Method, apparatus and design procedure for controlling multi-input, multi-output (MIMO) parameter dependent systems using feedback LTI' zation

A method of designing flight control laws using multi-input, multi-output feedback LTI'zation, said method comprising the following steps:

• determining coordinates for flight vehicle equations of motion;
• transforming the coordinates for the flight vehicle equations of motion into a multi-input linear time invariant system;
• establishing control laws yielding the transformed equations of motion LTI;
• adjusting the control laws to obtain a desired closed loop behavior for the controlled system;
• and
• converting the transformed coordinates control laws to physical coordinates.

A method of controlling a dynamic device having device characteristics, the device including a plurality of sensors for receiving device status signals and parameter signals and a plurality of control laws stored in a memory, the device operating in an environment with a plurality of external operating conditions, said method comprising the steps of:

• transforming the device characteristics into a multi-input linear time invariant system;
• selecting and applying physical gain schedules to the control laws, the gain schedules corresponding to current external operating conditions signals;
• determining and applying parameter rates of change to update the control laws;
• applying the status signals to update the control laws;
• converting the transformed coordinates control laws to physical coordinates;
• and
• controlling the device based on the updated control laws.

Computer executable software stored on a computer or processor readable medium, the code for developing control laws for a dynamic device having device characteristics, the code comprising;

• code to transform the device characteristics into a multi-input linear time invariant system;
• code to establish control criteria yielding the device characteristics in the transformed coordinates LTI;
• code to define at least one design point in the multi-input linear time invariant system;
• code to adjust the transformations to corresponding with the design point(s);
• code to develop a physical coordinates control law corresponding to the adjusted transformations;
• and
• code to apply reverse transformations to cover the full design envelope.

A multi-input parameter dependent control system for controlling an aircraft, said system comprising:

• receiving means for receiving a plurality of aircraft status signals and for receiving a plurality of current parameters signals;
• memory having at least one region for storing computer executable code;
• and
• a processor for executing the program code, wherein the program code includes code responsive to:
• (i) transform the aircraft characteristics into a multi-input linear time invariant system;
• (ii) select and apply gain schedules to flight control laws in transformed coordinates, the gain schedules corresponding to the received current parameter signals;
• (iii) determine parameter rates of change, and to apply the parameter rates of change to the flight control laws;
• (iv) apply the received aircraft status signals to the flight control laws;
• (v) convert the transformed coordinates control laws to physical coordinates;
• and (vi) control the aircraft based on the updated flight control laws.

A method of determining the operational status of a multi-input, multi-parameter dependent control system for controlling a dynamic device, said method comprising the steps of:

• receiving a plurality of current status signals representing current statuses of the device and a plurality of control signals for effecting control of the device;
• transforming the current status signals and the control signals to a multi-input linear time invariant system;
• estimating an expected behavior of the device using the transformed current status signals and the transformed control signals;
• and
• determining the operational status of the control system by comparing the expected behavior of the device to the actual behavior of the device.

A multi-parameter dependent control system for controlling a dynamic device having multiple inputs, said system comprising:

• receiving means for receiving a plurality of current state signals representing current states of the device and a plurality of control signals for effecting control of the device;
• transforming means for transforming the current state signals and the control signals to a linear time invariant system;
• estimating means for estimating an expected behavior of the device using the transformed current state signals and the transformed control signals and for generating estimate signals corresponding to the expected behavior;
• and
• determining means for determining the operational status of the control system by comparing the expected behavior of the device to the actual behavior of the device.

A method of designing control laws for a dynamic device, the device accepting multiple inputs and generating multiple outputs and operating in an environment having varying parameters, characteristics of the device being definable by equations of motion, said method comprising the steps of:

• transforming coordinates for the equations of motion into a linear-time invariant system;
• and
• establishing a closed loop behavior in the linear time invariant system, wherein
• said establishing step generates gain schedules for controlling the equations of motion throughout an operational envelope of the device.

A method of designing control laws for a dynamic device, the device accepting multiple inputs and generating multiple outputs, characteristics of the device being definable by equations of motion, said method comprising the steps of:

• defining an operating envelope including varying parameters throughout the envelope;
• determining control designs for a plurality of discrete points in the envelope;
• transforming the plurality of discrete point designs to a linear time invariant system (z-space) to provide corresponding gains in z-space and interpolating between the gains in z-space to provide linearly blended gains;
• and
• inversely transforming the z-space linearly blended gains to physical space.

A method of designing control laws for a dynamic device, the device accepting multiple inputs and generating multiple outputs, characteristics of the device being defined by at least one control law, said method comprising the steps of:

• determining in physical space gains corresponding to a discrete operating condition, the gains for use in the control law;
• transforming the gains obtained at the discrete operating condition to a linear time invariant system (z-space) and obtaining corresponding gains in z-space;
• and
• inversely transforming the z-space gains into physical space to correspond to a plurality of operating conditions throughout an envelope in which the device operates.

A method of designing control laws for a dynamic device, the device accepting multiple inputs and generating multiple outputs, the device operating in an environment having multiple parameters, said method comprising the steps of:

• defining a control law comprising derivative, proportional and integral gains and device inputs;
• and
• developing gain schedules to be applied to the control law so as to accommodate varying parameters, wherein
• transforming device characteristics into a liner-time invariant system generates the gain schedules and provides a stable closed loop behavior for the transformed characteristics.

A method of controlling a device having multi-inputs and operating in an environment having multiple operating parameters, said method comprising:

• defining a control law to describe characteristics of the device, the control law comprising derivative, proportional and integral gains;
• evaluating in real-time z-space gains for the control law according to current operating parameters;
• and
• transforming the z-space gains to physical space for use in the control law.

A method of controlling a dynamic device having multi-inputs and operating in an environment having multiple operating parameters comprising:

• providing a feedback LTI'zation control algorithm in the form of Eq. 11, in which arbitrary rates of change of the parameters are accommodated;
• determining in a linear time-invariant coordinates system gains corresponding to the control algorithm for discrete operating conditions;
• transforming the gains into physical space;
• and
• applying the gains to control the dynamic device.

A method of providing control of a dynamic device, comprising:

• defining a control law to control the behavior of the dynamic device, the control law comprising at least one gain variable;
• transforming the gain variable to a linear time invariant system (z-space) and determining a corresponding z-space gain;
• mapping the z-space gain into a plurality of physical space gains that each correspond respectively to a plurality of operating conditions;
• storing in memory the physical space gains;
• and
• accessing the stored gains in real-time for use in the control law under particular operating conditions.

A method of applying LTI design techniques to a transformed coordinates mathematical model of a dynamic device to yield a desired closed loop behavior for the model, the control law including feedback gains, said method comprising the steps of:

• designing the feedback gains in physical coordinates at a selected operating condition of the dynamic device;
• using the transformed coordinates to map the feedback gains into z-space;
• and
• reverse mapping the gains via a coordinates transformations and feedback LTI'ing control laws to determine physical coordinates control laws for operating conditions other than at design conditions.