Passivity-Based Design of Wireless Networked Control Systems for Robustness to Time-Varying Delays

Abstract

Abstract

Multi-rate networked control of conic (dissipative) systems

“…In [2] we proved that a fixed-rate (M = 1) digital control framework depicted in Fig. 1 could be used to control the position of a nonlinear robotic systems H p by i) rendering it strictly output passive (inside the sector [0, b p ], b p < ∞) with velocity feedback and gravity compensation; and ii) applying a digital controller H c to indirectly control the robot's position by integrating its velocity error e c (j) with a lag compensator.…”

“…As a result of being restricted to use indirect velocity feedback, the robotic manipulators position may drift due to imperfect cancellation of gravitational effects, contacting immovable obstacles, and losing data. One way to address this drift problem is to directly control the position of the robot y p (t); however, it is well known that the relationship between the position of the robot and the controlling torque input e M p (t) is not passive, a sufficient condition required of the earlier results presented in [2]. Therefore, we will show how to weaken this condition such that the continuous-time plant is only required to be a conic For simplicity of discussion, we will neglect gravitational effects and consider a LTI model of a single degree of freedom haptic paddle with mass M p which is subject to a low-pass filtered velocity feedback whose time constant is τ > 0 as depicted in Fig.…”

“…The relationships between the continuoustime and discrete-time wave variables is determined by the multi-rate passive sampler (denoted PS : M T s ) and multirate passive hold (denoted PH : M T s ). These two elements are a combination of the passive sampler and passive hold blocks (which have been instrumental in showing how to interconnect digital controllers to continuous-time systems in order to achieve L m 2 -stability [2], [11]; see [12]- [15] for interconnecting continuous-time plants to continuous-time controllers over digital networks) and a discrete-time passive upsampler and passive downsampler [3]. At the interface to the digital controller is an inner product equivalent sample (IPES) and zero-order (ZOH) hold block y ct (t) = y s (j), t ∈ [jM T s , (j + 1)M T s ) [11] which are used for analysis in order to relate continuous-time control inputs r ct (t) and continuous-time control outputs y ct (t) to the continuous-time plant inputs r p (t) and outputs y p (t).…”

“…Our team has investigated the use of passivity for the design of Networked Control Systems (NCS) [1] in the presences of time-varying delays [2], [3]. This paper presents an important new step in the design of networked control systems as it applies to control of a conic-(dissipative) plant inside the sector [a, b] in which |a| < b, 0 < b ≤ ∞.…”

Design of Networked Control Systems Using Passivity

“…The work presented in this paper demonstrates that passivity can be exploited to account for the effects of network uncertainties, thus improving orthogonality across the controller design and implementation design layers and empowering model-driven development. Part of this paper has been presented in [22]. The main extensions are: 1) experimental implementation and evaluation of the passivity-based architecture using a NCS; 2) detailed design of the digital passive controller; and 3) theoretical analysis that includes the proofs of passivity and stability for the proposed architecture.…”