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BDC Motor (OFB)
Published in Darren M. Dawson, Jun Hu, Timothy C. Burg, Nonlinear Control of Electric Machinery, 2019
Darren M. Dawson, Jun Hu, Timothy C. Burg
The reader should be aware that the observed integrator backstepping and nonlinear damping tools are the key to the design of the nonlinear observer-controller algorithm which ensures the boundedness of the internal signals inherent to the overall closed-loop system. That is, the separation principle [2] used in the design of linear feedback control systems utilizing state observers does not hold, in general, for nonlinear systems. Thus, one might question the validity of designing a controller using full state feedback and a state observer, and then simply using the observed states in place of the actual states. Rather, in this chapter, a more complex methodology motivated by the Lyapunov-like analysis is presented whereby the observer is designed in parallel with the controller. Specifically, the design of the composite observer-controller is based on a set of equations which describe the position tracking error dynamics, the observation error dynamics, and the corresponding Lyapunov-like functions. Moreover, the role of the observers is not limited to the usual function of providing an accurate estimate of a particular quantity but is expanded to include its contribution to the performance of the closed-loop system.
An Introduction to Sliding Mode Control
Published in Christopher Edwards, Sarah K. Spurgeon, Sliding Mode Control: Theory and Applications, 1998
Christopher Edwards, Sarah K. Spurgeon
As A+LC is a stable matrix it follows that the error vector will converge to zero from any initial condition and thus xˆ(t) will converge to x(t). Judicious choice for the poles of A+LC will ensure that the error tends to zero rapidly. It can easily be verified that when the observed state xˆ is used to represent the state vector in the closed-loop implementation, then the characteristic equation of the resulting closed-loop system has as its roots the poles allocated via the feedback design alone together with the poles due to the observer design alone. The design of the feedback controller and the observer can thus be completed independently and a separation principle is said to hold.
A New Feedback Control Design Principle/Approach
Published in Chia-Chi Tsui, Robust Control System Design, 2022
Separation principle first assumes that the information x(t) is already available, designs a state feedback control Kx(t) based on this assumption, and only then designs an observer to realize this control (Tsui, 2006, 2012). Hence, the designs of K and its realizing observer are completely separate. Because K is separately designed, it is arbitrarily given when the observer is designed.
Pseudo-spectral optimal control of stochastic processes using Fokker Planck equation
Published in Cogent Engineering, 2019
Ali Namadchian, Mehdi Ramezani
Stochastic optimal control is one of the main subfields of control theory. It is introduced due to considering more realistic models where many systems in different branches of science are subjected to randomness. It is the subject of study in traffic control (Zhong, Sumalee, Pan, & Lam, 2014), airspace industry (Okamoto & Tsuchiya, 2015), cancer chemotherapy (Coldman & Murray, 2000), cyber security systems in computer science (Shang, 2013, 2012), etc. When the system randomness is bounded and the bounds are known, the problem of finding a suitable control action can be dealt with robust control approaches (Doyle, Francis, & Tannenbaum, 2013; Wu & Lee, 2003; Zhou & Doyle, 1998). While the bounds of uncertainty are unknown and the probability distribution of the randomness is available, the stochastic framework should be carried out in optimal control (Åström, 2012; Herzallah, 2018; Sell, Weinberger, & Fleming, 1988; Touzi, 2012). There is a vast amount of literature on stochastic optimal control of linear systems with additive noise where the certainty equivalence property leads to the separation principle in stochastic control (Bar-Shalom & Tse, 1974; Mohammadkhani, Bayat, & Jalali, 2017). Under certain conditions, separation principle asserts that finding a control action for a stochastic system can be restated as designing a stable observer and a stable controller. In the other words, a stochastic problem can be recast as two deterministic problems. Linear quadratic Gaussian control (LQG) is one of the most prominent stochastic control methods. It is simply the combination of Kalman filter as an observer and a linear quadratic controller.
Output transformations and separation results for feedback linearisable delay systems
Published in International Journal of Control, 2018
F. Cacace, F. Conte, A. Germani
A general approach to the output feedback control problem is to use a state feedback controller that achieves stabilisation together with a state observer that provides an estimate converging to the true state value. When it is possible to separately design these two components, while retaining the stabilisation properties of the controller for known states, the system is said to satisfy a separation principle. It is well known that the separation principle holds for linear systems, but, in general, it does not for nonlinear systems (Khalil, 2015).
Feasibility Study of Actively-Controlled Tuned Inertial Mass Electromagnetic Transducers for Seismic Protection
Published in Journal of Earthquake Engineering, 2023
where and are called weighting matrices. Furthermore, the observation noise is assumed to be identically distributed, statistically independent Gaussian white noise processes. The separation principle is invoked to allow the control and estimation problems to be considered independently. The resulting controller is of the form (Stengel 1986)