Haipeng Zhao

Robust controller design for simultaneous control of throttle pressure and megawatt output in a power plant unit

This paper presents an application of H/sub /spl infin// and /spl mu/-synthesis controller design methods to a coal-fired power generation unit and compares the closed loop performance and robustness of H/sub /spl infin// and /spl mu/-synthesis control laws with those of an H/sub 2/ control law. All three controller synthesis procedures are applied to a two-input two-output plant model which has time delay, differential part, colored noise output disturbance and sensor noise disturbance. Application of the procedures to the model shows that when the shape of the closed loop control signals of all three designs Is closely matched, in the low frequency range the /spl mu/-synthesis and H/sub /spl infin// control laws have robustness much better than that of H/sub 2/ control law, while providing adequate robustness in the high frequency range. H/sub /spl infin// control law gives the best performance, and H/sub 2/-the worst of the three designs, exhibiting the largest overshoot. The balancing procedure permits significant reduction of the order of the controllers without degradation in performance and robustness. The comparative evaluation of three designs shows that in power plant control problem H/sub /spl infin// and /spl mu/-synthesis designs provide much more consistent and convenient performance/robustness trade-off than H/sub 2/ design.

Wavelet-based identification of fast linear time-varying systems using function space methods

The present work proposes a rigorous general framework and a rapidly convergent identification algorithm for high speed identification of fast linear time-varying systems in short time intervals. The identification speed-up is attained via utilizing both time and frequency localized bases. This feature permits identification of fewer coefficients without noticeable loss of accuracy of the identification results. Under an assumption that the inputs and outputs of the plants considered in the present work belong to l/sup p/ spaces, where p=2 or p=/spl infin/, their impulse responses are shown to belong to Banach spaces. Further on, by demonstrating that the set of all BIBO systems is a Banach space, the system modeling and identification are shown to be reducible to linear approximation problems in a Banach space setting. Simulation shows that the resulting identification algorithms can reject small persistent random disturbances as well as generate the short-term spiky descriptions of fast linear time-varying systems with nonsmooth coefficients.

Unconstrained H∞ predictive control with H∞ prediction: single‐input–single‐output case

Does the replacement of the quadratic (H2) predictor by the worst-case (H∞, or cumulative minimax) predictor robustify the predictive control laws? The present work provides a partial answer to this question, positive for the examples considered, representative of three broad classes of systems. The H∞ prediction is demonstrated to be a powerful and convenient tool for frequency shaping of the gain of the closed-loop complementary sensitivity function, capable of robustifying the closed loop for systems with different stability properties. The H∞-optimal k-step ahead predictor is derived for an unstable single-input–single- output CARMA model. A BIBO unstable filter for the disturbance rejection is obtained using the internal model principle and included into the closed loop, and the H∞ predictor is applied to the combination of this filter with the plant. The sum over a finite horizon of the current and the predicted tracking error and control signal power spectral densities (PSDs) is decomposed into two parts, one induced by the worst-case predicted disturbance and the other—by the known future reference input. A two degrees of freedom algorithm, referred to as the multi-step closed-loop polynomial H∞ predictive control law, is obtained that minimizes the peaks of the PSD of the first part and the integral on the unit circle of the PSD of the second. It is demonstrated on several systems that H∞ prediction introduces a very intuitive tuning knob in the form of the prediction horizon capable of setting a trade-off between the steady-state disturbance rejection perfor mance in terms of the output error variance and the closed-loop robustness, however the efficacy of the knob strongly depends on the stability properties of the system and its inverse. The trade-off becomes less pronounced or completely disappears when the H∞ predictor is replaced by the quadratic one. Copyright

Polynomial discrete-time SISO H/sub 2/ and H/sub /spl infin// controller synthesis: single Diophantine equation solution

Is solving a single Diophantine equation sufficient for synthesizing a polynomial discrete-time single-input-single-output (SISO) H/sub /spl infin// controller? This has been a longstanding question practically important due to the pervasive use of the polynomial-based discrete-time SISO self-tuners. The present work gives the answer to this question through the development of a novel polynomial algebra based reduction methodology. This reduction technique is also applied to the discrete-time SISO polynomial H/sub 2/ controller computation.

Block Diagram Reduction of the Interconnected Linear Time-Varying Systems in the Time-Frequency Domain

The problem of obtaining the time-frequency domain input-output model of a linear time-varying (LTV) system formed by linking the time-frequency domain blocks describing LTV subsystems is considered. Simultaneous input-output transformation of the constituent LTV subsystems modeled in terms of two-dimensional impulse responses into time-frequency domain is developed. It is shown that this transformation gives rise to the time-frequency domain subsystem representation which lends itself easily to: 1) deriving composition rules for obtaining the simplified overall interconnection model, and 2) revealing the constraints on individual subsystem modeling that need to be satisfied to admit such simplification. These composition rules are developed for the reduction of standard topologies including series, parallel, and feedback interconnections. The reduction of a more complicated topology using these rules is demonstrated.

Minimal order polynomial discrete-time SISO H/sub 2/ and H/sub /spl infin// controller synthesis: summary of the results and existence of solution

In a series of recent papers, on the basis of a novel algebraic reduction technique, a new methodology for the computation of the polynomial discrete-time SISO H/sub 2/ and H/sub /spl infin// controllers has been derived and shown to yield minimal order controllers. However, the existence of the H/sub /spl infin// controller solution has not been addressed. The present paper summarizes the results and presents a method of addressing the existence problem.

Single Diophantine Equation Polynomial Discrete-Time H 2 and H ∞ Controller Computation

Abstract In (Zhao and Bentsman, 2002) it has been shown that for most single-input-single-output linear discrete-time systems in polynomial format, a sequential solution of a Diophantine equation and an algebraic equation is, in theory, sufficient to calculate the corresponding H 2 and H ∞ controllers. Based on the results of (Zhao and Bentsman, 2002), the present work gives procedures for determining the sufficiency of a single Diophantine equation for controller calculation and for the actual calculation of the optimal controllers. Controller computations for non-minimum phase unstable plants have been carried out with relative ease.

H∞ prediction and unconstrained H∞ predictive control: Multi-input-multi-output case

Through the combination of the sequential spectral factorization and the coprime factorization, a k-step ahead MIMO H∞ (cumulative minimax) predictor is derived which is stable for the unstable noise model. This predictor and the modified internal model of the reference signal are embedded into the H∞ optimization framework, yielding a single degree of freedom multi-input–multi-output H∞ predictive controller that provides stochastic disturbance rejection and asymptotic tracking of the reference signals described by the internal model. It is shown that for a plant/disturbance model, that represents a large class of systems, the inclusion of the H∞ predictor into the H∞ control algorithm introduces a performance/robustness tuning knob: an increase of the prediction horizon enforces a more conservative control effort and, correspondingly, results in deterioration of the transient and the steady-state (tracking error variance) performance, but guarantees large robustness margin, while the decrease of the prediction horizon results in a more aggressive control signal and better transient and steady-state performance, but smaller robustness margin. Copyright

Multivariable H/sub /spl infin// predictive control based on minimax predictor

This paper presents a multi-input multi-output H/sub /spl infin// predictive controller design based on minimax predictor. Through the combination of the sequential spectral factorization and the coprime factorization, a k-step ahead MIMO H/sub /spl infin// predictor is derived which is stable for the unstable noise model. This predictor minimizes the H/sub /spl infin// norm of the power spectral density of the prediction error signal (and in fact flattens the spectrum), in contrast to the standard quadratic predictor which minimizes the variance of the error signal. It is also shown that the minimax and quadratic predictors are equivalent for one-step ahead predictions. The H/sub /spl infin// predictor and the internal model principle are embedded into the H/sub /spl infin// optimization framework to address the disturbance rejection and the tracking problems, respectively. The inclusion of the minimax predictor into the H/sub /spl infin// control algorithm introduces a tuning knob in the form of the prediction horizon, capable of setting a trade-off between the desired transient performance and the closed loop robustness.