Source: http://kvt-journal.org.ua/tag/zhiteckii-l-s/
Timestamp: 2019-04-23 12:14:00+00:00

Document:
Kibern. vyčisl. teh., 2018, Issue 2 (192), pp.
Introduction. The paper states and solves a new problem concerning the adaptive stabilization of a specific class of linear multivariable discrete-time memoryless systems with nonsquare gain matrices at their equilibrium states. This class includes the multivariable systems in which the number of outputs exceeds the number of control inputs. It is assumed that the unknown gain matrices have full rank.
The purpose of this paper is to answer the question of how the pseudoinverse model-based adaptive approach might be utilized to deal with the uncertain multivariable memoryless system if the number of control inputs is less than the number of outputs.
Results. It is shown that the parameter estimates generated by the standard adaptive projection recursive procedure converge always to some finite values for any initial values of system’s parameters. Based on these ultimate features, it is proved that the adaptive pseudoinverse model-based control law makes it possible to achieve the equilibrium state of the nonsquare system to be controlled. The asymptotical properties of the adaptive feedback control system derived theoretically are substantiated by a simulation experiment.
Conclusion. It is established that the ultimate behavior of the closed-loop control system utilizing the adaptive pseudoinverse model-based concept is satisfactory.
Keywords: adaptive control, multivariable system, discrete time, feedback, pseudoinversion, stability, uncertainty.
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Introduction. The problem of controlling interconnected systems subjected to arbitrary unmeasurable disturbances remains actual up to now. It is important problem from both theoretical and practical points of view. During the last decades, the internal model control principle becomes popular among other methods dealing with an improvement of the control system. A perspective modification of the internal model control principle is the so-called model inverse approach. Unfortunately, the inverse model approach is quite unacceptable if the systems to be controlled are square but singular or if they are nonsquare. It turned out that the so-called pseudoinverse (generalized inverse) model approach can be exploited to cope with the noninevitability of singular square and also nonsquare system.
The purpose of the paper is to generalize the results obtained by the authors in their last works which are related to the asymptotic properties of the pseudoinverse model-based method for designing an efficient steady-state control of interconnected systems with uncertainties and arbitrary bounded disturbances and also to present some new results.
Results. In this paper, the main effort is focused on analyzing the asymptotic properties of the closed-loop systems containing the pseudoinverse model-based controllers. In the framework of the pseudoinversion concept, new theoretical results related to the asymptotic behavior of these systems are obtained. Namely, in the case of nonsingular gain matrices with known elements, the upper bounds on the ultimate norms of output and control input vectors are found. Next, in the case of nonsquare gain matrices whose elements are also known, the asymptotic behavior of the feedback control systems designed on the basis of pseudoinverse approach are studied. Further, the sufficient conditions guaranteeing the boundedness of the output and control input signals for the linear and certain class of nonlinear interconnected systems in the presence of uncertainties are derived.
Conclusion. It has been established that the pseudoinverse model-based concept can be used as a unified concept to deal with the steady-state regulation of the linear interconnected discrete-time systems and of some classes of nonlinear interconnected systems with possible uncertainties in the presence of arbitrary unmeasured but bounded disturbances.
Keywords: discrete time, feedback, pseudoinversion, interconnected systems, optimality, stability, uncertainty.
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Zhiteckii L.S., Pilchevsky A.Yu., Solovchuk K.Yu.
Introduction. The optimal digital autopilot needed to control of the roll for an aircraft in the presence of an arbitrary unmeasured disturbances is addressed in this paper. This autopilot has to achieve a desired lateral motion control via minimizing the upper bound on the absolute value of the difference between the given and true roll angles. It is ensured by means of the two digital controllers. The inner controller is designed as the discrete-time PI controller in order to stabilize a given roll rate. This variable is formed by the external discrete-time P controller. To optimize this control system, the controller parameters are derived utilizing the so-called l1-optimization approach advanced in modern control theory. The motion parameters are assumed to be known.
The purpose of the paper is to synthesize a digital autopilot which is able to maintain a given roll orientation of an aircraft with a desired accuracy and to cope with an arbitrary external disturbance (a gust) whose bounds may be unknown.
Results. The necessary and sufficient conditions guaranteeing the stability of the two-circuit feedback discrete-time control system are established. First, the l1-optimal PI and P controller parameters are calculated simultaneously (in contrast with ). Second, the aileron servo dynamics are taken into account to establish the stability condition for optimizing the controller parameters. Third, random search algorithm is used to calculate the three optimal values of the autopilot parameters. To support the theoretical results obtained, in this work, several simulation experiments were conducted. We have established that the simultaneous l1-optimization of both controllers was more efficient than the sequential l1-optimization of inner and external controllers.
Conclusion. It was established that the two-circuit l1-optimal PI and P control laws can cope with the wind gust and ensure the desired roll orientation. This makes it possible to achieve the control objective which was stated. A distinguishing feature of the control algorithms is that they are sufficiently simple. This is important from the practical point of view.
Keywords: aircraft, lateral dynamics, digital control system, discrete time, stability, l1-optimization, random search algorithm.
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