On Optimal Input Design for Feed-forward Control

This paper considers optimal input design when the intended use of the identified model is to construct a feed-forward controller based on measurable disturbances. The objective is to find a minimum power excitation signal to be used in system identification experiment, such that the corresponding model-based feed-forward controller guarantees, with a given probability, that the variance of the output signal is within given specifications. To start with, some low order model problems are analytically solved and fundamental properties of the optimal input signal solution are presented. The optimal input signal contains feed-forward control and depends of the noise model and transfer function of the system in a specific way. Next, we show how to apply the partial correlation approach to closed loop optimal experiment design to the general feed-forward problem. A framework for optimal input signal design for feed-forward control is presented and numerically evaluated on a temperature control problem

Optimal Input Design for Active Parameter Identification of Dynamic Nonlinear Systems

There are many important aspects to be considered while designing optimal excitation signal for system identification experiment in control applications. Active parameter identification is an important issue in system and control theory. In this dissertation, the problem of optimal input design for active parameter identification of dynamic nonlinear system is addressed. Real life physical systems are identified by excitation with a suitable input signal and observing the resulting output behavior of the system. It is important to choose the input signal intelligently in the sense that it is responsible to determine the accuracy and nature of the unknown system characteristics. This leads to a spurred interest in designing such an optimal excitation signals that can yield maximal information from the identification experiment. The information obtained from parameter identification is usually not accurate due to incomplete knowledge of the system, disturbance as exogenous inputs and noisy measurements. Hence, the input spectrum is designed in such a way that it can improve the system performance and shape the quality of obtained information. A welldesigned input signal can maximize the amount of information and reduce the experimental cost and time. The input signal is usually given some a-priori characteristics (knowledge on the pdf) so that \u201cexcitation\u201d of the system is guaranteed. In this thesis, a closed-loop method is investigated which is able to improve the parameter identification on the basis of the actual system\u2019s behavior. The effectiveness of the proposed algorithm is presented by the experimental results which corresponds to the perfect identification of the unknown parameter vector. The major technical contribution of this work is to propose an optimal feedback input design method for active parameter identification of dynamic nonlinear systems. The proposed framework can design such optimal excitation signals, considering the information from the identified parameters, that can maximize the amount of information from the identified parameters, guarantee to meet the specified control performance and minimize some cost function of the error covariance matrix of the identified parameters. The problem is formulated in a receding horizon framework where extended Kalman filter is used for system identification and the optimal input is designed in a nonlinear model predictive control framework. In order to carry out a comparison study, also Unscented Kalman Filter and Gaussian Sum Filter are used for the active parameter identification of dynamic nonlinear system. Towards this end, a suitable optimality criterion related to the unknown parameters is proposed and motivated as an information measure. The aim of the optimal input design is to yield maximal information from the unknown system by minimizing the cost related to the unknown parameters while maintaining some process performance and satisfying the possible constraints. Simulations are performed to show the effectiveness of the proposed algorithm

Data-Driven Nonlinear Control Designs for Constrained Systems

Systems with nonlinear dynamics are theoretically constrained to the realm of nonlinear analysis and design, while explicit constraints are expressed as equalities or inequalities of state, input, and output vectors of differential equations. Few control designs exist for systems with such explicit constraints, and no generalized solution has been provided. This dissertation presents general techniques to design stabilizing controls for a specific class of nonlinear systems with constraints on input and output, and verifies that such designs are straightforward to implement in selected applications. Additionally, a closed-form technique for an open-loop problem with unsolvable dynamic equations is developed. Typical optimal control methods cannot be readily applied to nonlinear systems without heavy modification. However, by embedding a novel control framework based on barrier functions and feedback linearization, well-established optimal control techniques become applicable when constraints are imposed by the design in real-time. Applications in power systems and aircraft control often have safety, performance, and hardware restrictions that are combinations of input and output constraints, while cryogenic memory applications have design restrictions and unknown analytic solutions. Most applications fall into a broad class of systems known as passivity-short, in which certain properties are utilized to form a structural framework for system interconnection with existing general stabilizing control techniques. Previous theoretical contributions are extended to include constraints, which can be readily applied to the development of scalable system networks in practical systems, even in the presence of unknown dynamics. In cases such as these, model identification techniques are used to obtain estimated system models which are guaranteed to be at least passivity-short. With numerous analytic tools accessible, a data-driven nonlinear control design framework is developed using model identification resulting in passivity-short systems which handles input and output saturations. Simulations are presented that prove to effectively control and stabilize example practical systems

Probabilistic robust control: theory and applications

In this work, the development of a probabilistic approach to robust control is motivated by structural control applications in civil engineering. Often in civil structural applications, a system's performance is specified in terms of its reliability. In addition, the model and input uncertainty for the system may be described most appropriately using probabilistic or "soft" bounds on the model and input sets. The probabilistic robust control methodology contrasts with existing W... /A robust control methodologies that do not use probability information for the model and input uncertainty sets, yielding only the guaranteed (i.e., "worst-case") system performance, and no information about the system's probable performance which would be of interest to civil engineers. The design objective for the probabilistic robust controller is to maximize the reliability of the uncertain structure/controller system for a probabilistically-described uncertain excitation. The robust performance is computed for a set of possible models by weighting the conditional performance probability for a particular model by the probability of that model, then integrating over the set of possible models. This integration is accomplished efficiently using an asymptotic approximation. The probable performance can be optimized numerically over the class of allowable controllers to find the optimal controller. Also, if structural response data becomes available from a controlled structure, its probable performance can easily be updated using Bayes's Theorem to update the probability distribution over the set of possible models. An updated optimal controller can then be produced, if desired, by following the original procedure. Thus, the probabilistic framework integrates system identification and robust control in a natural manner. The probabilistic robust control methodology is applied to two systems in this thesis. The first is a high-fidelity computer model of a benchmark structural control laboratory experiment. For this application, uncertainty in the input model only is considered. The probabilistic control design minimizes the failure probability of the benchmark system while remaining robust with respect to the input model uncertainty. The performance of an optimal low-order controller compares favorably with higher-order controllers for the same benchmark system which are based on other approaches. The second application is to the Caltech Flexible Structure, which is a light-weight aluminum truss structure actuated by three voice coil actuators. A controller is designed to minimize the failure probability for a nominal model of this system. Furthermore, the method for updating the model-based performance calculation given new response data from the system is illustrated

System Identification and Control of Cavity Noise Reduction

This dissertation first presents indirect closed-loop system identification through residual whitening, then identifies the cavity noise system and applies controllers to reduce the noise. High speed air flow over the cavity produces a complex oscillatory flow-field and induces pressure oscillations within the cavity. The existence of cavities induces large pressure fluctuations which generate undesirable and loud noise. This may have an adverse effect on the objects, such as reducing the stability and performance of overall system, or damaging the sensitive instruments within the cavity. System identification is the process of building mathematical models of dynamical systems based on the available input and output data from the systems. The indirect system identification by residual whitening is used to improve the accuracy of the identification result, and the optimal properties of the Kalman filter could be enforced for a finite set of data through residual whitening. Linear Quadratic Gaussian (LQG) and deadbeat controllers are applied to obtain the desired system performance. Linear Quadratic Gaussian (LQG) control design is the technique of combining the linear quadratic regulator (LQR) and Kalman tilter together, namely, state feedback (LQR) and state estimation (Kalman filter). Deadbeat control design is to bring the output to zero, and both indirect and direct algorithms are applied. For the indirect method, one needs to calculate the finite difference model coefficient parameters first, then form the control parameters. In the recursive direct algorithms, however, one can compute the control parameters directly. When systems change with time, the system parameters become time-varying. An adaptive predictive control is needed for this situation. Since the system parameters are time-varying, the control parameters need to be updated in order to catch up with the systems\u27 changes. The classical recursive least-squares technique is used for the recursive deadbeat controller, and it could be operated for on-line application

Identification of linear periodically time-varying (LPTV) systems

A linear periodically time-varying (LPTV) system is a linear time-varying system with the coefficients changing periodically, which is widely used in control, communications, signal processing, and even circuit modeling. This thesis concentrates on identification of LPTV systems. To this end, the representations of LPTV systems are thoroughly reviewed. Identification methods are developed accordingly. The usefulness of the proposed identification methods is verified by the simulation results. A periodic input signal is applied to a finite impulse response (FIR)-LPTV system and measure the noise-contaminated output. Using such periodic inputs, we show that we can formulate the problem of identification of LPTV systems in the frequency domain. With the help of the discrete Fourier transform (DFT), the identification method reduces to finding the least-squares (LS) solution of a set of linear equations. A sufficient condition for the identifiability of LPTV systems is given, which can be used to find appropriate inputs for the purpose of identification. In the frequency domain, we show that the input and the output can be related by using the discrete Fourier transform (DFT) and a least-squares method can be used to identify the alias components. A lower bound on the mean square error (MSE) of the estimated alias components is given for FIR-LPTV systems. The optimal training signal achieving this lower MSE bound is designed subsequently. The algorithm is extended to the identification of infinite impulse response (IIR)-LPTV systems as well. Simulation results show the accuracy of the estimation and the efficiency of the optimal training signal design