Ketao Liu

Optimal controllers for finite wordlength implementation

When a controller is implemented by a digital computer with A/D and D/A conversion, numerical errors can severely affect the performance of the control system. There exist realizations of a given controller transfer function exhibiting arbitrarily large effects from computational errors. Assuming sufficient excitation of the system, the problem of designing an optimal controller in the presence of both external disturbances and internal roundoff errors is solved. The results reduce to the standard LQG controller when infinite-precision computation is used. For finite precision, however, the separation principle does not hold. A penalty is also added to the cost function to penalize the sum of the wordlengths used to compute the fractional part of each state variable of the controller. This sum can be used to represent the lower bound on computer memory needed for controller synthesis. It measures controller complexity and is minimized (penalized) here. >

Closed-loop identification and iterative controller design

An iterative controller design scheme is presented which takes into account the inter-dependence of the modeling and controller design problems. This iterative scheme consists of closed-loop identification and controller redesign cycles. In each cycle, the plant model is identified in a closed-loop using the controller designed in the previous cycle. Then a new controller is redesigned by using the identified model. The iterative process continues until convergence. The q-Markov cover algorithm obtains system state-space models which have the same first q-Markov parameters and covariance parameters as the physical system generating the input-output data. At convergence the controller and the plant model are considered to be consistent.<<ETX>>

Q-Markov covariance equivalent realization and its application to flexible structure identification

The Q-Markov covariance equivalent realization algorithm is applied to NASAs Minimast structure to identify state-space models for the purpose of designing closed-loop controllers, and laboratory test results are shown for the identification and for the closed-loop performance. The paper also presents for the first time a deterministic formulation of covariance parameters from a pulse response, a stochastic formulation of Markov parameters from a white-noise response, and a simple Q-Markov covariance equivalent realization formulation. This requires only pulse laboratory tests or only white-noise laboratory tests to generate Q-Markov covariance equivalent realizations.

Integrated modeling and controller design with application to flexible structure control

Abstract It is well known that modeling and control problems are not independent. Hence, the final step in any practical control design is a ‘try and see’ procedure. There will always be a need for on-line tuning by the test engineer. The purpose of mathematical theories of modeling and control is therefore not to replace the ‘try and see’ requirement of the engineer, but to help reduce the number of iterations the engineer must use to find a suitable solution to the real physical problem (which defies exact mathematical description). This paper presents an iterative method to integrate the two problems of modeling and control and demonstrates the procedure in a physical application. Specifically, we present a controller design scheme integrating a Q-Markov Covariance equivalent realization (QMC) identification algorithm, a Modal Cost Analysis (MCA) model reduction algorithm, and an Output Variance Constraint (OVC) controller design algorithm. The identified model is used as a truth model for subsequent (off-line) controller evaluation. In the first step of the integrated procedure, this model is reduced for controller design. Closed-loop evaluation provides information to improve the reduced model (this is the integration of the two model reduction and control disciplines that is contributed by this paper). The process repeats iteratively for low order and high performance controller design. This procedure is applied to NASAs ACES flexible structure at the Marshall Space Flight Center. The experimental results demonstrate the effectiveness of the procedure for large flexible structure control.

Modeling Hubble Space Telescope Flight Data by Q-Markov Cover Identification

This Paper presents a state space model for the Hubble space telescope under the influence of unknown disturbances in orbit. This model was obtained from flight data by applying the Q-Markov Covariance Equivalent Realization identification algorithm. This state space model guarantees the match of the first Q Markov parameters and covariance parameters of the Hubble system. The flight data were partitioned into high and low frequency components for more efficient Q-Markov Cover modeling, to reduce some computational difficulties of the Q-Markov Cover algorithm. This identification revealed more than 20 lightly-damped modes within the bandwidth of the attitude control system. Comparisons with the analytical (TREETOPS) model are also included.

Modeling Hubble Space Telescope flight data by Q-Markov cover identification

This Paper presents a state space model for the Hubble space telescope under the influence of unknown disturbances in orbit. This model was obtained from flight data by applying the Q-Markov Covariance Equivalent Realization identification algorithm. This state space model guarantees the match of the first Q Markov parameters and covariance parameters of the Hubble system. The flight data were partitioned into high and low frequency components for more efficient Q-Markov Cover modeling, to reduce some computational difficulties of the Q-Markov Cover algorithm. This identification revealed more than 20 lightly-damped modes within the bandwidth of the attitude control system. Comparisons with the analytical (TREETOPS) model are also included.

Control of large flexible structures-an experiment on the NASA Mini-Mast facility

The output variance constraint controller design procedure is integrated with model reduction by modal cost analysis. A procedure is given for tuning MIMO controller designs to find the maximal RMS performance of the actual system. Controller designs based on a finite element model of the system are compared with controller designs based on an identified model (obtained using the Q-Markov cover algorithm). The identified model and the finite-element model led to similar closed-loop performance, when tested in the Mini-Mast facility at Langley Research Center, The linear controllers designed tolerated significant Coulomb friction in the joints of the structure, even though robustness with respect to parameter variations was not included in the design.<<ETX>>

Optimal Controllers for Finite Wordlength Implementation

When a controller is implemented in a digital computer, with A/D and D/A conversion, the numerical errors of the computation can drastically affect the performance of the control system. There exists realizations of a given controller transfer function yielding arbitrarily large effects from computational errors. Since, in general, there is no upper bound, it is important to have a systematic way of reducing these effects. Optimum controller designs are developed which take account of the digital round-off errors in the controller implementation and in the A/D and D/A converters. These results provide a natural extension to the LQG theory since they reduce to the standard LQG controller when infinite precision computation is used. But for finite precision the separation principle does not hold.