to control nonlinear systems with hysteresis. An equivalent representation of the hysteretic system as a LPV system is proposed. The design approach is demonstrated using a two-mass-spring system with a hysteretic spring force. The LPV controller is scheduled based on real-time measurements of the spring stiffness. The results are compared to a robust H ∞ control design. It is shown that the LPV design provides superior performance and avoids the conservatism of the robust H ∞ design. Thus, LPV gain-scheduling is an effective approach to control hysteretic systems.