Piecewise Linear Control Systems

This thesis treats analysis and design of piecewise linear control systems. Piecewise linear systems capture many of the most common nonlinearities in engineering systems, and they can also be used for approximation of other nonlinear systems. Several aspects of linear systems with quadratic constraints are generalized to piecewise linear systems with piecewise quadratic constraints. It is shown how uncertainty models for linear systems can be extended to piecewise linear systems, and how these extensions give insight into the classical trade-offs between fidelity and complexity of a model. Stability of piecewise linear systems is investigated using piecewise quadratic Lyapunov functions. Piecewise quadratic Lyapunov functions are much more powerful than the commonly used quadratic Lyapunov functions. It is shown how piecewise quadratic Lyapunov functions can be computed via convex optimization in terms of linear matrix inequalities. The computations are based on a compact parameterization of continuous piecewise quadratic functions and conditional analysis using the S-procedure. A unifying framework for computation of a variety of Lyapunov functions via convex optimization is established based on this parameterization. Systems with attractive sliding modes and systems with bounded regions of attraction are also treated. Dissipativity analysis and optimal control problems with piecewise quadratic cost functions are solved via convex optimization. The basic results are extended to fuzzy systems, hybrid systems and smooth nonlinear systems. It is shown how Lyapunov functions with a discontinuous dependence on the discrete state can be computed via convex optimization. An automated procedure for increasing the flexibility of the Lyapunov function candidate is suggested based on linear programming duality. A Matlab toolbox that implements several of the results derived in the thesis is presented

DIFFERENTIAL EVOLUTION FOR OPTIMIZATION OF PID GAIN IN ELECTRICAL DISCHARGE MACHINING CONTROL SYSTEM

ABSTRACT PID controller of servo control system maintains the gap between Electrode and workpiece in Electrical Dis- charge Machining (EDM). Capability of the controller is significant since machining process is a stochastic phenomenon and physical behaviour of the discharge is unpredictable. Therefore, a Proportional Integral Derivative (PID) controller using Differential Evolution (DE) algorithm is designed and applied to an EDM servo actuator system in order to find suitable gain parameters. Simulation results verify the capabilities and effectiveness of the DE algorithm to search the best configuration of PID gain to maintain the electrode position. Keywords: servo control system; electrical discharge machining; proportional integral derivative; con- troller tuning; differential evolution

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Short-Term load forecasting using a neuro-fuzzy model based on entropy maximisation

International audienceThe paper presents a new short-term load forecasting approach based on dynamic fuzzy logic modelling. The developed model produces forecasts for the next 48 hours, which are updated every hour. Such a sliding window scheme is different than conventional models that operate usually once a day. The paper emphasizes on developing appropriate learning and on-line adaptation schemes based on the maximal entropy principle. In contrast to the traditional approach, such schemes permit to avoid overfitting of the model to the data. Thus, the ability of the model to predict new data (generalisation) is maximized. The architecture of the model is selected using non-linear optimisation techniques such the non-linear Simplex. The model has been developed in the frame of the EU research project More-Care and implemented for on-line use at the islands of Crete and Madeira. Results from the case studies are presented showing the efficiency of the approach

Analytical results for the multi-objective design of model-predictive control

In model-predictive control (MPC), achieving the best closed-loop performance under a given computational resource is the underlying design consideration. This paper analyzes the MPC design problem with control performance and required computational resource as competing design objectives. The proposed multi-objective design of MPC (MOD-MPC) approach extends current methods that treat control performance and the computational resource separately -- often with the latter as a fixed constraint -- which requires the implementation hardware to be known a priori. The proposed approach focuses on the tuning of structural MPC parameters, namely sampling time and prediction horizon length, to produce a set of optimal choices available to the practitioner. The posed design problem is then analyzed to reveal key properties, including smoothness of the design objectives and parameter bounds, and establish certain validated guarantees. Founded on these properties, necessary and sufficient conditions for an effective and efficient solver are presented, leading to a specialized multi-objective optimizer for the MOD-MPC being proposed. Finally, two real-world control problems are used to illustrate the results of the design approach and importance of the developed conditions for an effective solver of the MOD-MPC problem

Missile Attitude Control via a Hybrid LQG-LTR-LQI Control Scheme with Optimum Weight Selection

This is the author accepted manuscript. The final version is available from IEEE via the DOI in this record.This paper proposes a new strategy for missile attitude control using a hybridization of Linear Quadratic Gaussian (LQG), Loop Transfer Recovery (LTR), and Linear Quadratic Integral (LQI) control techniques. The LQG control design is carried out in two steps i.e. firstly applying Kalman filter for state estimation in noisy environment and then using the estimated states for an optimal state feedback control via Linear Quadratic Regulator (LQR). As further steps of performance improvement of the missile attitude control system, the LTR and LQI schemes are applied to increase the stability margins and guarantee set-point tracking performance respectively, while also preserving the optimality of the LQG. The weighting matrix (Q) and weighting factor (R) of LQG and the LTR fictitious noise coefficient (q) are tuned using Nelder-Mead Simplex optimization technique to make the closed-loop system act faster. Simulations are given to illustrate the validity of the proposed technique

Model-free controller design for nonlinear underactuated systems with uncertainties and disturbances by using extended state observer based chattering-free sliding mode control

MakaleWOS:000912458400001Most of the control strategies require a mathematical model or reasonable knowledge that is difficult to obtain for complex systems. Model-free control is a good alternative to avoid the difficulties and complex modeling procedures, especially if the knowledge about the system is insufficient. This paper presents a new control scheme completely independent of the system model. The proposed scheme combines sliding mode control (SMC) with intelligent proportional integral derivative (iPID) control based on a local model and extended state observer (ESO). Although the iPID control makes the proposed method model-free, it cannot guarantee that the tracking errors converge to zero asymptotically except the system is in a steady-state regime. Therefore, the SMC is added to the control scheme to ensure the convergence by minimizing the estimation errors of the observer. The proposed iPIDSMC controller is tested in the presence of different parameter variations and external disturbances on an inverted pendulum - cart (IPC), which is a highly unstable underactuated system with nonlinear coupled dynamics. The proposed controller is compared with the PID, iPID and Hierarchical Sliding Mode Control (HSMC) for a clearer evaluation. Simulation results showed that the proposed controller is extremely insensitive to parameter variations, matched and mismatched disturbances and the control signal of the proposed method is chattering-free, even though it is based on a discontinuous control action

Disturbance rejecting PID-FF controller design of a non-ideal buck converter using an innovative snake optimizer with pattern search algorithm.

The optimal design of a proportional-integral-derivative controller with two cascaded first-order low-pass filters (PID-FF) for non-ideal buck converters faces significant challenges, including effective disturbance rejection, robustness to parameter variations, and the mitigation of high-frequency signal noise, with existing approaches often struggling and leading to suboptimal performance in practical applications. This study addresses these challenges by introducing a constraint on the open-loop crossover frequency to mitigate high-frequency noise and ensuring the controller prioritizes maintaining constant output voltage and robust responsiveness to input voltage and load current variations. This study also introduces an innovative metaheuristic algorithm, the opposition-based snake optimizer with pattern search (OSOPS), designed to address these limitations. OSOPS enhances the Snake Optimizer (SO) by integrating opposition-based learning (OBL) and Pattern Search (PS), thereby improving its exploration and exploitation capabilities. The proposed algorithm design includes a crossover frequency constraint aimed at counteracting high-frequency noise and ensuring robust performance under diverse disturbances. The efficacy of the OSOPS algorithm is demonstrated through rigorous statistical box plot analysis and convergence response comparisons with the original SO algorithm. Additionally, we systematically compare the performance of the OSOPS-based PID-FF-controlled non-ideal buck converter system against systems utilizing the original SO algorithm and the classical pole placement (PP) method. This evaluation encompasses transient and frequency responses, disturbance rejection, and robustness analysis. The results reveal that the OSOPS-based system outperforms the SO- and PP-based systems with 14.21 % and 32.10 % faster rise times, along with 15.38 % and 84.95 % faster settling times, respectively. The OSOPS and SO systems also exhibit higher bandwidths, exceeding the PP-based system by 18.74 % and 17.03 %, respectively. By addressing the key challenges in PID-FF controller design for non-ideal buck converters, this study provides a substantial advancement in control strategy, promising enhanced performance in practical applications