LTR design of proportional‐integral observers

Niemann, Hans Henrik; Stoustrup, Jakob; Shafai, B.; Beale, S.

doi:10.1002/rnc.4590050706

Cited by 87 publications

(48 citation statements)

References 19 publications

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“…Derivation of an LQGLTR design method for discrete-time systems parallels the derivation for continuous-time systems given in [9] with the exception that a design can be obtained with zero weighting …”

Section: B Lqg/ltr Design Of Full-order Observersmentioning

confidence: 99%

“…By using this proportionalintegral (PI)-observer in connection with LTR design, it is possible to obtain time recovery, i.e., recovery as t + 3c'. The continuous-time case has been thoroughly investigated in [9], where it has been shown that it is possible to obtain time recovery for nonminimum phase systems. In this paper we show explicitly that it is also possible to obtain time recovery in the discrete-time case by using a PI-observer for both minimum phase as well as for nonminimum phase systems.…”

Section: Introductionmentioning

confidence: 99%

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LTR design of discrete-time proportional-integral observers

Shafai

Beale

Niemann

et al. 1996

IEEE Trans. Automat. Contr.

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A Monte Carlo simulation with 500 experiments was executed, and the results are presented in Fig. 3. In each experiment, the measurement model in effect at each point of time was randomly chosen according to (65). In Fig. 3(a), the root-mean-square-error (RMSE) in the state estimate versus time is presented. Averaging the RMSE's over the time interval gives an average error of 10.75 for the IMM filter, 9.32 for the smoother of Method 1, and 9.42 for Method 2. Fig. 3(b) presents the probability of error in the system-stmcture detection versus time (i.e., the probability of choosing the incorrect measurement model at each point of time). Averaging the probabilities over the time interval gives an average probability of error of 0.19 for the IMM filter, 0.15 for Method 1, and 0.16 for Method 2.The two smoothers provided noticeably better performances than the IMM filter, while the smoother of Method 1 provided slightly better performance than Method 2. The smoother of Method 1 provided the best overall performance because it considered the most hypotheses.A simulation example comparing the performances of these algorithms in reconstructing the trajectory of a maneuvering target has also been performed. Detailed results are not presented because of space limitations. Both smoothers provided significantly better performance than the IMM filter in estimating the system state. However, unlike the system-structure simulation results above, the Method 1 smoother provided significantly better mode estimates than the Method 2 smoother. The mode estimates from the Method 2 smoother and the IMM filter were comparable. V. SUMMARYSuboptimal approaches to the one-step fixed-lag smoothing problem for Markovian switching systems were examined in this paper. Two algorithms for generating one-step fixed-lag smoothed estimates were presented. In the first algorithm, the models over the two most recent sampling periods were considered. For n models, there are n2 possible ways of conditioning on models in two sampling periods, and this algorithm evaluated the n2 hypotheses using n2 parallel one-step smoothers. In the second algorithm, only the models in the most recent sampling period were considered, and it evaluated 72 hypotheses using n parallel one-step smoothers. A simulation of a system-structure detection problem was used to compare the performances of the two smoothers and an IMM filter. The results show that the smoother of Method 1 provided the best overall performance. Variants of these one-step smoothing algorithms have been used in conjunction with IMM filtering algorithms to develop techniques for the alignment of asynchronous sensors [ 6 ] . Finally, approaches similar to the ones presented in this paper have been applied to the fixed-interval smoothing problem for Markovian switching systems ~71. Abstract-This paper applies the proportional-integral (PI) observer in connection with loop-transfer recovery (LTR) design for discrete-time systems. Both the prediction and the filtering versions of the PI observer are consid...

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Section: B Lqg/ltr Design Of Full-order Observersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

LTR design of discrete-time proportional-integral observers

Shafai

Beale

Niemann

et al. 1996

IEEE Trans. Automat. Contr.

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“…It is also possible to derive a reduced-order PI-observer, which has an interesting connection to exact LTR condition of P-observer case (see [41] for more details). It is shown that the reduced-order PI-observer achieves exact LTR if and only if its corresponding reduced-order P-observer achieves exact LTR.…”

Section: Fig 2 Pi-observer-based State Feedback Control Systemmentioning

confidence: 99%

“…This approach was further investigated and led to a design procedure known as LQG/LTR [37]. Due to limitation of increasing gain and solving parametrized ARE as well as numerical issues, other approaches based on reduced-order observer and proportional integral observer have been proposed (see [38], [41] and the references therein). Simply stated, the loss of robustness in observer-based controller design is due to the signal transfer from the control u to the observer through the control distribution matrix.…”

Section: P-observer and Loop Transfer Recoverymentioning

confidence: 99%

Proportional-Integral Observer in Robust Control, Fault Detection, and Decentralized Control of Dynamic Systems

Shafai

Saif

2015

Studies in Systems, Decision and Control

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Abstract. This chapter initially reviews observer theory as it was developed over the past few decades. The state observer and its order reduction including functional observer in connection to state feedback control design are briefly discussed. The robustness of observer-based controller design is also explored. The loss of robustness due to the inclusion of observer in optimal linear quadratic regulator (LQR) and its recovery procedure (LTR) are summarized. The subsequent development of new observer structures such as disturbance observer (DO), unknown input observer (UIO), and proportional-integral observer (PIO) for disturbance estimation and fault detection is highlighted. Throughout the chapter we concentrate mainly on important advantages of PI-observer. Finally, we consider the problem of designing a decentralized PI observer with prescribed degree of convergence for a set of interconnected systems. Under the assumption of linear interactions, we provide a direct design procedure for the PI observer which can effectively be used in disturbance estimation and observer-based control design enhancing the robustness properties. In this connection we also extend the results to the case of designing controllers that attenuate the disturbance while preserving the stability. It is shown that the design can be formulated in terms of LMI which efficiently solve the problem.

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“…This is done by augmenting the state vector with additional state variables. This approach has been given various names over the decades such as bias estimation [13,17,18], garbage collector [10], or integral observer [3,22]. Note that, with integral observers, unbiased estimation of all states typically requires the measurement of all states [24,28], or of at least as many independent outputs as there are independent sources of disturbance [25], which is rather impractical.…”

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confidence: 99%

On the design of integral observers for unbiased output estimation in the presence of uncertainty

Bodizs

Srinivasan

Bonvin

2011

Journal of Process Control

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Integral observers are useful tools for estimating the plant states in the presence of non-vanishing disturbances resulting from plant-model mismatch and exogenous disturbances. It is well known that these observers can eliminate bias in all states, given that as many independent measurements are available as there are independent sources of disturbance. In the most general case, the dimensionality of the disturbance vector affecting the plant states corresponds to the order of the system and thus all states need to be measured. This condition, which is termed integral observability in the literature, represents a fairly restrictive situation. This study focuses on the more realistic case, where only the output variables are measured. Accordingly, the objective reduces to the unbiased estimation of the output variables. It is shown that both stability and asymptotically unbiased output estimation can be achieved if the system is observable, regardless of the dimensionality of the disturbance vector. Furthermore, a condition is provided under which, using output measurements, the errors in all states can be pushed to zero. It is also proposed to use off-line output measurements to tune the observer using a calibration-like approach. Integral observers and integral Kalman filters are evaluated via the simulation of a fourth-order linear system perturbed by unknown non-vanishing disturbances.

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LTR design of proportional‐integral observers

Cited by 87 publications

References 19 publications

LTR design of discrete-time proportional-integral observers

LTR design of discrete-time proportional-integral observers

Proportional-Integral Observer in Robust Control, Fault Detection, and Decentralized Control of Dynamic Systems

On the design of integral observers for unbiased output estimation in the presence of uncertainty

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