Bounds on limit cycles in two-dimensional bang-bang control systems with an almost time-optimal switching curve

1964 ◽  
Vol 9 (4) ◽  
pp. 448-457 ◽  
Author(s):  
J. O'Donnell
Keyword(s):  
Control Systems ◽  
Limit Cycles ◽  
Two Dimensional ◽  
Optimal Switching ◽  
Switching Curve ◽  
Time Optimal ◽  
Bang Bang Control

Switching Strategy for Optimal Adaptive Third Order Control Systems

1970 ◽  
Vol 3 (10) ◽  
pp. T168-T172
Author(s):  
Satish C. Mohleji ◽  
Paul A. V. Thomas
Keyword(s):  
Control Systems ◽  
State Variables ◽  
Optimal Switching ◽  
Optimal Control Strategy ◽  
Actual System ◽  
Third Order ◽  
Time Optimal ◽  
The Difference ◽  
Bang Bang Control ◽  
Derivatives Of

The conventional design of bang bang control systems for time optimal performance involves an accurate mathematical model of the system and complex computations to determine the optimal switching conditions. Such a design is normally based on the assumption that the system parameters remain fairly constant. Recomputation of optimal trajectories becomes necessary for any change in the parameters. This paper describes a simple adaptive-optimal control strategy for systems representable in phase space and can be easily adopted on a digital controller. Projections of optimal curves are obtained by storing sections of actual system trajectories in the form of tables in the computer memory. Optimal switching instants are determined by shifting and comparing the stored trajectory with the actual trajectory. Since no manipulations are required and the switching curves are obtained by constantly storing and updating the system trajectories, the control remains optimum even when there is a change in parameters. The proposed strategy requires only measurement of error in the system, derivatives of error are formed by using the difference equations, a method well suited for digital formulation of state variables.

14.—Dynamic Programming applied to Some Non-linear Stochastic Control Systems

1976 ◽  
Vol 74 ◽  
pp. 175-203
Author(s):  
A. T. Fuller
Keyword(s):  
Dynamic Programming ◽  
Control Systems ◽  
Deterministic System ◽  
Optimal Switching ◽  
Error Performance ◽  
Deterministic Systems ◽  
Switching Curve ◽  
Rough Approximation ◽  
Random Disturbances ◽  
Continuous Dynamic

SynopsisOptimal switching curves are investigated for some second-order control systems with random disturbances, saturating control, and a mean-square-error performance index.It is first shown that the optimal switching curves are asymptotic at infinity to the optimal switching curves for corresponding deterministic systems.The systems are then discretised in time and state, and ordinary dynamic programming is applied to the resulting Markov chain models. The discretisation techniques are described in some detail.The same techniques are applied to a deterministic system for which the optimal switching curve is known, and it is found that the resulting discretisation errors are considerable.Thus it turns out that ordinary discrete dynamic programming gives only a rough approximation to the optimal switching curve. It seems desirable to tackle the equations of continuous dynamic programming by techniques more refined than crude discretisation. One such technique is suggested.

Electrochemical reactor systems for pollution control and the removal of toxic metals from industrial wastewaters

1988 ◽  
Vol 53 (6) ◽  
pp. 1107-1133 ◽  
Author(s):  
Bernard Fleet
Keyword(s):  
Control Systems ◽  
Pollution Control ◽  
Waste Treatment ◽  
Three Dimensional ◽  
Electrochemical Reactor ◽  
Two Dimensional ◽  
Chemical Waste ◽  
Control Applications ◽  
Recovery Processes ◽  
Key Features

A review of electrochemical reactor systems for the recovery of metals and for pollution control applications is presented. The major engineering factors which influence the design of reactors are evaluated and the key features of two-dimensional and three-dimensional reactor designs are discussed. Some examples of the application of electrochemical reactors to the recovery of metals from dilute solutions are given in the form of case studies, covering both pollution control and resource recovery processes. Finally a comparison is made of the relative technical and economic merits of electrochemical recovery pollution control systems and conventional chemical waste treatment routes.

Comparative studies of the set up of two-dimensional pneumatic arm systems by muscle and rotational actuators

2007 ◽  
Vol 221 (5) ◽  
pp. 743-748 ◽  
Author(s):  
Y-T Wang ◽  
R-H Wong ◽  
J-T Lu
Keyword(s):  
Control Systems ◽  
Fuzzy Controller ◽  
Control Algorithms ◽  
Two Dimensional ◽  
Pneumatic Control ◽  
Learning Mechanism ◽  
Set Up ◽  
And Control ◽  
Self Learning ◽  
System Characteristics

As opposed to traditional pneumatic linear actuators, muscle and rotational actuators are newly developed actuators in rotational and specified applications. In the current paper, these actuators are used to set up two-dimensional pneumatic arms, which are used mainly to simulate the excavator's motion. Fuzzy control algorithms are typically applied in pneumatic control systems owing to their non-linearities and ill-defined mathematical model. The self-organizing fuzzy controller, which includes a self-learning mechanism to modify fuzzy rules, is applied in these two-dimensional pneumatic arm control systems. Via a variety of trajectory tracking experiments, the present paper provides comparisons of system characteristics and control performances.

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