Lower order generalized aggregated model and suboptimal control

This paper presents a suboptimal control strategy for the linear quadratic regulator problem of Markov jump linear systems subject to control in jumps. The system under study has a dual switching structure, in a manner that the system parameters jump according to both a Markov chain and a given switching control rule. The suboptimal control policy, derived via dynamic programming argument, relies on a special set of positive semidefinite matrices, in the sense that the number of elements of this set increases via a combinatorial step-by-step argument, applied at each time stage. An example is presented to illustrate the result.

Sub-optimal control of fuzzy linear dynamical systems under granular differentiability concept

Design of Suboptimal Controller Using Model Reduction Technique

Advantageous strategies in differential games for a class of suboptimal control laws

Time optimal control problems involving high dimensional systems are generally very difficult to solve. Instead of using suboptimal control based on reduced system, iterative dynamic programming is used directly to establish the time optimal control policy of a binary distillation column described by 11 ordinary differential equations. The resulting optimal control policy that is bang‐bang in nature was obtained very rapidly. The minimum time of 2236 seconds obtained here is substantially better than 4120 seconds obtained by a suboptimal control policy. Simulations show that the procedure may be used for on‐line optimal control of the distillation column, since the optimal control policy can be established very fast on a personal computer.

The work presented in this dissertation was conducted in an effort to achieve improvement in conventional and digital control methods applied to chemical processes. Emphasis was placed on simplicity and effectiveness in an attempt to provide control improvements which are easily implemented and yet efficient in their tasks. In these studies digital simulation was used exclusively utilizing the IBM 7040 and 360 and the XDS Sigma V computers. Initially the inaccuracies involved in obtaining a firstorder plus dead time model graphically from an open loop response curve are discussed. It is pointed out that fine tuning of two and three mode controllers based on these inaccurate models is necessary and presently must be done by trial and error. Modifications of existing controller tuning relations are presented which guide fine tuning attempts and eliminate much of the trial and error procedure. Second, the subject of linear discrete models applied to sampled-data systems is considered. A multiple linear least squares technique is applied to sampled system input/output records to identify parameters of a linear discrete model. The method is demonstrated to give good results when applied xii to linear and non-linear systems with and without dead time. The simplicity and flexibility of implementing this modeling technique are discussed. Application of this method to systems with measurement noise are shown to be improved when the data are filtered. Third, the implementation of linear discrete models in Deadbeat, Dahlin and Kalman controller synthesis methods are presented. It is demonstrated that the form of the models fits well into each of these controller design philosophies. The Dahlin algorithms which incorporate a tuning parameter give the most consistent performance for model orders and sampling times considered. In general, the performance of controllers based on low order models is seen to compare well with that of higher order controllers. Fourth, utilizing the speed of the multiple linear regression identification, the application of this technique in an adaptive control scheme is presented. Applying a recursive solution of the regression equation enables the updating of the linear discrete model at each sample instant and subsequently the adaptation of the control strategy. This scheme is demonstrated to provide closer control of a non linear, time-variant system than is possible with a stationary model. xiii CHAPTER I The form of the transfer function, HG(z), comprised of the digital hold device and the process itself, is such that multiple linear regression techniques can be applied to identify the model constants (parameters). Model identification is then based only on a linear regression of the sampled-data records of the system input and output. A modeling technique based on multiple linear regression only requires the solution of a set of normal equa tions and therefore is rapid enough to be applied on-line. Model order can also be changed with relative ease requiring only an other pass through the system input/output response data already collected. The effectiveness of this identification method is demonstrated on linear systems as well as on a simulated non linear plug flow reactor system. The effect of measurement noise on modeling accuracy is also considered, and comparison of identification using both filtered and unfiltered data are presented. The advantage of filtering data under these operating conditions is illustrated. Linear discrete models obtained for the simulated reactor were demdnstrated in their capacities as both one step ahead predictor models and as free running models. In these studies the higher order models provided significantly better results. Digital controller synthesis methods are the subject of Chapter IV. The discrete form of the model fits well into these design methods. Flexibility in varying model order is carried over to allow: for flexibility in controller order. The advantages of this flexibility are illustrated with the Deadbeat, Dahlin and Kalman controller design algorithms. Controllers based on each of these design methods are implemented in the plug flow reactor system and compared as to overall control performance and manipulate variable action. Comparisons are made also for both fast and slow sampling rates. Finally, Chapter V incorprates the multiple linear regres sion modeling technique with a direct controller synthesis method in an attempt to achieve an adaptive control scheme. The intent here is to update the process model with each new sample taken, and therefore adapt the controller, which is di rectly based on this model to any variation in the operating levels of the system. Adaptive control in this fashion is demonstrated in application to the non-linear plug flow reactor system with a slowly changing feed rate. The result is a demonstration of an adaptive control strategy which has the capability to function in many possible process applications.

In order to examine the ability of low-order physical models of vertical axis wind turbines to accurately reproduce key flow characteristics, experimental data are presented for the mean flow patterns and turbulence spectra associated with pairs of rotating turbines, rotating solid cylinders, and stationary porous flat plates (of both uniform and non-uniform porosities). The experiments were conducted at a nominal model-diameter Reynolds number of 600 and rotation tip speed ratios between 0 and 6. By comparing the induced flow fields of the different models both qualitatively and quantitatively, it was concluded that the two dimensional horizontal mean flow fields induced by the porous flat plates were quantitatively similar to those induced by slowly rotating turbine models. However, over the range of the experimental parameters examined, the porous flat plates were unable to produce vertical flows similar to those associated with the slowly rotating turbine models. Conversely, the moderately rotating cylinders induced three dimensional mean flow fields quantitatively similar to those induced by rapidly rotating turbine models. These findings have implications for both laboratory experiments and numerical simulations, which have previously used analogous low order models in order to reduce experimental/computational costs. Specifically, over the range of parameters examined, the comparison between induced flow fields of the different model fidelities allows identification of the lowest cost model for which the specific goals of a study can be obtained, to within the desired accuracy. And if a lower fidelity model is used, it is possible to incorporate into the analysis of the collected data an understanding of how the results would be expected to vary from a higher fidelity case.

This paper presents an effective approach for lower-order (LO) modeling of an electric vehicle–integrated off-grid microgrid (OMG) system. The seventh-order system (SOS) of the OMG is reduced to a second-order model (SOM) while preserving the original system’s dynamic characteristics and ensuring computational efficiency. The Taylor series (TS) and Laurent series (LS) expansions are employed to simplify the complex system that plays a significant role in the reduction process. The expansion parameters of the higher-order system (HOS) of OMG and its lower-order model (LOM) are exploited to construct the fitness function. The proposed approach constructs three sub-objective functions based on TS and LS. These sub-objective functions are then combined into a single fitness function to obtain an improved LOM by enhancing the transient and steady-state responses with respect to the HOS of OMG. To minimize the error, the resultant fitness function is optimized using the brown bear optimization (BBO) algorithm. The optimization is performed under two key constraints: (i) ensuring zero steady-state error, and (ii) satisfying the Hurwitz stability criterion. To demonstrate the efficacy of the proposed LOM, it is compared with other LOMs obtained from different approximation techniques. The proposed LOM and other LOMs are graphically validated through step, impulse, Bode, Nichols, and Nyquist response comparisons with the HOS. Additionally, the performance error criteria (PEC), time-domain specifications (TDSs) and frequency domain specifications (FDSs) of the proposed LOM are compared with other LOMs using the HOS to establish the validation and applicability of the proposed method.

Math models of wheeled ground vehicle dynamics, including flexible body effects, have been the subject of research and development for many years. These models are typically based on a finite system of simultaneous ordinary differential equations (e.g., state-space models). Higher order models that include flexible body effects offer improved accuracy over a wider frequency range than lower order rigid body models; however, higher order models are typically more sensitive to uncertainties in the model parameters and have increased computational requirements. Lower order models with the desired accuracy may be achieved by model reduction of higher order models. A new more general infinite dimensional Laplace transfer function is derived for beam bending governed by a fourth order wave equation. The resulting infinite dimensional transfer functions for beam bending are then used to develop a transfer function model of a “half-car” with a flexible body. The infinite dimensional transfer function of the half-car model is then used to assess the accuracy of the state-space models. Differences between the models due to model reduction are compared to theoretical upper bounds.

A grey-box machine learning based model of an electrochemical gas sensor

Through the heat exchanger example of.Koppel et at. (1968) u rapid sub-optimal control algorithm is developed for optimal regulator problems in linear distributed parameter systems. The Galerkin approximation is first applied to obtain a lumped ODE model for the distributed parameter system. Then, a sub-optimal open-loop control for the resulting linear ODE optimal regulator problem is obtained through the Ritz-Trefftz algorithm of Bosarge and Johnson (1970). One-dimensional polynomial basis functions (modes) are employed to approximate both time and spatial behaviour throughout. To facilitate mode selection, emphasis is placed upon sequential ono-dimensional approximations rather than upon a single multidimensional approximation. Applications of the resulting algorithm are characterized by low storage and on-line computational requirements. Numerical results for the heat exchanger example are presented and compared with those currently available in the literature. Performance of the algorithm with a small number of polynomial modes is assessed and experimental user-oriented guidelines are provided.

Differential Dynamic Programming as a Tool for Dynamic Optimization in a Travelling-Grate Pelletizing Plant

Analytical expressions for the performance of optimal and suboptimal control policies in trajectory tracking problems are derived. Special attention is devoted to the finite preview problem. In the time-invariant infinite-duration case correspondence of the performance indices for finite energy, finite power, and stationary stochastic trajectories, all with the same spectral density, is established. Using this correspondence, the performance of different control policies is studied in the frequency domain. Simulation results demonstrate the facility of the theory of this paper.

This paper deals with the problem of finding a low-complexity estimate of the impulse response of a linear time-invariant discrete-time dynamic system from noise-corrupted input-output data. To this purpose, we introduce an identification criterion formed by the average (over the input perturbations) of a standard prediction error cost, plus a weighted l 1 regularization term which promotes sparse solutions. While it is well known that such criteria do provide solutions with many zeros, a critical issue in our identification context is where these zeros are located, since sensible low-order models should be zero in the tail of the impulse response. The flavor of the key results in this paper is that, under quite standard assumptions (such as i.i.d. input and noise sequences and system stability), the estimate of the impulse response resulting from the proposed criterion is indeed identically zero from a certain time index n l (named the leading order) onwards, with arbitrarily high probability, for a sufficiently large data cardinality N. Numerical experiments are reported that support the theoretical results, and comparisons are made with some other state-of-the-art methodologies.

Mathematical modelling and control system design of Czochralski and liquid encapsulated Czochralski processes: the basic low order mathematical model