Rachit Mehra

Shaping the Energy of Mechanical Systems Without Solving Partial Differential Equations

Control of underactuated mechanical systems via energy shaping is a well-established, robust design technique. Unfortunately, its application is often stymied by the need to solve partial differential equations (PDEs). In this technical note a new, fully constructive, procedure to shape the energy for a class of mechanical systems that obviates the solution of PDEs is proposed. The control law consists of a first stage of partial feedback linearization followed by a simple proportional plus integral controller acting on two new passive outputs. The class of systems for which the procedure is applicable is identified imposing some (directly verifiable) conditions on the systems inertia matrix and its potential energy function. It is shown that these conditions are satisfied by three benchmark examples.

Impact of Topology on the Propagation of Cascading Failure in Power Grid

In the past two decades the frequent occurrences of large scale blackouts and catastrophic events has reduced the reliability of power grid to a great extent. A thorough analysis of the propagation of failures, in terms of line outages, combined with the topological characteristics of the grid aids, has been done to take corrective actions to save the system from complete collapse. It also helps to investigate the progress and understand the nature and intensity of blackouts. This motivates to establish the relationship between the network topological characteristics and cascading failure in the power grid. In this paper, the basic topological characteristics of the power network are studied in detail and the average propagation of failure under varying topological conditions is calculated as a branching process parameter. The variation in the mean propagation is studied in detail using a number of test bed networks with the alternate realistic networks derived from the standard IEEE networks imitating the real network conditions. The results confirm a qualitative agreement between the variations in topological parameter and the failure propagation rate in the cascading regime. Based on the analysis mentioned above, data clearly shows that the average failure propagation factor varies linearly with the variations in the statistical metrics.

Analysis of PCA based compression and denoising of smart grid data under normal and fault conditions

This paper describes application of principal component analysis (PCA) based data compression approaches for smart grid (SG) data storage. PCA methods are applied and compared for steady state operations and various system fault conditions. For signals with Gaussian noise data, a variant of PCA, labelled Iterative PCA (IPCA) is applied to simulated phasor data. The phasor data is simulated for IEEE New England 30-bus system using ETAP software. The simulated data is then stored using the PCA and IPCA, which exploit the sparsity and collinearity among variables in the simulated data. The results indicate that proposed methods compress both the steady state and transient signals effectively while simultaneously removing the Gaussian noise contained in the signals.

Passivity based controller for underactuated PVTOL system

This paper proposes a control law for Planar Vertical Take Off and Landing (PVTOL) system based on feedback passivation method. The PVTOL system is a benchmark control system problem which embodies in itself many control theoretic challenges due to its nonlinear and underactuaed dynamics. Trajectory tracking of PVTOL system with its roll angle control is investigated in the paper. Stability of the PVTOL roll angle is ensured by the property that the equilibrium point of a passive system always remains stable. The equivalence of PVTOL dynamics with the pendulum dynamics is exploited to design a simple passivity based feedback controller. The proposed framework interprets PVTOL dynamics as pendulum dynamics and integrator systems whose interconnection can be made passive under the action of the designed control law. The forces exerted by the actuators can be synthesized from the control law.

Differentiation of faults from power swings and detection of high impedance faults by distance relays

For maintaining security and reliable operation of distance relays power swing blocking is necessary to prevent maloperation during power swings and high impedance faults detection is necessary for operation of distance relays, since distance relays may treat high impedance faults as load since the fault will be out of reach of the relay. This paper proposes an algorithm for differentiation of faults from power swing and high impedance fault detection by distance relay simultaneously by a single algorithm, based on extracting current waveform components using Prony method. The merit of this method is demonstrated by simulating different high impedance faults and also during power swing conditions using the ATP version of the EMTP.

Modes preserving wavelet based multi-scale PCA algorithm for compression of smart grid data

In this paper, wavelet based multiscale PCA algorithm is proposed for effective compression of smart grid data under normal as well as fault conditions. The signal decomposition is done using wavelet transform, followed by the de-correlation using PCA, to achieve maximum compression, while simultaneously preserving the dominant modes of the signal and bad data rejection. The optimum decomposition scale of wavelet transform is selected based on the energy of wavelet coefficients in each scale. The proposed algorithm employing multiscale PCA computes the principal components of the wavelet coefficients at each scale, followed by combining the results at relevant scales. The wavelet coefficients of a particular scale corresponding to the dominant eigen values are retained for signal compression. The dominant modes in the signal are sorted based on their energy content. This overcomes the drawback of false detection of modes and lower accuracy of estimation which arises when systems of higher order are used. Prony analysis is performed to check ability of the compression strategy to preserve the modal information. The phasor data are simulated under fault conditions in the IEEE 30-bus system. The results from Prony analysis indicate that multiscale PCA effectively compresses the disturbance signals while preserving the model information of the signal.

Control of a class of underactuated mechanical systems obviating matching conditions

Abstract The presently established techniques for control of underactuated mechanical systems are dependent on solving partial differential equations (PDEs) arising out of matching conditions. In this brief a novel controller design methodology for (asymptotic) stabilization of nonlinear systems is proposed that obviates the need of solving PDEs to obtain the control laws. The geometry based energy shaping methodology forms the fully constructive procedure for control of underactuated mechanical systems. The control methodology is based on manipulating symmetric structure of the system such that the power flow is established between the controller and unactuated part of the system. The modifications leads to identification of the two new passive outputs which are further utilized for kinetic and potential shaping and the desired controller is obtained using passivity based techniques. The theory is illustrated with two benchmark examples.

Blended algorithm for feedback linearization of single input control system

A new algorithm is proposed for computing locally the linearizing output of a single input nonlinear affine system. The algorithm relies on Goursat normal form, which is suitably modified, to obtain the successive integrations of one dimensional distributions of control system. The algorithm takes ideas from both vector field approach of feedback linearization and exterior differential system tools, hence the name Blended Algorithm is proposed. The proposed algorithm leads to a simple method of finding a linearizing output and has many advantages over the existing methods. The algorithm exhibits reduced computational complexity and can be extended to multi input system and partial linearizable system because of the underlying tower like structure.

Passivity based control of stochastic mechanical system

In this paper, a new method is proposed for controller design for a class of stochastic underactuated mechanical system. A controller is designed for stochastic double integrator system derived by backstepping procedure and the idea is to cancel noise at its source without allowing it to enter the system dynamics. The proposed control strategy is then applied to stochastic underactuated mechanical system. We represent actuated dynamics in the stochastic double integrator form. This approach was found to be suitable for cancellation of multiplicative noise influencing actuated coordinates of the system. The effectiveness of the proposed control law is tested on the stochastic SpiderCrane model with underactuation of degree one.

Feedback Linearization of Single-Input and Multi-Input Control System

Abstract A new algorithm is proposed for computing locally the linearizing output of single-input and multi-input nonlinear affine system. The algorithm modifies the extended Goursat normal form to iteratively obtain the successive integrations of one dimensional distributions of control system. The algorithm takes ideas from both vector field approach of feedback linearization and exterior differential system tools, hence the name Blended Algorithm. The proposed algorithm leads to a tower like structure depending upon the number of system inputs. Within individual tower, the coordinates are reduced one by one by finding the annihilators of vector fields at each step. The process is repeated till the single vector field is obtained for exact linearizable system. The scheme exhibits reduced computational complexity over the existing methods and can be extended to address feedback linearization of various class of control systems.