Eigenstructure Assignment by State-derivative and Partial Output-derivative Feedback for Linear Time-invariant Control Systems

This paper introduces a parametric approach for solving the problem of eigenstructure assignment via state-derivative feedback for linear control time-invariant systems. This problem is always solvable for any controllable systems if the open-loop system matrix is nonsingular. In this work, the parametric solution to the feedback gain matrix is introduced that describes the available degrees of freedom offered by the state-derivative feedback in selecting the associated eigenvectors from an admissible class. These freedoms can be utilized to improve the robustness of the closed-loop system. Finally, the eigenstructure assignment problem via partial output-derivative feedback is introduced. Numerical examples are included to show the effectiveness of the proposed approach

A Complete Parametric Solutions of Eigenstructure Assignment by State-Derivative Feedback for Linear Control Systems

In this paper we introduce a complete parametric approach for solving the problem of eigenstructure assignment via state-derivative feedback for linear systems. This problem is always solvable for any controllable systems iff the open-loop system matrix is nonsingular. In this work, two parametric solutions to the feedback gain matrix are introduced that describe the available degrees of freedom offered by the state-derivative feedback in selecting the associated eigenvectors from an admissible class. These freedoms can be utilized to improve robustness of the closed-loop system. Accordingly, the sensitivity of the assigned eigenvalues to perturbations in the system and gain matrix is minimized. Numerical examples are included to show the effectiveness of the proposed approach.

A Direct Algorithm for Pole Placement by State-derivative Feedback for Single-input Linear Systems

This paper deals with the direct solution of the pole placement problem for single-input linear systems using state-derivative feedback. This pole placement problem is always solvable for any controllable systems if all eigenvalues of the original system are nonzero. Then any arbitrary closed-loop poles can be placed in order to achieve the desired system performance. The solving procedure results in a formula similar to the Ackermann formula. Its derivation is based on the transformation of a linear single-input system into Frobenius canonical form by a special coordinate transformation, then solving the pole placement problem by state derivative feedback. Finally the solution is extended also for single-input time-varying control systems. The simulation results are included to show the effectiveness of the proposed approach

LQR and H_2 Controllers Design Using State Derivative Feedback for Multivariable Systems

This paper presents the design of LQR (linear quadratic regular) and  controller using state derivative feedback. This design is solvable for all controllable systems.  The state derivative feedback is used instead of state feedback in many mechanical systems because the main sensors of vibration are accelerometers. A multivariable active suspension system is used in this paper to show the effectiveness of the proposed controllers. The obtained results are compared to the same approaches when a state feedback is used. It is shown that the design using state derivative feedback can achieve a better performance

Stabilizability and Disturbance Rejection with State-Derivative Feedback

In some practical problems, for instance in the control of mechanical systems using accelerometers as sensors, it is easier to obtain the state-derivative signals than the state signals. This paper shows that (i) linear time-invariant plants given by the state-space model matrices {A,B,C,D} with output equal to the state-derivative vector are not observable and can not be stabilizable by using an output feedback if det⁡(A)=0 and (ii) the rejection of a constant disturbance added to the input of the aforementioned plants, considering det⁡(A)≠0, and a static output feedback controller is not possible. The proposed results can be useful in the analysis and design of control systems with state-derivative feedback

Optimal Torque Control for an Electric-Drive Vehicle with In-Wheel Motors: Implementation and Experiments

© SAE, Athari, A., Fallah, S., Li, B., Khajepour, A. et al., "Optimal Torque Control for an Electric-Drive Vehicle with In-Wheel Motors: Implementation and Experiments," SAE Int. J. Commer. Veh. 6(1):82-92, 2013, doi:10.4271/2013-01-0674.This paper presents the implementation of an off-line optimized torque vectoring controller on an electric-drive vehicle with four in-wheel motors for driver assistance and handling performance enhancement. The controller takes vehicle longitudinal, lateral, and yaw acceleration signals as feedback using the concept of state-derivative feedback control. The objective of the controller is to optimally control the vehicle motion according to the driver commands. Reference signals are first calculated using a driver command interpreter to accurately interpret what the driver intends for the vehicle motion. The controller then adjusts the braking/throttle outputs based on discrepancy between the vehicle response and the interpreter command. A test vehicle equipped with four in-wheel electric motors, vehicle sensors, communication buses, and dSPACE rapid prototyping hardware is instrumented and the control performance is verified through vehicle handling tests under different driving conditions.Automotive Partnership CanadaOntario Research FundGeneral Motor

Semi-active suspension with semi-active inerter and semi-active damper

This paper investigates the application of semi-active inerter in semi-active suspension. A semi-active inerter is defined as an inerter whose inertance can be adjusted within a finite bandwidth by on-line control actions. A force-tracking approach to designing semi-active suspension with a semi-active inerter and a semi-active damper is proposed, where the target active control force derived by LQR control in the 'Reciprocal State-Space' (RSS) framework is tracked by controlling the semi-active damping coefficient and semi-active inertance. One of the advantages of the proposed method is that it is straightforward to use the acceleration information in the controller design. Simulation results demonstrate that the semi-active suspension with a semi-active inerter and a semi-active damper can track the target active control force much better than the conventional semi-active suspension (which only contains a semi-active damper) does. As a consequence, the overall performance in ride comfort, suspension deflection and road holding is improved, which effectively demonstrates the necessity and the benefit of introducing semi-active inerter in vehicle suspension.preprin

Systems Structure and Control

The title of the book System, Structure and Control encompasses broad field of theory and applications of many different control approaches applied on different classes of dynamic systems. Output and state feedback control include among others robust control, optimal control or intelligent control methods such as fuzzy or neural network approach, dynamic systems are e.g. linear or nonlinear with or without time delay, fixed or uncertain, onedimensional or multidimensional. The applications cover all branches of human activities including any kind of industry, economics, biology, social sciences etc