By R. Colgren
This ebook bargains a three-step method of producing a strong nonlinear controller: modeling, synthesis and robustness research. The booklet is concentrated to training engineers and graduate-level scholars operating in assistance, details command and keep watch over platforms, and CAD/CAM. The tools coated during this e-book permit the person to layout and learn nonlinear controllers for nonlinear platforms with numerous very important and specific features: the power to specify the closed loop system's frequency reaction through specifications at the sensitivity (S) and complementary sensitivity (T), the power to without delay reduce an bad resonance or height within the frequency reaction whereas concurrently remaining all loops from the enter to the output vector in basically one unmarried layout step, and the facility to investigate the soundness features for a number of autonomous and based challenge variables. The strategy uniquely permits the person to accomplish good and powerful functionality for structures that are either risky and comprise discontinuous nonlinearities utilizing adaptive nonlinear controllers.
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Extra resources for Applications of Robust Control to Nonlinear Systems (Progress in Astronautics and Aeronautics)
9 The closed-loop system with the proportional controller. This method can be interpreted in terms of the Nyquist plot. Using PID control it is possible to move a given point on the Nyquist curve to an arbitrary position in the complex plane. Now, the first step in the frequency response method is to determine the point − 1 ,0 ku where the Nyquist curve of the open-loop transfer function intersects the negative real axis. We will study how this point is changed by the PID controller. 4671) since Tu wu = 2π .
This will be clearly borne out by the following discussion. Assume that the plant to be controlled is a first-order model with deadtime: G(s) = k e−Ls . 1 + Ts 16 THREE TERM CONTROLLERS The control objective is to minimize the L2 norm of the tracking error due to setpoint changes. Using Parseval’s Theorem, this is equivalent to choosing 1 ˆ Q(s) for which min [1 − G(s)Q(s)]R(s) 2 is achieved, where R(s) = s is the Laplace transform of the unit step command. Approximating the deadtime with a first-order Pad´e approximation, we have L ∼ 1− 2s .
This relay feedback can be used to determine the ultimate gain and ultimate period. The relay block is a nonlinear element that can be represented by a describing function. This describing function is obtained by applying a sinusoidal signal asin(wt) at the input of the nonlinearity and calculating the ratio of the Fourier coefficient of the first harmonic at the output to a. This function can be thought of as an equivalent gain of the nonlinear system. For the case of the relay its describing function is given by N (a) = 4d aπ where a is the amplitude of the sinusoidal input signal and d is the relay amplitude.