Cart
-springRobust control applied to a cart-spring pendulum system with uncertainty
Dan Dai Advisor: Professor Roy Smith University of California, Santa Barbara
II. ROBUST C ONTROL STATEMENT The objective of this project is to design a controller that meets the specified robust performance criteria. When the cart-spring pendulum system is considered, these criteria reflects on robustness to outside disturbance and plant uncertainty. To get this controller, it is necessary to set up this problem in a very systematic way. The cart-spring pendulum system is a complex system and it has a few important properties to study. For the purpose of deriving a model, the experimental system will be considered to be composed of a massless spring attached to a frictionless cart from which a slender rod freely hangs. The output of the system is the position p of the cart, in meters, relative to the spring’s equilibrium point and the angular position θ of the pendulum, in radians, relative to the vertical; both positions are measured with optical encoders. The physical inputs of the system are the voltage u applied to the armature of the dc motor, in Volts, and a disturbance force w, in Newtons. The operating range of D/A converter, is [-5,5] Volts. The disturbance w is a force in the plane of motion orthogonal to the pendulum of length 2l and acts at a disturbance of (4/3)l from the cart-pendulum hinge. A nonlinear model of the system can be derived by applying standard Euler-Lagrange techniques, see [1]. Moreover, consider the plant as ˙ xp = Ap xp + Bp,u u + Bp,w w y = Cp,y xp + Dp,yu u + Dp,yw w z =C x +D p,z p p,zu u + Dp,zw w
Abstract— This paper describes the application of robust control theory extended to a cart-spring pendulum system with uncertainties and disturbances. Weighting functions are chosen such that the system could meet the performance requirements. The design of the H∞ controller is done with µ-synthesis in Matlab. Simulation of the H∞ controller was
Dan Dai Advisor: Professor Roy Smith University of California, Santa Barbara
II. ROBUST C ONTROL STATEMENT The objective of this project is to design a controller that meets the specified robust performance criteria. When the cart-spring pendulum system is considered, these criteria reflects on robustness to outside disturbance and plant uncertainty. To get this controller, it is necessary to set up this problem in a very systematic way. The cart-spring pendulum system is a complex system and it has a few important properties to study. For the purpose of deriving a model, the experimental system will be considered to be composed of a massless spring attached to a frictionless cart from which a slender rod freely hangs. The output of the system is the position p of the cart, in meters, relative to the spring’s equilibrium point and the angular position θ of the pendulum, in radians, relative to the vertical; both positions are measured with optical encoders. The physical inputs of the system are the voltage u applied to the armature of the dc motor, in Volts, and a disturbance force w, in Newtons. The operating range of D/A converter, is [-5,5] Volts. The disturbance w is a force in the plane of motion orthogonal to the pendulum of length 2l and acts at a disturbance of (4/3)l from the cart-pendulum hinge. A nonlinear model of the system can be derived by applying standard Euler-Lagrange techniques, see [1]. Moreover, consider the plant as ˙ xp = Ap xp + Bp,u u + Bp,w w y = Cp,y xp + Dp,yu u + Dp,yw w z =C x +D p,z p p,zu u + Dp,zw w
Abstract— This paper describes the application of robust control theory extended to a cart-spring pendulum system with uncertainties and disturbances. Weighting functions are chosen such that the system could meet the performance requirements. The design of the H∞ controller is done with µ-synthesis in Matlab. Simulation of the H∞ controller was