Relationship between conventional-control-theory figures of merit and quadratic performance index in optimal control theory for a single-input/single-output system

1973 ◽  
Vol 120 (1) ◽  
pp. 138 ◽  
Author(s):  
C.H. Houpis ◽  
C.T. Constantinides
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Single Input Single Output ◽  
Figures Of Merit ◽  
Single Output ◽  
Quadratic Performance Index ◽  
Output System ◽  
Quadratic Performance ◽  
Single Input

A New Approach on Stabilization Control of an Inverted Pendulum, Using PID Controller

2011 ◽  
Vol 403-408 ◽  
pp. 4674-4680 ◽  
Author(s):  
Kaveh Razzaghi ◽  
Ali Akbar Jalali
Keyword(s):  
Inverted Pendulum ◽  
System Analysis ◽  
Single Input Single Output ◽  
Stabilization Control ◽  
Single Output ◽  
Standard Problem ◽  
Angle Of Deviation ◽  
Output System ◽  
Single Input ◽  
Two Parameters

Inverted Pendulum is a standard problem in control systems and is appropriate for depicting linear control principles. In this system there is an inverted pendulum connected to a cart that moves along a horizontal track with the help of a motor. We can determine the cart’s position and velocity from the motor and the rail track limits the cart’s movement in a bidirectional path. The pendulum’s angle of deviation and the position of the cart are determined by two sensors mounted on the system. Essential measurements and motor control signals are generated by a medium control board linking the computer and the system. Analysis of the results and yielding the control commands are done with the help of a MATLAB program. This is indeed a single input- dual output system because we must be able to control two parameters (pendulum’s angle and cart’s position) with just one control signal to the motor. Since the PID (Proportional Integral Derivative) controller is usually proper for SISO (Single Input Single Output) systems, we are eager to propose a procedure to control one of these parameters underneath the other. In this paper two tactics are described: 1. controlling the cart’s position beneath the pendulum’s angle, and 2. controlling the pendulum’s angle beneath the cart’s position. Regarding the results, one method is proven to be superior. We also mention some practical considerations in this paper.

On the Design of Adaptive Servosystems

1975 ◽  
Vol 97 (4) ◽  
pp. 326-332
Author(s):  
M. Tomizuka
Keyword(s):  
Dynamical System ◽  
Optimal Control ◽  
Computer Simulation ◽  
Tracking Error ◽  
Pole Assignment ◽  
Single Input Single Output ◽  
Assignment Method ◽  
Single Output ◽  
Single Input ◽  
Command Signal

This paper deals with tracking problems in which the plant is single-input single-output and the desired trajectory (command signal) is regarded as the output of an unknown free dynamical system. Two procedures are presented for designing adaptive servosystems which enable the plant output to follow the command signal with zero ultimate tracking error. The first procedure uses a pole assignment method and the second utilizes a result of optimal control. An illustrative example is given, and the effectiveness of the adaptive servosystem is verified by computer simulation.

Sign in / Sign up

Export Citation Format

Share Document