Controllers, observers, and applications thereof

A method of monitoring the health of a system comprising:

• receiving sensor data from a sensor operably connected to the system to measure an output (y);
• storing an input (u) applied to the system that is coupled to the output (y);
• processing the input (u) and the output (y) using an extended state observer, the extended state observer designed to estimate at least one state and a disturbance (ƒ) associated with a model that couples the input (u) with the output (y);
• and
• comparing the disturbance (ƒ) against a nominal disturbance to create a variance.

A health monitoring system for a plant comprising:

• a computer adapted to receive a signal from a sensor operably connected to the plant;
• an output (y) of the plant that is determined from the signal;
• an input (u) is determined from a control signal applied to the plant;
• an extended state observer adapted to estimate a state and a disturbance (ƒ) associated with the input (u) and the output (y);
• a monitor adapted to compare the disturbance (ƒ) with a nominal disturbance;
• and
• a model of specific fault information that is matched to the monitor to determine a specific fault.

A computer-implemented method to generalize an extended state observer, comprising:

• representing a plant with a continuous-time differential equation of an nth order plant, y(n)=ƒ(y, {dot over (y)}, . . . , y((n−1)),w,t)+bu, where y(n) denotes the nth derivative of y, u is a control signal, and b is an estimate of a value;
• constructing an n+h order state space model of the nth order plant using h-cascaded integrators to represent a disturbance f and its h derivatives;
• discretizing the state space model by applying one of Euler, zero order hold, or first order hold methods;
• creating a predictive discrete estimator from the discretized state space model;
• creating a current discrete estimator from the discretized state space model;
• implementing the current discrete estimator in a computer component that receives a signal from a sensor that is operably connected with the plant;
• and
• processing the signal using the discrete estimator to estimate the value of the disturbance f and its h derivatives.

A method to enhance performance of an active disturbance rejection controller by providing transient tracking control, comprising:

• representing a plant with a continuous-time differential equation of an nth order plant, y(n)=ƒ(y, {dot over (y)}, . . . , y(n−1), w, t)+bu y(II)=f(y,:/, . . . ,y(II-I), w, f)+bu, where yen) denotes the nth derivative of y, u is a control signal, and b is a known value;
• constructing an extended state observer to estimate generalized disturbance, output y, and n−1 derivatives of the output;
• applying a disturbance rejection control law to cancel the generalized disturbance using an estimated disturbance value from the extended state observer;
• reducing the plant to n cascaded integrators;
• applying a point-to-point control law to the reduced plant to form a desired closed-loop transfer function;
• adding an inverse of the closed-loop transfer function to a reference input of the controller to form a new closed loop transfer function equal to one, or its relative order equal to zero;
• implementing the extended state observer, the disturbance rejection control law, and the point-to-point control law in a computer component that receives a signal from a sensor that is operably connected with the nth order plant;
• processing the signal using the extended state observer, the disturbance rejection control law and, the point-to-point control law to estimate a control signal u;
• and,
• applying a control command representing the control signal u to the nth order plant.

A computer-implemented method to discretely implement an extended state observer, comprising:

• representing a plant with a continuous-time differential equation of an nth order plant, y(n)=(y,{dot over (y)},w,t)+bu where f is a function of an internal system dynamics, an external disturbance w, and b is a constant;
• constructing a n+1 order state space model of the nth order plant;
• discretizing the state space model by applying one of Euler, zero order hold, or first order hold methods;
• and
• creating a predictive discrete estimator from the discretized state space model;
• creating a current discrete estimator from the discretized state space model;
• implementing the current discrete estimator in a computer component that receives a signal from a sensor that is operably connected with the plant;
• and
• processing the signal using the current discrete estimator to estimate the value of the function ƒ.

A method for designing a system to control a multiple-input, multiple-output system, comprising:

• discretizing a system model to describe one or more distinct states, where each input has a distinct output and disturbance;
• constructing an extended state estimator from the discretized system model;
• implementing the extended state estimator in a computer component that receives a signal from a sensor that is operably connected to the system;
• determining one or more correction terms as a function of a single tuning parameter;
• and
• utilizing the correction terms with the extended state estimator and the signal to estimate system states and extended states of one or more orders.

A method to provide health monitoring to a system, comprising:

• determining appropriate coupled control inputs and control outputs;
• determining order of each input/output coupling;
• building a matching extended state observer to estimate states and a disturbance;
• adjusting a value of at least one tuning parameter that provides stable output tracking;
• determining at least one nominal condition for an estimated disturbance;
• implementing the matching extended state observer in a computer component that receives a signal from a sensor that is operably connected to the system;
• processing the signal using the matching extended state observer to estimate the disturbance;
• monitoring a variation between the estimated disturbance and the at least one nominal condition;
• and
• extracting fault information from the variation.

A method for controlling a turbofan, comprising:

• creating a model of a portion of a turbofan system as a nonlinear input-output vector function;
• approximating a general disturbance of the modeled system;
• reducing the system to a second model that distinguishes between an instantaneous input and one or more dynamic variables to be estimated in real time;
• representing the system by one or more state vectors, wherein an extended state is assigned to track the general disturbance;
• determining a disturbance rejection control law;
• implementing the disturbance rejection control law on a computer component that receives a signal from a sensor that is operably connected to the turbofan;
• utilizing the disturbance rejection control law to decouple the system and reduce it to one or more parallel integrators;
• controlling the simplified parallel integrator system;
• and
• generating a control signal that is applied to the turbofan.

A method of adding disturbance information into the linear extended state observer is described, comprising:

• representing a plant with a continuous-time differential equation of an nth order plant, where the nth derivative of the output y(t) equals a generalized disturbance ƒ(t) plus an input bu(t) where b is a constant;
• constructing a state space model of the plant;
• creating an extended state observer based on the state space model, having correction terms that are a function of a single parameter;
• and
• adding a term to the extended state observer that is composed of the derivative of ƒ(t) if it is known or partially known.