Controller Design For Dynamic Systems Research Articles

Neuro-Evolution of Continuous-Time Dynamic Process Controllers

Artificial neural networks are means which are, among several other approaches, effectively usable for modelling and control of non-linear dynamic systems. In case of modelling systems input and output signals are a-priori known, supervised learning methods can be used. But in case of controller design of dynamic systems the required (optimal) controller output is a-priori unknown, supervised learning cannot be used. In such case we only can define some criterion function, which represents the required control performance of the closed-loop system. We present a neuro-evolution design for control of a continuous-time controller of non-linear dynamic systems. The controller is represented by an MLP-type artificial neural network. The learning algorithm of the neural network is based on an evolutionary approach with genetic algorithm. An integral-type performance index representing control quality, which is based on closed-loop simulation, is minimised. The results are demonstrated on selected experiments with controller reference value changes as well as with noisy system outputs.

Closed-Form Representations of Friction

The current developed friction models are basically based on the assumption of the normal forces exerted between the contact surfaces known in advance, less work has been done for closed-form (i.e., analytic) modeling in complex mechanical systems where the normal forces vary greatly over time. In this paper, the closed-form representations of friction forces in mechanical systems are newly derived in a way of dynamics. The Udwadia-Kalaba equation is first used to calculate the normal force exerted by the contact surface in mechanical system. The friction force is then calculated via existing friction models. Such closed-form expressions of friction forces contain both the magnitude and direction at any instant of time, even as the normal force is nonconstant. The novel representations offer an effective way for analytically expressing friction force in dynamical systems, which makes it possible for accurate simulation and control design of dynamical systems with non-negligible friction forces.

Continuous Fixed‐Time Controller Design for Dynamic Systems with Unmeasurable States Subject to Unbounded Disturbances

AbstractThis paper presents a nonlinear continuous observer‐based controller that provides fixed‐time convergence to the origin (a vicinity of the origin) of a higher‐order dynamic system subject to unbounded disturbances, whose only measurable state is the highest relative degree one. The settling time estimation problem is solved computing an uniform upper bound of the fixed convergence time of the designed controller. Finally, the designed algorithm is verified in a case study of an industrial armature‐controlled DC motor.

An efficient methodology for robust control of dynamic systems with interval matrix uncertainties

ABSTRACTInterval models are frequently used for dealing with uncertainties of control systems. However, it is well known that direct analysis and synthesis of a controlled dynamic system with interval matrix uncertainties may be a NP-hard problem. In this work, an efficient methodology for robustness analysis and robust control design of dynamic systems with interval matrix uncertainties is presented systematically, in which the uncertainties appearing in the controlled plant and controller realisation are taken into account simultaneously in an integrated framework. The fundamental problems, such as quadratic stability, guaranteed cost control and H∞ control of uncertain systems are taken as examples to show the methodology. Necessary and sufficient conditions for linear dynamic systems with interval matrices are derived by transforming all the interval matrices into some more tractable forms. The whole reasoning process is logical and rigorous, and NP-hard problem is successfully avoided. The presented formulations are within the framework of linear matrix inequality and can be implemented conveniently. In contrast to existing vertex-set methods, in which the vertices of interval matrices need to be constructed and checked, the presented methods are more efficient. Three numerical examples are investigated to demonstrate the effectiveness and feasibility of the presented method.

Continuous Fixed-Time Controller Design for Dynamic Systems with Unmeasurable States

This paper presents a nonlinear continuous observer-based controller that provides fixed-time convergence to the origin (a vicinity of the origin) of a higher-order dynamic system subject to unbounded disturbances, whose only measurable state is the highest relative degree one. The settling time estimation problem is solved computing an uniform upper bound of the fixed convergence time of the designed controller. Finally, the designed algorithm is verified in a case study of an industrial armature-controlled DC motor.

Robust reliability method and reliability‐based performance optimization for non‐fragile robust control design of dynamic system with bounded parametric uncertainties

SummaryAn efficient robust reliability method for non‐fragile robust control design of dynamic system with bounded parametric uncertainties is presented systematically, in which the uncertainties existing in the controlled plant and controller realization are taken into account simultaneously in an integrated framework. Reliability‐based design optimization of non‐fragile robust control for parametric uncertain systems is carried out by optimizing the H2 and H∞ performances of the closed‐loop system, with the constraints on robust reliabilities. The non‐fragile robust controller obtained by the presented method may possess a coordinated optimum performance satisfying the precondition that the system is robustly reliable with respect to the uncertainties existing in controlled plant and controller. Moreover, the robustness bounds of uncertain parameters can be provided. The presented formulations are within the framework of linear matrix inequality and thus can be carried out conveniently. It is demonstrated by a numerical example that the presented method is effective and feasible. Copyright © 2016 John Wiley & Sons, Ltd.

Parameter estimation and controller design for dynamic systems from the step responses based on the Newton iteration

In this paper, a new Newton iterative identification method is presented for estimating the parameters of a second-order dynamic system utilizing the obtained data from the step response. In order to obtain the desired dynamic performance, a controller design method based on the root locus is presented to meet the requirement of the dynamic performance of the overshoot. The simulation results indicate that the proposed Newton iterative identification method is effective and the system response can meet the requirement of system dynamic performances.

Power Conserving Bond Graph Based Modal Representations and Model Reduction of Lumped Parameter Systems

Dynamic analysis is extensively used to study the behavior of continuous and lumped parameter linear systems. In addition to the physical space, analyses can also be performed in the modal space where very useful frequency information of the system can be extracted. More specifically, modal analysis can be used for the analysis and controller design of dynamic systems, where reduction of model complexity without degrading its accuracy is often required. The reduction of modal models has been extensively studied and many reduction techniques are available. The majority of these techniques use frequency as the metric to determine the reduced model. This paper describes a new method for calculating modal decompositions of lumped parameter systems with the use of the bond graph formulation. The modal decomposition is developed through a power conserving coordinate transformation. The generated modal decomposition model is then used as the basis for reducing its size and complexity. The model reduction approach is based on the previously developed model order reduction algorithm (MORA), which uses the energy-based activity metric in order to generate a series of reduced models. The activity metric was originally developed for the generic case of nonlinear systems; however, in this work, the activity metric is adapted for the case of linear systems with single harmonic excitation. In this case closed form expressions are derived for the calculation of activity. An example is provided to demonstrate the power conserving transformation, calculation of the modal power and the elimination of unimportant modes or modal elements.

Probabilistic analysis and control of systems with uncertain parameters over non-hypercube domain

Generalized polynomial chaos expansion provides a computationally efficient way of quantifying the influence of stochastic parametric uncertainty on the states and outputs of a system. In this study, a polynomial chaos-based method was proposed for an analysis and design of control systems with parametric uncertainty over a non-hypercube support domain. In the proposed method, the polynomial chaos for the hypercube domain was extended to non-hypercube domains through proper parameterization to transform the non-hypercube domains to hypercube domains. Based on the proposed polynomial chaos framework, a constrained optimization problem minimizing the mean under the maximum allowable variance was formulated for a robust controller design of dynamic systems with the parametric uncertainties of the non-hypercube domain. Several numerical examples ranging from integer to fractional order systems were considered to validate the proposed method. The proposed method provided superior control performance by avoiding the over-bounds from a hypercube assumption in a computationally efficient manner. From the simulation examples, the computation time by gPC analysis was approximately 10–100 times lower than the traditional approach.

Optimal process and control design under uncertainty: A methodology with robust feasibility and stability analyses

This paper presents a new methodology for the optimal process and control design of dynamic systems under uncertainty. Robust feasibility and stability analyses are incorporated within the proposed methodology to ensure process dynamic operability and asymptotic stability. These analyses are formulated as convex mathematical problems; thus, the present approach is computationally attractive since it does not require the solution of an MINLP to evaluate dynamic feasibility and stability as it has been proposed by recent dynamic optimization-based methodologies. A norm-bounded metric based on Structured Singular Value (SSV) analysis is employed to estimate the worst-case deviation in the process constraints in the presence of critical realizations in the disturbances. The robust stability test is based on Lyapunov theory and guarantees process asymptotic stability. Accordingly, the optimal process and control design alternative obtained by the method proposed here is dynamically feasible and asymptotically stable since it accommodates the most critical realizations in the disturbances. A ternary distillation system featuring a rigorous tray-by tray process model is used to illustrate the application of the proposed method.

Modal analysis reduction of multi-body systems with generic damping

Modal analysis of multi-body systems is broadly used to study the behavior and controller design of dynamic systems. In both cases, model reduction that does not degrade accuracy is necessary for the efficient use of these models. Previous work by the author addressed the reduction of modal representations by eliminating entire modes or individual modal elements (inertial, compliant, resistive). In that work, the bond graph formulation was used to model the system and the modal decomposition was limited to systems with proportional damping. The objective of the current work is to develop a new methodology such that model reduction can be implemented to modal analysis of multi-body systems with non-proportional damping that were not modeled using bond graphs. This extension also makes the methodology applicable to realistic systems where the importance of modal coupling terms is quantified and potentially eliminated. The new methodology is demonstrated through an illustrative example.

Simultaneous process synthesis and control design under uncertainty: A worst‐case performance approach

A new methodology that includes process synthesis and control structure decisions for the optimal process and control design of dynamic systems under uncertainty is presented. The method integrates dynamic flexibility and dynamic feasibility in a single optimization formulation, thus, reducing the costs to assess the optimal design. A robust stability test is also included in the proposed method to ensure that the optimal design is stable in the presence of magnitude‐bounded perturbations. Since disturbances are treated as stochastic time‐discrete unmeasured inputs, the optimal process synthesis and control design specified by this method remains feasible and stable in the presence of the most critical realizations in the disturbances. The proposed methodology has been applied to simultaneously design and control a system of CSTRs and a ternary distillation column. A study on the computational costs associated with this method is presented and compared to that required by a dynamic optimization‐based scheme. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2497–2514, 2013

Simultaneous Design and Control under Uncertainty Using Model Predictive Control

This work presents a new methodology for the simultaneous process flowsheet and control design of dynamic systems under uncertainty using a model predictive control (MPC) strategy. Although several...

Thermal behavior of high-temperature fuel cells: reliable parameter identification and interval-based sliding mode control

In this contribution, we present interval methods for mathematical modeling, for parameter identification, and for control design of dynamical systems. The corresponding approaches are applied to the thermal subsystem of a high-temperature solid oxide fuel cell (SOFC) which is available as a test rig at the Chair of Mechatronics at the University of Rostock. In practice, most internal parameters of SOFC stack modules cannot be measured directly. Therefore, system characteristics such as heat capacities or internal thermal resistances cannot be identified exactly, but only bounded. For this reason, intervals represent a good first approach to dealing with parameter uncertainty. In the first part of the paper, we present interval methods for the parameter identification aiming at the computation of globally optimal parameterizations. In comparison with classical local optimization procedures, the approximation quality is improved by the presented identification approach. The corresponding bounds for admissible domains are used to design a robust sliding mode control law for arbitrary operating points compensating the impact of disturbances and parameter uncertainties in a reliable way. In the second part of the paper, we show a simple approach to handling non-smoothness appearing in SOFC models based on ordinary differential equations in a verified way. We use a generalized derivative definition for a certain type of non-smooth functions inside the algorithm of the verified solver ValEncIA-IVP to be able to compute solutions to non-smooth initial value problems. The applicability of our method is demonstrated using the designed sliding mode controller.

Switching Fuzzy Model Construction and Controller Design for Dynamical Systems with Input Nonlinearity

Fuzzy model-based control mainly deals with dynamical systems which affinely depend on control inputs. In this paper, dynamical systems which is permitted to have nonlinearity not only in the states, but also in the inputs is considered. Input nonlinearity makes a nonlinear system complicated and makes the number of fuzzy model rules increase. Thus, switching fuzzy control approach is employed. Firstly, the switching fuzzy model construction with arbitrary linear dividing planes, which is an extension of the ordinary switching fuzzy model construction method with dividing planes corresponding to quadrants, is introduced. Secondly, by applying the switching fuzzy model construction method to the dynamical system with input nonlinearity, the switching fuzzy model with membership functions which depend on control inputs is constructed. Finally, by utilizing the dynamic state feedback control approach, we show that membership functions which depend on control inputs can be calculated. Moreover, by employing augmented system approach, the switching fuzzy dynamic state feedback controller design conditions based on the switching Lyapunov function are derived in terms of linear matrix inequalities. A design example illustrates the utility of this approach.

Kharitonov-like theorems for robust performance of interval systems

The sensitivity function of a control system is an important concept in performance analysis, classical filter design as well as modern robust H ∞ control. For an interval system, we prove that the maximal H ∞ norm of its sensitivity function is achieved at twelve (out of sixteen) Kharitonov vertices. Similar Kharitonov-like results are established for the complementary sensitivity function and strict positive realness of interval systems. These results are useful in robust performance analysis and H ∞ control design for dynamic systems under parametric perturbations.

Frequency Conditions in Controller Design for Dynamical Systems in Hilbert Spaces

The present paper develops the results of [1], where a generalization of H∞-optimal control theory to the case of dynamical systems in Hilbert spaces and, in particular, systems governed by delay differential equations was considered. It was mentioned in Remark 4 in [1] that the main difficulty encountered in the design of an H∞-optimal dynamic controller is in finding a positive definite solution of the corresponding operator equation or inequality. In practice, one sidesteps this difficulty by passing to a finite-dimensional approximation with the subsequent use of numerical methods. It would be more logical not to use solutions of any operator equations or inequalities in the controller equations, as was done in [2] for the finite-dimensional version of the problem. The aim of the present paper is to generalize this “inverse” approach [3, 4] in control law design to systems with infinite-dimensional state space. In this case, it becomes unnecessary to find solutions of operator equations or inequalities, and “frequency” inequalities for positive matrix functions used in this approach become inequalities for matrix functions of a more general class. Note that such a generalization was once carried out in absolute stability theory [5].