Abstract
A double inverted pendulum plant has been in the domain of control researchers as an established model for studies on stability. The stability of such as a system taking the linearized plant dynamics has yielded satisfactory results by many researchers using classical control techniques. The established model that is analyzed as part of this work was tested under the influence of time delay, where the controller was fine tuned using a BAT algorithm taking into considering the fitness function of square of error. This proposed method gave results which were better when compared without time delay wherein the calculated values indicated the issues when incorporating time delay.
Highlights
Double Inverted Pendulum(DIP) is a typical underactuated non-linear plant which has potential applications in the field of defense, aerospace, mechatronic systems and other industrial applications which use various levels of manipulators
A typical double inverted pendulum has a cart and two pendulums at the center which are free to oscillate about its axes from the unstable equilibrium position to the stable equilibrium position
This paper investigates the case of including a time delay in the signal transmitted to the motor that control the input of the rotary inverted pendulum
Summary
Double Inverted Pendulum(DIP) is a typical underactuated non-linear plant which has potential applications in the field of defense, aerospace, mechatronic systems and other industrial applications which use various levels of manipulators. This paper investigates the case of including a time delay in the signal transmitted to the motor that control the input of the rotary inverted pendulum. A linearized model is obtained by small signal approximation using the above equations This will yield the state space matrices that define the system for such a model would be given as follows below x& 1 x&2. Where Γ in equation refers to the time delay in the control input which is applied to the cart. Introducing a new state variable into the system as the state x7, The time delay parameter would dynamics would involve an additional state defined from the following xm Where Γ in equation refers to the time delay in the control input which is applied to the cart position and Xm denotes the modified output state condition. The modified state matrices because of addition of time delay parameter causes a new state to arise which modifies the system as given below: x& 1 x& 2
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