Dynamics Analysis and Robust Control for Electric Unicycles Under Constrained Control Force

International audience

This paper reviews robust feedback control applications in power system. Robust control concept in power system control area evolves by the way of uncertainty modeling. Uncertainties can be caused by variation of loading, load parameters, network topology and machine parameters. One direct way to take into consideration of uncertainties is to enumerate various system operating conditions and use a set of linear time invariant systems to model the power systems. Enumeration method is used in robust control signal selection and robust controller design. Another way is to model uncertainties as structured or unstructured uncertainties. Controllers are designed based on nominal system condition to tolerate uncertainty as much as possible. The controller synthesis problem is solved by either Algebraic Ricatti Equation (ARE) or Linear Matrix Inequality (LMI). LMI is shown to be more flexible in controller design since it provides a way to specify system dynamic performance. Most recently, linear parameter varying (LPV) concept expands the use of enumeration method to express a set of linear time invariant (LTI) systems with state space dependent on linear parameters. LPV based control methods extend gain scheduling to design linear control for each operating conditions and overall a nonlinear controller for the varying parameter system.

Preface Notation Part I. Introduction. Robust Decision Problems in Engineering: A linear matrix inequality approach L. El Ghaoui and S.-I. Niculescu Part II. Algorithms and Software: Mixed Semidefinite-Quadratic-Linear Programs J.-P. A. Haeberly, M. V. Nayakkankuppam and M. L. Overton Nonsmooth algorithms to solve semidefinite programs C. Lemarechal and F. Oustry sdpsol: A Parser/Solver for Semidefinite Programs with Matrix Structure S.-P. Wu and S. Boyd Part III. Analysis: Parametric Lyapunov Functions for Uncertain Systems: The Multiplier Approach M. Fu and S. Dasgupta Optimization of Integral Quadratic Constraints U. Jonsson and A. Rantzer Linear Matrix Inequality Methods for Robust H2 Analysis: A Survey with Comparisons F. Paganini and E. Feron Part IV. Synthesis. Robust H2 Control K. Y. Yang, S. R. Hall and E. Feron Linear Matrix Inequality Approach to the Design of Robust H2 Filters C. E. de Souza and A. Trofino Robust Mixed Control and Linear Parameter-Varying Control with Full Block Scalings C. W. Scherer Advanced Gain-Scheduling Techniques for Uncertain Systems P. Apkarian and R. J. Adams Control Synthesis for Well-Posedness of Feedback Systems T. Iwasaki Part V. Nonconvex Problems. Alternating Projection Algorithms for Linear Matrix Inequalities Problems with Rank Constraints K. M. Grigoriadis and E. B. Beran Bilinearity and Complementarity in Robust Control M. Mesbahi, M. G. Safonov and G. P. Papavassilopoulos Part VI. Applications:Linear Controller Design for the NEC Laser Bonder via Linear Matrix Inequality Optimization J. Oishi and V. Balakrishnan Multiobjective Robust Control Toolbox for LMI-Based Control S. Dussy Multiobjective Control for Robot Telemanipulators J. P. Folcher and C. Andriot Bibliography Index.

We study, in this work, the robust iterative learning control RILC design for uncertain systems. The control law design is based on H∞ concept and tow dimensional 2D theory. A Proportional type, Derivative type and Proportional Derivative type RILC laws will be proposed to achieve the desired performance of repetitive systems. A comparison between the three proposed control laws will be presented. The monotonic convergence and the robust stability will be demonstrated by using this control laws. Based on H∞ concept, sufficient settings for asymptotic convergence of our approaches are presented in terms of LMI (linear matrix inequality). An academic example is presented here to prove the efficiency of the proposed schemes.

In this study, an LMI (Linear Matrix Inequality) based H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> robust controller design approach is proposed to improve the performance of the designed U-pole placement control systems. Unlike the classical design procedures, the control-oriented U-model based nonlinear control systems cancel the nonlinearity of the nonlinear models. Therefore, the closed loop transfer function of U-pole placement control system can be regarded as a linear block. The solvability and sub-optimality of discrete-time H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> robust control are converted to find feasible solutions for LMIs. Once the internal parameters changed, the LMI based H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controllers have a higher level of robustness compared with U-pole placement controllers. A nonlinear dynamic model is selected to test the performance of the LMI robust controller to demonstrate the proposed approach effective.

In this article, the problem of robust exponential stability and reliable stabilisation for a class of continuous-time networked control systems (NCSs) with a sample-data controller and unknown time-varying sampling rate is considered. The analysis is based on average dwell-time, Lyapunov–Krasovskii functional and linear matrix inequality (LMI) technique. The delay-dependent criteria are developed for ensuring the robust exponential stability of the considered NCSs. The obtained conditions are formulated in terms of LMIs that can easily be solved by using standard software packages. Furthermore, the result is extended to study the robust stabilisation for NCS with parameter uncertainties. A state feedback controller is constructed in terms of the solution to a set of LMIs, which guarantee the robust exponential stabilisation of NCS and the controller. Finally, numerical examples are presented to illustrate the effectiveness of the obtained results.

Robust Fuzzy Model Predictive Control with time delays for Nonlinear Systems

This paper proposes the use Fuzzy logic controller and a Particle Swarm Optimization (PSO) based Linear Quadratic Regulator (LQR) controller for the balance of an electric unicycle. It also examines dynamics of the electric unicycle's schematic design, which has a backing seat for the passenger and is analogous to the Segway device equipped with a handle shaft for direction. A proportional derivative controller incorporated with a Fuzzy logic controller was designed for the suggested model of the electric unicycle for speed and position control (Fuzzy controller), and a Proportional Derivative (PD) controller was utilized to control the angle rate and angle of the unicycle. Comparison of the Fuzzy logic controller with a Particle Swarm Optimization (PSO) Linear Quadratic Regulator (LQR) controller was carried out based on error deviation and time response simulations. Command tracking or regulation of some initial state condition were examined and demonstrated by time based simulations of the modelled system. The results evidently indicate that the Fuzzy Proportional Derivative (PD) controller can effectively attain attitude equilibrium for the two wheeled unicycle and preventing it from falling down.

Optimized robust control for improving frequency response of delay dependent AC microgrid with uncertainties

This paper addresses robust control design problem for parameter dependent (PD) systems subject to actuator saturation. The dead-zone nonlinearity is considered for regional stability and performance analysis of control design strategy. The parallel distributed compensation static output feedback controller is derived in new gain-scheduling scheme satisfied the generalized sector condition. Based on the fuzzy Lyapunov function approach, the parametrized stabilization non-convex conditions are reformulated in linear matrix inequalities (LMI) by congruence transformations. The proposed method leads to less conservative constraint on saturated PD controller synthesis. The effectiveness of the design methodology is demonstrated through simulations.

This paper proposes a new robust stability condition for Takagi-Sugeno (T-S) fuzzy control system with parametric uncertainties. The condition is represented in the form of linear matrix inequalities (LMIs) and is less conservative than some relaxed quadratic stabilization conditions published recently in the literature by collecting the interrelations of fuzzy subsystems into a set of matrices, not just into a single matrix. Based on the LMI-based conditions derived, one can easily synthesize controllers for state feedback robust stabilization for T-S fuzzy control system with parametric uncertainties. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. Finally, the validity of the proposed approach is successfully demonstrated in the the control of simulation table.

Robust STATCOM voltage controller design using loop-shaping technique

A robust dynamic output feedback controller synthesis algorithm considering H∞/H2performance and regional pole placement is addressed for a nonlinear system with parameter uncertainties and external disturbance. First, the formulation of a gain‐scheduled mixed‐objective robust dynamic output feedback controller for continuous‐time polytopic linear parameter varying (LPV) systems is presented. To reduce conservativeness, some auxiliary slack variables and parameter‐dependent Lyapunov functions are employed in addition to well‐established performance conditions. Then, sufficient conditions for the desired gain‐scheduled mixed‐objective robust dynamic output feedback controllers are cast into an efficiently tractable finite‐dimensional convex optimization problem in terms of linear matrix inequalities (LMIs). Finally, numerical simulation shows the validity of the proposed controller, which has good stability, strong robustness, satisfied disturbance attenuation ability, and smooth dynamic properties.

LMI based robust load frequency control for time delayed power system via delay margin estimation

For the speed control system of autonomous electric vehicle (AEV), challenge happens with how to determine an appropriate driving speed to satisfy the dynamic environment while resisting uncertainty and disturbance. Therefore, this paper proposes a robust optimal speed control approach based on hierarchical architecture for AEV through combining deep reinforcement learning (DRL) and robust control. In decision‐making layer, a deep maximum entropy proximal policy optimization (DMEPPO) algorithm is presented to obtain an optimal speed via dynamic environment information, heuristic target entropy and adaptive entropy constraint. In motion control layer, to track the learned optimal speed while resisting uncertainty and disturbance, a robust speed controller is designed by the linear matrix inequality (LMI). Finally, simulation experiment results show that the proposed robust optimal speed control scheme based on hierarchical architecture for AEV is feasible and effective.