Quasi-Optimum Control of a Flexible Booster

1967 ◽  
Vol 89 (2) ◽  
pp. 273-282 ◽  
Author(s):  
V. Cohen ◽  
B. Friedland
Keyword(s):  
Rigid Body ◽  
Linear Time ◽  
Bending Moment ◽  
Performance Criterion ◽  
Control Law ◽  
Time Varying ◽  
Bending Moments ◽  
Optimum Control ◽  
Satisfactory Performance ◽  
Structural Loading

The problem of minimizing both the in-flight bending moments as well as the terminal drift of a flexible vehicle is considered. The performance criterion V(T)=12y2(T)+k¯2∫tTM2(ξ)dξ, where y(T) is the drift, and M is the in-flight bending moment, is selected to achieve a compromise between excessive drift and excessive structural loading. The two-point boundary value problem for the design of the rigid-body control system is solved analytically for the linear, time-varying optimum control law. The flexibility of the vehicle is then accounted for, in a model consisting of two rigid sections hinged together with a torsional spring, by augmenting the rigid-body optimum control law with feedback terms proportional to the vehicle flexure and its rate. The results of a digital computer simulation indicate that the quasi-optimum control law obtained by this technique results in satisfactory performance, while the rigid-body control law is inadequate for a vehicle of moderate flexibility.

scholarly journals Analytical Fuzzy Predictive Control Applied to Wastewater Treatment Biological Processes

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-29 ◽  
Author(s):  
Pedro M. Vallejo LLamas ◽  
Pastora Vega
Keyword(s):  
Wastewater Treatment ◽  
Predictive Control ◽  
Treatment Process ◽  
Linear Time ◽  
Real Data ◽  
Control Law ◽  
Time Varying ◽  
Wastewater Treatment Process ◽  
Starting Point ◽  
Fuzzy Predictive Control

A novel control fuzzy predictive control law is proposed and successfully applied to a wastewater treatment process in this paper. The proposed control law allows us to evaluate the control signal in an analytical way, each sampling time being a nonlinear and fuzzy alternative to other classic predictive controllers. The control law is based on the formalization of the internal fuzzy predictive model of the process as linear time-varying state space equations that are updated every discrete time instant to take into account the nonlinearity effects due to disturbance action and changes in the operating point with time. The model is then used to evaluate the predictions, and, taking them as a starting point and considering them as a paradigm of the predictive functional control strategy, a control law, it is derived in an analytical and explicit way by imposing on the outputs of the follow-up of certain reference trajectories previously established. The work presented here addresses the application of this particular strategy of intelligent predictive control to the case of an activated sludge wastewater treatment process successfully in a simulation environment of a real plant taking into account real data for the disturbance records. Such a process is multivariable, nonlinear, time varying, and difficult to control due to its biological nature. The proposed control law can be straightforwardly used within a dual-mode MPC scheme to handle constraints, as a nonlinear and fuzzy alternative to the classic state feedback control law.

Singularly perturbed implicit control law for linear time varying SISO systems

2013 ◽  
Vol 24 (10) ◽  
pp. 1530-1549 ◽  
Author(s):  
S. Puga ◽  
M. Bonilla ◽  
M. Malabre ◽  
R. Lozano
Keyword(s):  
Linear Time ◽  
Singularly Perturbed ◽  
Control Law ◽  
Time Varying ◽  
Siso Systems

Application of semi-active inerter in a two-body point absorber via force tracking

2021 ◽  
pp. 014233122110093
Author(s):  
Yinlong Hu ◽  
Tianyang Hua ◽  
Michael Z. Q. Chen ◽  
Shang Shi ◽  
Yonghui Sun
Keyword(s):  
Wave Energy ◽  
Linear Time ◽  
State Space Model ◽  
Relative Displacement ◽  
Control Law ◽  
Time Varying ◽  
Active Force ◽  
Power Absorption ◽  
Point Absorber ◽  
Force Tracking

In this paper, a self-reaction point absorber (PA) wave energy converter is studied, where wave energy is collected by the relative motion of the on-board plate and the buoy. The purpose of this study is to increase the relative displacement to obtain the maximum power. A semi-active inerter (SAI) is applied in the system, which is controlled by a force-tracking (FT) strategy. Two parts are required in the FT strategy: a target active control law; and a proper control law to adjust the inertance to track the active force (AF). The target control law is obtained by the full-state feedback of the state-space model of a two-body PA . The control law to adjust the inertance is to saturate the AF between the maximal and minimal semi-active force of an SAI. Both linear time-invariant system and linear time-varying system are studied. Power absorption is improved in both two systems by the application of SAIs. Moreover, the influence of dimensionless parameters on the ratio of power absorption improvement in the considered linear time-varying system is studied. Numerical simulation shows that the ratio of power absorption improvement is most sensitive to the changes of mass ratio of the on-board plate and the buoy.

Design and Convergence of a Time-Varying Iterative Learning Control Law

2004 ◽  
Author(s):  
Marina Tharayil ◽  
Andrew Alleyne
Keyword(s):  
Frequency Domain ◽  
Iterative Learning Control ◽  
Linear Time ◽  
Learning Control ◽  
Convergence Condition ◽  
Iterative Learning ◽  
Control Law ◽  
Equivalent Condition ◽  
Time Varying ◽  
Linear Time Invariant

This paper presents a novel linear time-varying (LTV) iterative learning control law that can provide additional performance while maintaining the robustness and convergence properties comparable to those obtained using traditional frequency domain design techniques. Design aspects of causal and non-causal linear time-invariant (LTI), along with the proposed LTV, ILC update laws are discussed and demonstrated using a simplified example. Asymptotic as well as monotonic convergence, robustness and performance characteristics of such systems are considered, and an equivalent condition to the frequency domain convergence condition is presented for the time-varying ILC. Lastly the ILC algorithm developed here is implemented on a Microscale Robotic Deposition system to provide experimental verification.

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