CONTROL SYSTEM USING A NONLINEAR DELTA-SIGMA MODULATOR WITH

NONLINEAR PROCESS MODELING

John L. Melanson

Cross-reference to Related Application

(1) This application claims the benefit under 35 U.S.C. § 119(e) and 37 C.F.R. § 1.78 of U.S. Provisional Application No. 60/915,547, filed May 2, 2007, and entitled "Power Factor Correction (PFC) Controller Apparatuses and Methods," and is incorporated by reference in its entirety.

BACKGROUND OF THE INVENTION

Field of the Invention

(2) The present invention relates in general to the field of signal processing, and more specifically to a control system utilizing a nonlinear delta-sigma modulator having a nonlinear feedback model that models a nonlinear process.

DESCRIPTION OF THE RELATED ART

(3) Many electronic systems utilize nonlinear processes to generate output signals. For example, plant systems, such as servo control systems and power conversion systems, often utilize nonlinear processes. Power conversion systems often utilize a switching power converter to convert alternating current (AC) voltages to direct current (DC) voltages or DC-to-DC. Switching power converters often include a nonlinear energy transfer process to provide power factor corrected energy to a load.

(4) Figure 1 depicts a plant and control system 100, which includes a switching power converter 102 and a plant 104. Plant 104 is, for example, a servo control system or a power supply system. The switching power converter 102 provides constant voltage power to load 112. The switching power converter 102 operates in accordance with a nonlinear process in discontinuous current mode. A full, diode bridge rectifier 103 rectifies AC voltage V _1n (X) provided by AC voltage source 101 to generate a rectified, time-varying input voltage V _x (t). The

switch 108 of switching power converter 102 regulates the transfer of energy from the rectified, time-varying input voltage V _x (t), through inductor 110, to capacitor 106. The peak of input current i _in is proportionate to the 'on-time' of switch 108, and the energy transferred is proportionate to the 'on-time' squared. Thus, the energy transfer process is one embodiment of a nonlinear process. In at least one embodiment, control signal Cs is a pulse width modulated signal, and the switch 108 is an n-channel field effect transistor that conducts when the pulse width of Cs is high. Thus, the 'on-time' of switch 108 is determined by the pulse width of control signal Cs. Accordingly, the energy transferred is proportionate to a square of the pulse width of control signal Cs. Diode 111 prevents reverse current flow into inductor 110. Energy transferred from inductor 110 is stored by capacitor 106. Capacitor 106 has sufficient capacitance to maintain an approximately constant voltage Vc while providing current to load 112. In at least one embodiment, the switching power converter 102 is a boost-type converter, i.e. the voltage Vc is greater than the peak of input voltage V _x (t).

(5) The plant and control system 100 also includes a switch state controller 114. The switch state controller 114 generates control signal Cs with a goal of causing switching power converter 102 to transfer a desired amount of energy to capacitor 106, and, thus, to load 112. The desired amount of energy depends upon the voltage and current requirements of load 112. To provide power factor correction close to one, switch state controller 114 seeks to control the input current i _in so that input current i _in tracks the input voltage V _x (t) while holding the capacitor voltage Vc constant.

(6) The process of transferring energy from inductor 110 to capacitor 106 represents a nonlinear process. The peak of input current i _in is proportionate to the pulse width of the control signal Cs, i.e. the 'on' (conductive) time of switch 108, and the energy transferred to capacitor 106 is proportionate to the square of the pulse width of the control signal Cs and inversely proportionate to the period of control signal Cs. Thus, the energy transfer process between inductor 110 and capacitor 106 is inherently nonlinear. Because the energy transfer process of switching power converter 102 is nonlinear, generation of control signal Cs to maintain power correction, efficiency, and stable output power is inherently more difficult.

SUMMARY OF THE INVENTION

(7) In one embodiment of the present invention, a signal processing system includes a nonlinear delta-sigma modulator. The nonlinear delta-sigma modulator includes a loop filter, a quantizer coupled to the loop filter, and a feedback path coupled between the loop filter and the quantizer, wherein the feedback path includes a nonlinear feedback model that models nonlinearity of a nonlinear process of a power factor correction circuit.

(8) In another embodiment of the present invention, a method of processing signals utilizing a nonlinear delta-sigma modulator configured to model nonlinearities of a nonlinear system process includes generating a quantizer output signal. The method further includes applying a nonlinear function to the quantizer output signal in a feedback loop of the nonlinear delta-sigma modulator to generate a feedback signal, wherein the nonlinear function models the nonlinearities of the nonlinear process and combining the feedback signal with a nonlinear delta- sigma modulator input signal to generate a difference signal.

(9) In a further embodiment of the present invention, a control system to provide a control signal to a nonlinear plant, wherein the nonlinear plant generates a response signal that is responsive to the control signal, includes a nonlinear delta-sigma modulator. The nonlinear delta-sigma modulator includes a loop filter, a quantizer coupled to the loop filter, and a feedback path coupled between the loop filter and the quantizer, wherein the feedback path includes a nonlinear feedback model that models nonlinearity of a nonlinear plant process of the nonlinear plant. During operation, the nonlinear delta-sigma modulator is configured to generate a quantizer output signal to control at least one aspect of the control signal and the nonlinear delta-sigma modulator is configured to shape noise in a spectral domain of the response signal.

(10) In another embodiment of the present invention, a method of controlling a nonlinear process, wherein the nonlinear process generates an output signal responsive to a control signal generated by a control system, includes receiving an input signal. The method further includes spectrally shaping the input signal with a nonlinear delta-sigma modulator to shift noise out of a baseband of the nonlinear process output signal and generating a nonlinear delta-sigma modulator output signal having a value representing the spectral shaping of the input signal. The method also includes using the nonlinear delta-sigma modulator output signal to generate the control signal.

BRIEF DESCRIPTION OF THE DRAWINGS

(11) The present invention may be better understood, and its numerous objects, features and advantages made apparent to those skilled in the art by referencing the accompanying drawings. The use of the same reference number throughout the several figures designates a like or similar element.

(12) Figure 1 (labeled prior art) depicts a switching power converter with a power factor correction stage.

(13) Figure 2 depicts a nonlinear system having a nonlinear delta-sigma modulator.

(14) Figure 3 depicts a nonlinear delta-sigma modulator.

(15) Figure 4 depicts a plant and control system.

(16) Figure 5 depicts a switch state controller.

(17) Figure 6 depicts a nonlinear delta-sigma modulator with a squaring nonlinear system feedback model.

(18) Figure 7 depicts a program that emulates a nonlinear delta-sigma modulator.

(19) Figure 8 depicts a graph of a switch state controller input signal over time.

(20) Figure 9 depicts a graph of a nonlinear delta-sigma modulator output signal over time.

(21) Figure 10 depicts plant energy transfer over time.

DETAILED DESCRIPTION

(22) A control system includes a nonlinear delta-sigma modulator, and the nonlinear delta- sigma modulator includes a nonlinear process model that models a nonlinear process in a signal processing system, such as a nonlinear plant. The nonlinear delta-sigma modulator generates one or more signals that can be used to, for example, control a nonlinear process. Conventional delta-sigma modulators spectrally shape the output of the delta-sigma modulator to shift noise out of the baseband of the delta-sigma modulator output signal rather than spectrally shaping

noise in the spectral domain of the nonlinear process response signal. In at least one embodiment, the nonlinear delta-sigma modulator includes a feedback model that models the nonlinear process being controlled and facilitates spectral shaping to shift noise out of a baseband in a spectral domain of a response signal of the nonlinear process.

(23) In at least one embodiment, the nonlinear delta-sigma modulator is part of a control system that controls power factor correction and output voltage of a switching power converter. In at least one embodiment, the switching power converter includes a switch to regulate energy transfer from a power factor correction stage to a load and regulate the output voltage of the switching power converter. The conductivity of the switch is controlled by a pulse width modulated control signal generated by the control system that includes the nonlinear delta-sigma modulator. The control system controls the pulse width and period of the control signal to control power factor correction and the output voltage level. In at least one embodiment, the nonlinear delta-sigma modulator generates a signal to control the pulse width of the control signal, and another subsystem generates a signal to control the period of the control signal.

(24) Figure 2 depicts a plant and control system 200. The plant and control system 200 includes control system 202 and plant 206. Control system 202 generates a control signal Cs that controls the nonlinear process 204 of plant 206. In response to the control signal Cs, the nonlinear process 204 generates a response signal Rs. In at least one embodiment, the nonlinear process 204 is a square function. For example, in at least one embodiment, plant 206 is a power converter, and the nonlinear process 204 represents an energy transfer process from an input stage to a load 210. The load 212 can be any load and includes for example, another power transfer stage. The control system 202 includes a nonlinear delta-sigma modulator 208, and the nonlinear delta-sigma modulator 208 includes a nonlinear process model 210 that models nonlinearities of nonlinear process 204. As explained subsequently in more detail, the nonlinear delta-sigma modulator 208 is used by control system 202 to generate the control signal Cs.

(25) In at least one embodiment, the control system 202 generates the control signal Cs so that the frequency spectrum of the response signal R _s is noise shaped, i.e. noise is shifted out of the response signal Rs baseband frequencies and into out-of-band frequencies. Many plants have a natural low pass frequency response. Thus, noise shaping removes noise at low frequencies and prevents the noise from otherwise becoming part of the control signal Cs. Shifting noise out of the baseband of response signal R _s removes unwanted signals from the response signal R _s that

could, for example, adversely affect the operation of the load 212 and/or be parasitically coupled to other circuits in the plant 206. The nonlinear process model 210 facilitates the noise shaping of the response signal Rs by modeling the nonlinear process 204.

(26) Figure 3 depicts a nonlinear delta-sigma modulator 300, which is one embodiment of nonlinear delta-sigma modulator 208. The nonlinear delta-sigma modulator 300 includes a 'nonlinear system' feedback model 302 in a feedback path 304 of nonlinear delta-sigma modulator 300. The feedback model 302 models nonlinearities of a nonlinear process 204. In at least one embodiment, the feedback model 302 is represented by f(x). The nonlinear delta-sigma modulator output signal y(n) is fed back through a delay 306, and the feedback model 302 processes the delayed quantizer output signal y(n-l) in accordance with f(y(n-l)). The combiner 308 determines a difference signal d(n) representing a difference between the feedback model 302 output f(y(n-l)) and an input signal x(n). A k ^th order loop filter 310 filters the difference signal d(n) to generate a loop filter output signal u(n), where k is an integer greater than or equal to one and the value of Hs a design choice. Generally, increasing values of £ decrease baseband noise and increase out-of-band noise.

(27) The nonlinear delta-sigma modulator 300 includes a nonlinearity compensation module 312. However, in at least one embodiment, a nonlinearity compensation module is not included as part of the nonlinear delta-sigma modulator 300. The nonlinearity compensation module 312 compensates for nonlinearities introduced by the nonlinear feedback model 302. In at least one embodiment, the nonlinearity compensation module 312 processes the loop filter output signal u(n) using a compensation function f ^x (x), which is an inverse of the feedback model 302 function f(x), e.g. if f(x) = x ² , then f ^x (x) = x ^1/2 . Quantizer 314 quantizes the output of compensation module 312 to determine a nonlinear delta-sigma modulator 300 output signal y(n). In at least one embodiment, the compensation function f ^x (x) of compensation module 312 is an estimate of the inverse of the nonlinear system feedback model 302. In at least one embodiment, the compensation function f ^x (x) in the forward path 311 of nonlinear delta-sigma modulator 300 provides good noise shaping across all frequencies. In at least one embodiment, an imperfect compensation function, i.e. approximate f ^x (x), allows more noise at all frequencies. In at least one embodiment, the compensation function f ^x (x) provides stability to nonlinear delta- sigma modulator 300.

(28) In at least one embodiment, the nonlinearity compensation module 312 is incorporated as part of the quantizer 314 rather than as a process separate from a quantization process. The compensation module 312 causes the quantizer 314 to quantize the loop filter output signal u(n) in accordance with a quantization compensation function. In at least one embodiment, the quantizer compensation function determines the nonlinear delta-sigma modulator output signal y(n) in accordance with a derivative df(x) of the feedback model 302. For example, if the nonlinear system feedback model 302 function f(x) equals x ² , then the quantizer compensation function is 2x. The quantizer compensation function can be estimated as x. Decision points of the quantizer 314 are then x +/- ¹ A.

(29) Figure 4 represents a plant and control system 400, which is one embodiment of plant and control system 200. The plant and control system 400 includes a switching power converter 402 and a plant 404. Plant 404 represents an embodiment of plant 206. The switching power converter 402 operates in accordance with a nonlinear process in discontinuous current mode. The switch 408 of switching power converter 402 regulates the transfer of energy from the rectified, time-varying input voltage V _x (t), through inductor 410, to capacitor 406. The peak of input current i _m is proportionate to the 'on-time' of switch 408, and the energy transferred is proportionate to the 'on-time' squared. In at least one embodiment, control signal Csi is a pulse width modulated signal, and the switch 408 is an n-channel field effect transistor that conducts when the pulse width of Csi is high. Thus, the 'on-time' of switch 408 is determined by the pulse width of control signal Csi. Accordingly, the energy transferred is proportionate to a square of the pulse width of control signal Csi. Thus, the energy transfer process is a squaring process and represents one embodiment of nonlinear process 205. Diode 412 prevents reverse current flow into inductor 410. Energy transferred from inductor 410 is stored by capacitor 406. Capacitor 406 has sufficient capacitance to maintain an approximately constant voltage Vci while providing current to load 412. In at least one embodiment, the switching power converter 402 is a boost-type converter, i.e. the voltage Vci is greater than the peak of input voltage V _x (t).

(30) The plant and control system 400 also includes a switch state controller 414, which represents one embodiment of control system 202. The switch state controller 414 controls the pulse width PW and period T of control signal Csi Thus, switch state controller 414 controls the nonlinear process of switching power converter 402 so that a desired amount of energy is transferred to capacitor 406. The desired amount of energy depends upon the voltage and current

requirements of load 412. The duty cycle of control signal Cs ₁ is set to maintain the desired capacitor voltage Vc ₁ and load voltage V _L , and, in at least one embodiment, the duty cycle D of control signal Cs ₁ equals [V _I /(V _CI +V _L )]. Energy transfer increases during a period of time as the input voltage V _x (t) increases. To regulate the amount of energy transferred and maintain a power factor correction close to one, switch state controller 414 varies the period of control signal Cs ₁ so that the input current i _in tracks the changes in input voltage V _x (t) and holds the capacitor voltage Vc ₁ constant. Thus, as the input voltage V _x (t) increases, switch state controller 414 increases the period T of control signal Cs ₁ , and as the input voltage V _x (t) decreases, switch state controller 414 decreases the period of control signal Cs ₁ . At the same time, the pulse width PW of control signal Cs ₁ is adjusted to maintain a constant duty cycle D, and, thus, hold the capacitor voltage Vc ₁ constant. In at least one embodiment, the switch state controller 414 updates the control signal Cs ₁ at a frequency much greater than the frequency of input voltage V _x (t). The frequency of input voltage V _x (t) is generally 50-60 Hz. The frequency 1/T of control signal Cs ₁ is, for example, between 25 kHz and 100 kHz. Frequencies at or above 25 kHz avoids audio frequencies and at or below 100 kHz avoids significant switching inefficiencies while still maintaining good power factor correction, e.g. between 0.9 and 1, and an approximately constant capacitor voltage Vci.

(31) Figure 5 depicts switch state controller 500, which represents one embodiment of switch state controller 414. The switch state controller 500 generates the control signal Csi to control the nonlinear energy transfer process of switching power converter 402. The nonlinear delta- sigma modulator 300 receives an input signal v(n) indicating a desired amount of energy transfer during the next cycle of control signal Csi to maintain a desired load voltage V _L . The nonlinear delta-sigma modulator 300 processes the input signal v(n) and generates a quantizer output signal Q _PW - The nonlinear feedback model 302 (Figure 3) of nonlinear delta-sigma modulator 300 models the nonlinear energy transfer process of switching power converter 402 so that the quantizer output signal Q _PW represents a pulse width for control signal Csi that matches the energy transfer needed by capacitor 406 to maintain an approximately constant load voltage V _L . The input signal v(n) is discussed in more detail in conjunction with Figure 4.

(32) In at least one embodiment, input signal V _x (t) is a rectified voltage and, thus, rises and falls over time. The switch state controller 500 is configured to track the changes in input signal V _x (t) and adjust the period of control signal Csi to increase as input signal V _x (t) increases and to

decrease as input signal V _x (t) decreases. To determine each period of control signal Cs ₁ , switch state controller 500 includes an input signal estimator 502 to estimate the instantaneous values of input voltage V _x (t) for each cycle of control signal Cs ₁ and generate an estimated voltage value e(n). The input signal V _x to input signal estimator 502 is, for example, an actual or scaled version of the input voltage V _x (t) or sample of the input voltage V _x (t). The switch state controller 500 includes a conventional delta-sigma modulator 504 to process the estimated voltage value e(n) and convert the estimated voltage value e(n) into a quantizer output signal Q _τ . The quantizer output signal Q _T represents a period of control signal Cs ₁ for the estimated value of input voltage V _x (t). Exemplary conventional delta-sigma modulator design and operation is described in the book Understanding Delta-Sigma Data Converters by Schreier and Temes, IEEE Press, 2005, ISBN 0-471-46585-2.

(33) The switch state controller 500 includes a pulse width modulator 506 to convert the quantizer output signal Qpw(n) into a pulse width and quantizer output signal Qτ(n) into a period for control signal Cs ₁ , where n can be a number representing a particular instance of the associated variable. To perform the conversions, in at least one embodiment, pulse with modulator 506 includes a counter. The quantizer output signal Qpw(n) indicates that number of counts for the pulse width of control signal Cs ₁ , and the quantizer output signal Qτ(n) indicates the number of counts for the period of control signal Cs ₁ . The pulse width modulator 506 translates the number of counts for the quantizer output signal Qpw(n) and the quantizer output signal Qτ(n) into the respective pulse width and period of control signal Cs ₁ . In at least one embodiment, switch state controller 500 is implemented using digital technology. In other embodiments, switch state controller 500 can be implemented using analog or mixed digital and analog technology.

(34) Referring to Figures 3, 4, and 5, when nonlinear delta-sigma modulator 300 is used as part of a switch state controller, such as switch state controller 500 (Figure 5), for maintaining power factor correction, the input signal v(n) is proportional to (l-(V _x (t)/Vci)-K. "V _x (t)" and "Vc ₁ " are described in conjunction with Figure 4. "K" is a constant representing power demand by load 412 as determined by a proportional integral compensator (not shown) that compares the load voltage V _L (Figure 4) to a reference voltage and determines a feedback signal that is a combination an integral and proportionate function of the output voltage error. An example of a proportional integral compensator is described in Alexander Prodic, "Compensator Design and

Stability Assessment for Fast Voltage Loops of Power Factor Correction Rectifiers", IEEE Transactions on Power Electronics, Vol. 22, No. 5, September 2007 and Erickson and Maksomovic, "Fundamentals of Power Electronics", 2 ^nd ed., Boston, MA: Kluwer, 2000. The input signal v(n) is constrained to ensure that switching power converter 402 operates in discontinuous current mode.

(35) Figure 6 depicts nonlinear delta-sigma modulator 600, which represents one embodiment of nonlinear delta-sigma modulator 300. The nonlinear energy transfer process of switching power converter 402 can be modeled as a square function, x ² . Nonlinear delta-sigma modulator 600 includes a nonlinear system feedback model 602 represented by x ² . Thus, the output of feedback model 602 is the square of the delay -by-one quantizer output signal Q _PW (n), i.e. [Qpw(n-l)] . The nonlinear delta-sigma modulator 600 in the same manner as nonlinear delta- sigma modulator 300 and includes a compensation module 604 that is separate from quantizer

314. The nonlinearity compensation module 604 processes output signal u(n) of the loop filter 310 with a square root function x ^1/2 . The output c(n) of compensation module 604 is quantized by quantizer 314 to generate quantizer output signal Qpw(n).

(36) Figure 7 depicts a Mathematica® program that emulates nonlinear delta-sigma modulator 300 for function f(x) = x ² of a nonlinear feedback model 302 and a nonlinearity compensation module 312 implemented as a quantizer compensation function representing a modified derivative of f(x) with quantizer decision points of x +/- ¹ A The Mathmatica® program is available from Wolfram Research, Inc. with office in Champaign, Illinois.

(37) Figure 8 depicts a graph 800 of switch state controller input signal v(n) over time. The switch state controller input signal v(n) is linear over time and tracks changes in the time-varying input voltage V _x (t) so that energy transfer in switching power converter 402 tracks changes in the input voltage V _x (t).

(38) Figure 9 depicts a graph 900 of nonlinear delta-sigma modulator output signal Qpw(n) of nonlinear delta-sigma modulator 600 (Figure 6) over time. The nonlinear delta-sigma modulator 600 performs a square root operation so that the average of output signal Qpw(n), as indicated by dashed line 902, is the square root of switch state controller input signal v(n).

(39) Figure 10 depicts a graph 1000 of a response signal R _s of nonlinear process 204 of plant 206 to an input stimulus represented by graph 900 when the nonlinear process 203 has an x ²

transfer function. Because the nonlinear delta-sigma modulator 600 includes the nonlinear system feedback model 602 that models the squaring energy transfer process of switching power converter 402, the response signal Rs is linear as indicated by dashed line 1002.

(40) Thus, the nonlinear delta-sigma modulator includes a feedback model that models a nonlinear process being controlled and facilitates spectral shaping to shift noise out of a baseband in a spectral domain of a response signal of the nonlinear process.

(41) Although the present invention has been described in detail, it should be understood that various changes, substitutions and alterations can be made hereto without departing from the spirit and scope of the invention as defined by the appended claims.